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Analysis of mean velocity and turbulencemeasurements with ADCPs

ARTICLE in ADVANCES IN WATER RESOURCES MAY 2015

Impact Factor: 3.42 DOI: 10.1016/j.advwatres.2014.11.006

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Francesca De Serio

Technical University of Bari, Italy

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Michele Mossa

Politecnico di Bari

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Analysis of mean velocity and turbulence measurements with ADCPs

Francesca De Serio , Michele Mossa

Department of Civil, Environmental, Building Engineering and Chemistry DICATECh, Technical University of Bari, Via E. Orabona 4, 70125 Bari, Italy

a r t i c l e i n f o

Article history:

Available online xxxx

Keywords:

Log law velocity profile

Variance method

Reynolds stress

Turbulent kinetic energy

Bottom drag coefficient

Wind drag coefficient

a b s t r a c t

The present study examines the vertical structure of the coastal current in the inner part of the Gulf of

Taranto, located in the Ionian Sea (Southern Italy), including both the Mar Grande and Mar Piccolo basins.

To this aim, different measuring stations investigated by both a Vessel Mounted Acoustic Doppler CurrentProfiler (VM-ADCP) and a bottom fixed ADCP were taken into consideration. Two surveys were carried

out in the target area on 29.12.2006 and on 11.06.2007 by the research unit of the Technical University

of Bari (DICATECh Department), using a VM-ADCP to acquire the three velocity components along the

water column in selected stationing points. The measurements were taken in shallow waters, under

non-breaking wave conditions, offshore the surf zone. Due to the recording frequency of the instrument

time-averaged vertical velocity profiles could be evaluated in these measuring stations. Water tempera-

ture and salinity were also measured at the same time and locations by means of a CTD recorder. A rigidly

mounted ADCP, located on the seabed in the North-Eastern area of the Mar Grande basin, provided cur-

rent data relative to the period 1020 February 2014. Set to acquire the three velocity components with

higher frequency with respect to the VM-ADCP, it allowed us to estimate the turbulent quantities such as

Reynolds stresses and turbulent kinetic energy by means of the variance method.

Therefore, the present research is made up of two parts. The first part examines the current pattern

measured by the VM-ADCP and verifies that, for each station, the classical log law reproduces well the

vertical profile of the experimental streamwise velocities extending beyond its typical limit of validity

up to the surface i.e. reaching great heights above the sea bed. This behavior is quite new and not always

to be expected, being generally limited to boundary layers. It has been convincingly observed in only few

limited experimental works. In the present study this occurred when two conditions were met: (i) the

flow was mainly unidirectional along the vertical; (ii) the interested layer was non-stratified.

The second part of the research studies the turbulent statistics derived from the beam signals of the

fixed ADCP by means of the variance method. This technique had the advantage of being able to measure

the time evolution of the turbulent mixing throughout the entire water column, thus making it possible

to perform a detailed study on momentum transfer and turbulence. The deduced vertical profiles of the

Reynolds stresses and of the turbulent kinetic energy TKE showed an increasing trend toward the surface,

in agreement with previous results in literature.

New data-sets of mean velocities and shear stresses, coming from field measurements, are always

needed. In fact they represent the first step to derive reliable reference values of coefficients and param-

eters for the implementation and calibration of the used mathematical hydrodynamic models.

Consequently, an effort was made to evaluate consistent bottom drag and wind drag coefficients, on the

basis of the calculated bottom and surface shear stresses, respectively.

2014 Elsevier Ltd. All rights reserved.

1. Introduction

The open North-Eastern part inside the Gulf of Taranto in the

Ionian Sea, along the Southern Italy coast (Fig. 1), is considered a

vulnerable and sensitive area, affected by massive chemical and

biological pollutant discharges due to the presence of heavy indus-

try. The natural assimilative capacity of the sea, accomplished by

initial mixing and successive dispersion, as well as sediment trans-

port, are phenomena strictly dependent on the magnitude and

directions of the current[1]. Hence, a knowledge of the coastal cur-

rent pattern is desirable, being a useful support for the local

authorities in the planning and management of the coastal area.

This purpose may be achieved with both field measurements and

http://dx.doi.org/10.1016/j.advwatres.2014.11.006

0309-1708/ 2014 Elsevier Ltd. All rights reserved.

Corresponding author. Tel.: +39 080 5963557; fax: +39 080 5963414.

E-mail address: [email protected](F. De Serio).

Advances in Water Resources xxx (2014) xxxxxx

Contents lists available at ScienceDirect

Advances in Water Resources

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / a d v w a t r e s

Please cite this article in press as: De Serio F, Mossa M. Analysis of mean velocity and turbulence measurements with ADCPs. Adv Water Resour (2014),

http://-/?-http://-/?-http://-/?-http://dx.doi.org/10.1016/j.advwatres.2014.11.006mailto:[email protected]://dx.doi.org/10.1016/j.advwatres.2014.11.006http://www.sciencedirect.com/science/journal/03091708http://www.elsevier.com/locate/advwatreshttp://dx.doi.org/10.1016/j.advwatres.2014.11.006http://dx.doi.org/10.1016/j.advwatres.2014.11.006http://www.elsevier.com/locate/advwatreshttp://www.sciencedirect.com/science/journal/03091708http://dx.doi.org/10.1016/j.advwatres.2014.11.006mailto:[email protected]://dx.doi.org/10.1016/j.advwatres.2014.11.006http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-

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numerical model results. Collecting a large amount of data in wide-

spread areas is challenging because of technical and economic lim-

itations. Numerical models represent a more rapid and a less

expensive solution, simulating the hydrodynamics of extended

areas with the desired level of accuracy and in a relatively short

time. Nevertheless, in order to be accurate, models need to be cal-

ibrated and successively validated by field measurements [2,3].

These procedures often require as input condition the vertical lawsobeyed by the current velocity in order to derive parameters

involved in the model equations, i.e. the bottom roughness length

or the bottom drag coefficient.

For this reason, the first aim of the present paper is to analyze

the field velocity data measured by means of a VM-ADCP and to

reproduce the vertical velocity profiles testing the applicability of

the classical log law. The data were acquired during two cruises,

carried out by the research group of the DICATECh Department

of the Technical University of Bari on 29.12.2006 and on

11.06.2007 respectively. It is worth pointing out that the log law

was deduced experimentally in simple pipe or channel configura-

tions with uniform flows and it should represent accurately the

velocity profile in the inner region of free surface flows [4]. Exper-

imentally, it was proven that this distribution may be extended to

the entire flow in some particular cases, referring to open-channel

flows, where the maximum velocity value is observed close to the

free surface[5] and also referring to tidal flows[6].The use of the

log law in a complex marine scenario is not a foregone conclusion.

Moreover, in the examined case, the applicability of the log law far

beyond its typical limit of validity was proven, provided that the

flow was almost unidirectional and not stratified[7].

As a second aim, the present research intends to estimate the

vertical distributions of the turbulent quantities (using a single

measuring station, taking advantage of the rapid sampling of a

fixed ADCP) and to compare them with trends in literature. In

the quest to measure turbulence parameters the use of ADCPs

has become common practice in recent years [810].Also a valida-

tion by comparing ADCP Reynolds stresses with estimates from

other instrumentation has been carried out [11]. More recentlyWiles et al. [12]used the structure function method to estimate

the TKE dissipation. In the present case, the variance method was

used to compute the turbulent shear stresses and the turbulent

kinetic energy TKE[1315]. The fixed ADCP was installed in Mar

Grande basin in December 2013 as part of RITMARE project funded

by PON R&C 20072013.

The investigated area (Fig. 1), with composite topography and

exposed to urban and industrial discharges, includes the open

sea, the Mar Grande and the inner basin called the Mar Piccolo.

The Mar Grande covers an area of 35 km2 with an average depth

of about 15 m and connects with the open Ionian Sea through

two openings. The Mar Piccolo has a surface area of about

21 km2 and is structured in two embayments, with an average

depth of about 12 m. The area where measurements were carriedout is westward of the Mar Grande, in the open sea, with depths

in the range of [15 m to 30 m].

It is worth pointing out the importance of this kind of study,

because accurate estimates of mean velocities and shear stresses

are essential for the study of flow structures [14].Moreover, labo-

ratory experiments may represent a stringent test of the ability of

ADCPs to measure mean velocities and turbulence. Because length

and time scales of the turbulence in a laboratory flume are smaller

than those in a river or coastal area, ADCPs may resolve the turbu-

lence better in the field, even if flow inhomogeneity could affect

measurements. Therefore, it is worth doing further tests of ADCPs

on site[15].

The paper is structured as follows. Section 2 briefly describes

the theoretical background for both the logarithmic law and the

variance technique. The survey equipment and procedure are illus-

trated in Section3, together with the acquired velocity, tempera-

ture and salinity data. Section 4 illustrates and discusses the

applicability and validity of the log law, while Section 5 analyses

the turbulent behavior of the current in the fixed station. Finally

in Section6, the bottom stress coefficient and the wind coefficient

are estimated by means of friction velocity and shear stress.

2. Theoretical background

2.1. Log law velocity profiles in turbulent flows

Two regions with distinct scalings characterize wall bounded

turbulent flows: the inner region, in which the viscous effect pre-vails, and the outer region, with prevailing flow inertia. On the

Fig. 1. Location of the target area where the survey was carried out. Source: Googlemap.

Fig. 2. The Janus ADCP configuration, from Dewey and Stringer [20], showing

relation of transducer beams to coordinates axes and angles.

Table 1

Main characteristics of the VM-ADCP system and of the CTD probe.

Probe Type Value

V M-AD CP Ac oust ic frequenc y 60 0 kH z

Velocity range 10 m/s horizontal; 5 m/s vertical

Velocity accuracy 1% of measured value 0.5 cm/s

CTD Pressure range 07000 m

Pressure accuracy 1

Temperature range 5 to 35 C

Temperature accuracy 5

2 F. De Serio, M. Mossa / Advances in Water Resources xxx (2014) xxxxxx


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basis of the mean momentum equation, the velocity and length

scales in the inner region are taken to be respectively the shear

or friction velocityU and the viscous lengthm/U, beingmthe kine-matic viscosity. In the outer region, the velocity scale continues to

beU, while the length scale is assumed to be the boundary layer

thickness d or a scale related to it. The limit between the inner

and outer region has been experimentally fixed at z/h= 0.2 in the

case of open channels [4], zbeing the vertical distance from thebottom and h the channel depth.

In literature[16,17]a debate is still open about the most suit-

able law, between the power law and the log law, to reproduce

the velocity profiles in channels and boundary layer flows. With

the exception of few objectors, the log law is generally accepted

as the correct scaling for the inner region of a turbulent boundary

layer. Hence, in the inner region, on the basis of the dimensional

analysis and with the assumption of Prandtls mixing length, the

mean velocity profileU(z) can be expressed with inner variables as

Uz

U

1

kln

Uz

t B

2:3

k log

Uz

t B 1

wherek is the von-Karmans constant equal to 0.41 and B is a func-

tion of flow properties and wall roughness, derived from integration[7]. As written, the log law should represent accurately the velocity

profile in the inner region of free surface flows, up toz/h 0.2. More

recently, Anwar[18], Lueck and Lu[6] and De Serio and Mossa[7]

stated that the log-layer height can reach many meters above the

bottom. De Serio and Mossa[7], analyzing some velocity field data

recorded during marine cruises, observed that, when the flow was

mainly unidirectional, the log law well reproduced the vertical dis-

tribution of the velocity also beyond the inner region, but failed

when stratification started to affect the water.

2.2. Variance technique

When current measurements are acquired by means of an

ADCP, an important limitation for turbulence measurement arises,

because the three velocity components are computed by combin-

ing velocities measured along acoustic beams oriented in different

directions and measured in distant fluid particles. Therefore it is

necessary to evaluate all the statistical moments along each beam.

For this reason, in applying the variance method, it is assumed

that: (i) turbulence is horizontally homogeneous, i.e. turbulence

statistics are the same at all four beam locations; (ii) turbulent sta-

tistics are steady over the averaging interval [15,19].

The basic methodology of the variance method uses the along-

beam velocities from a four-beam ADCP in the Janus configuration

(as is the case, seeFig. 2) to compute profiles of the vertical Rey-

nolds stress in the two horizontal directions [14,9,20]. Theoreti-

cally, equations for the vertical stresses at a given depth can be

derived from the along-beam velocity equations from the two

opposing beam pairs.

The along-beam velocities, positive toward the ADCP head, are

respectively:

b1 u sin hwcos h 2

b2 usin hwcos h 3

2694000 2696000 2698000 2700000 2702000 2704000 2706000

longitude [m]

4476000

4478000

4480000

4482000

4484000

4486000

4488000

latitude[m]

2

3

4

5

6

7

8

9

10

4 m

6 m

8 m

10 m

12 m

14 m

16 m

18 m

velocity scale0.1 m/s

depth fromsurface:

Fig. 3. Maps of the horizontal velocities measured at some selected depths during survey S1. Gauss Boaga reference system used.

F. De Serio, M. Mossa / Advances in Water Resources xxx (2014) xxxxxx 3


http://-/?-http://-/?-http://-/?-http://-/?-https://www.researchgate.net/publication/229092084_The_logarithmic_layer_in_a_tidal_channel?el=1_x_8&enrichId=rgreq-2dc57f8e-8e6a-4df1-ad1c-e41d3d638672&enrichSource=Y292ZXJQYWdlOzI2ODY4OTcwNztBUzoxODUwODA5ODMwNzI3NzBAMTQyMTEzODE1MzU5MA==http://-/?-http://-/?-http://-/?-http://-/?-https://www.researchgate.net/publication/240685542_Using_a_broadband_ADCP_in_a_tidal_channel_Part_II_Turbulence?el=1_x_8&enrichId=rgreq-2dc57f8e-8e6a-4df1-ad1c-e41d3d638672&enrichSource=Y292ZXJQYWdlOzI2ODY4OTcwNztBUzoxODUwODA5ODMwNzI3NzBAMTQyMTEzODE1MzU5MA==https://www.researchgate.net/publication/240685542_Using_a_broadband_ADCP_in_a_tidal_channel_Part_II_Turbulence?el=1_x_8&enrichId=rgreq-2dc57f8e-8e6a-4df1-ad1c-e41d3d638672&enrichSource=Y292ZXJQYWdlOzI2ODY4OTcwNztBUzoxODUwODA5ODMwNzI3NzBAMTQyMTEzODE1MzU5MA==http://dx.doi.org/10.1016/j.advwatres.2014.11.006https://www.researchgate.net/publication/229092084_The_logarithmic_layer_in_a_tidal_channel?el=1_x_8&enrichId=rgreq-2dc57f8e-8e6a-4df1-ad1c-e41d3d638672&enrichSource=Y292ZXJQYWdlOzI2ODY4OTcwNztBUzoxODUwODA5ODMwNzI3NzBAMTQyMTEzODE1MzU5MA==https://www.researchgate.net/publication/240685542_Using_a_broadband_ADCP_in_a_tidal_channel_Part_II_Turbulence?el=1_x_8&enrichId=rgreq-2dc57f8e-8e6a-4df1-ad1c-e41d3d638672&enrichSource=Y292ZXJQYWdlOzI2ODY4OTcwNztBUzoxODUwODA5ODMwNzI3NzBAMTQyMTEzODE1MzU5MA==http://dx.doi.org/10.1016/j.advwatres.2014.11.006http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-

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b3 vsin hwcos h 4

b4 vsin hwcos h 5

whereu, v, andw are thex,y, andzvelocities in a right handed coor-

dinate system (the earth system, in the present case) and h is theangle of the beams away from vertical.

Combining equation(2)(5), the three velocity components are

derived:

u b1b22sin h

v b3b42sinh

w b1b2b3b44cos h

8>>>:

6

All the velocities can be split into a mean part and a fluctuating

part using the Reynolds decomposition, where the overbar denotes

the time averaged value and the prime symbol denotes the turbu-

lent fluctuation:

u uu0

v v v0

w ww0

bi bib0i with i 1;2;3;4

8>>>>>:

7

Consequently, the along-beam velocity variances can be

expressed as:

b021 u

02 sin2h 2u0w0 sin h cos hw02 cos2 h 8

b022 u

02 sin2h 2u0w0 sin h cos hw02 cos2 h 9

b023 v

02 sin2h 2v0w0 sin h cos hw02 cos2 h 10

b024 v02 sin

2

h 2v0w0 sin h cos hw02 cos2

h 11

The difference between Eqs.(8) and (9)provides the component

u0 w0 of the Reynolds stress, as well as the differences between Eqs.

(10) and (11)gives the component v0 w0:

sxzq

u0w0 b

021 b

022

4sinh cos h 12

syzq

v0w0 b

023 b

024

4sin h cos h 13

whereq is the water density.The turbulent kinetic energy TKE, defined as

q2=2 u02 v02 w02 .2, cannot be measured by a four beamADCP, because it is necessary to have an independent estimate of

the componentw02 or, alternatively, to make an assumption on the

anisotropy ratio[15]. Nevertheless, by taking the sum of the vari-

ances in Eqs.(8)(11)some terms related to TKE can be obtained.

For fully isotropic turbulence, the following equation is derived:

q2

2

3

8 b

021 b

022 b

023 b

024

14

which represents the lower bound for the TKE evaluated in the caseof anisotropic turbulence.

It is worth pointing out that the variance technique used in the

present work has the benefit of measuring the time evolution of

the turbulent mixing throughout the entire water column, thus

allowing a detailed analysis of turbulence.

3. Equipment and methods used in the experiments

3.1. Surveys description

As mentioned above, during two cruises carried out by the

research group of the DICATECH Department of the Technical Uni-

versity of Bari on 29.12.2006 and on 11.06.2007, a Nortek AWAC

(Acoustic Wave And Current) VM-ADCP was used to measure thesea three-current-velocity components. It was connected to a gyro

and a DGPS in order to take into account the vessel velocity and

thus to acquire the current velocity with respect to the seabed.

Moreover, the DGPS was used to locate the pre-determined sta-

tioning points. The main features of the AWAC current meter sys-

tem are shown in Table 1. Its standard configuration has three

beams 120apart, slanted at 25, and one vertical, whose opening

angle is 1.7.

During all the surveys, the measurements of the flow were

assessed with an acquisition frequency of 0.5 Hz, therefore only

Table 2

Coordinates (Gauss Boaga reference system) and depths of the investigated stations.

Station Latitude (m) Longitude (m) Investigated depthh (m)

2 4480764.327 2705232.721 7

3 4481394.107 2701484.235 14

4 4483733.500 2700887.939 13

5 4484128.685 2697868.626 29

6 4486055.929 2698246.621 19

7 4485265.881 2695249.971 228 4483311.498 2696278.078 24

9 4482696.431 2698611.702 25

10 4479062.819 2699292.504 25

A 4484671.597 2697889.231 18

B 4486122.866 2698193.836 17

C 4483632.316 2696217.672 19

D 4483129.511 2698434.854 19

E 4481024.285 2698654.767 20

O 4481072.540 2707747.910 21

Fig. 4. Examples of time moving average of the measured easternu, northern vand

verticalwvelocity components (top) and of their variances (bottom) at station 5, at6 m from the surface.



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the mean velocities were deduced and are examined in the present

paper. The measurements were acquired starting from 4 m below

the water surface, as it was the blanking distance of the instru-

ment. The bin size and number depended on the investigated local

depths and are specified in the following subsections. The mea-surements of all the surveys were assessed by anchoring the boat

and acquiring the velocities for a total time equal to 10 min on

average and not less than 5 min for each investigated station. This

duration was chosen following the sampling times used in

literature in similar cases[10,12].Moreover, it was also taken into

account that this time period had to be both sufficiently shortto consider the flow steady and sufficiently long to satisfy the

z/h

1

0

.1

.2

.3

.4

.5

.6

.7

.8

.9

1

2 13 14 15

T

16

[C]17 18 19

st 2

st 3

st 4

st 5

st 6

st 7

st 8

st 9

st 10

20

z/h

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

7.5 38

S[psu]38.5

st 2

st 3

st 4

st 5

st 6

st 7

st 8

st 9

st 1

39

0

Fig. 5. Vertical profiles of measured temperatureTand salinityS in the investigated stations during survey S1.

2692000 2696000 2700000 2704000 2708000

longitude [m]

4476000

4478000

4480000

4482000

4484000

4486000

4488000

latitude

[m]

A

B

C

D

E

4 m

6 m

8 m

10 m

12 m

14 m16 m

velocity scale0.1 m/s

depth fromsurface:

Fig. 6. Maps of the horizontal velocities measured at some selected depths during survey S2. Gauss Boaga reference system used.



https://www.researchgate.net/publication/225804116_Estimates_of_Reynolds_stress_in_a_highly_energetic_shelf_sea?el=1_x_8&enrichId=rgreq-2dc57f8e-8e6a-4df1-ad1c-e41d3d638672&enrichSource=Y292ZXJQYWdlOzI2ODY4OTcwNztBUzoxODUwODA5ODMwNzI3NzBAMTQyMTEzODE1MzU5MA==https://www.researchgate.net/publication/225804116_Estimates_of_Reynolds_stress_in_a_highly_energetic_shelf_sea?el=1_x_8&enrichId=rgreq-2dc57f8e-8e6a-4df1-ad1c-e41d3d638672&enrichSource=Y292ZXJQYWdlOzI2ODY4OTcwNztBUzoxODUwODA5ODMwNzI3NzBAMTQyMTEzODE1MzU5MA==http://dx.doi.org/10.1016/j.advwatres.2014.11.006https://www.researchgate.net/publication/225804116_Estimates_of_Reynolds_stress_in_a_highly_energetic_shelf_sea?el=1_x_8&enrichId=rgreq-2dc57f8e-8e6a-4df1-ad1c-e41d3d638672&enrichSource=Y292ZXJQYWdlOzI2ODY4OTcwNztBUzoxODUwODA5ODMwNzI3NzBAMTQyMTEzODE1MzU5MA==http://dx.doi.org/10.1016/j.advwatres.2014.11.006http://-/?-http://-/?-http://-/?-

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well-known acquisition procedure of an ergodic system. A CTDrecorder system by Idronaut Srl (Table 1) was used to measure

the water temperature and salinity along the water column during

the same time interval. More detailed characteristics of the instru-

ments used are described in Mossa[1].

3.1.1. Survey of 29.12.2006 S1

From 9.30 a.m. till 13.30 p.m. (local time), for each investigated

station the current measurements were collected along the water

column with a vertical resolution of 2 m. Stations 3, 4, 6 and 7

(Fig. 3) were located along the coast following the bathymetric line

of 20 m; stations 5, 8, 9 and 10 were in the open sea, approaching

the 30 m bathymetric line; station 2 was inside the Mar Grande

basin. Their geographical coordinates and depths are summed up

inTable 2.Fig. 3plots a map of the measured horizontal velocityfor depths in the range 4 m to 18 m starting from the sea sur-

18 19 20 21 22 23 24 25 26

T[C]

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

z/h

st A

st B

st C

st D

st E

37 37.5 38 38.5 39

S[psu]

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

z/h

st A

st B

st C

st D

st E

Fig. 7. Vertical profiles of measured temperatureTand salinity S in the investigated stations during survey S2.

Fig. 8. Location of the fixed ADCP in Mar Grande basin. Google Earth source.

Table 3

Main characteristics of the fixed ADCP.

ADCP configuration

Model Workhorse monitor ADCP

Frequency 600 kHz

Beam angle h 20 relative to vertical

Transducer 4 beam convex

Bin size 0.5 m

Blank 1.6 m

Sample interval 0.5 s

Heading 252

Tilt 1 (pitch) 0 (beam 34 axis)

Tilt 2 (roll) 0 (beam 12 axis)

Velocity accuracy 0.3% of water velocity 0.3 cm/s

Velocity resolution 0.1 cm/s

Velocity range 5 m/s



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face, in order to show the principal pattern of the current. The

shape of the gulf seems to constrain the sea current to follow the

shoreline particularly in stations 7, 6, 4, 3 and 10. Thus, the coastal

flow has a mainly anticyclonic trend and the current bends toward

east and southeast. The vertical velocity component can be disre-

garded when compared to the horizontal one, for each examined

stationing points. InFig. 4, referring to one of the investigated sta-

tions, the time moving average and the variance of the acquiredvelocity signals are plotted for each velocity component, showing

that the acquisition time was sufficient enough to have a stationary

measurement, as already written. During the survey time, the wind

data showed an average intensity equal to 4 m/s and an average

direction of N310E.

The vertical profiles of temperature Tand salinity Smeasured by

the CTD recorder system are shown in Fig. 5. In all the examined

stations, the temperature values are almost invariant along the ver-

tical andstabilize around 15

C, with the exception of stations 2 and3, which are the nearest to the Mar Grande and are characterized by

Fig. 9. Vertical profiles of the measured streamwise velocity in the investigated stations during survey S1, with error bars.

Fig. 10. Vertical profiles of the measured streamwise velocity in the investigated stations during survey S2, with error bars.



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T= 14 C. In stations 6 and 7 a decreasing trend of Taffects the

superficial layer, where a small reduction of temperature of 2%

occurs. The vertical homogeneous trend is also evident for salinity,

whose value is 38.10 psu on average for stations 2 and 3 and

38.35 psu on average for all the other stations. Only in stations 4

and 7, which are more affected by industrial and urban discharges,

the salinity respectively increases and decreases from the

surface with increasing depth, but with a rate of 3%. Therefore, in

this survey the flow is not influenced by stratification along thewhole depth, also considering that the value of the calculated

Richardson number is less than 1, thus assuring the absence of

stratification.

3.1.2. Survey of 11.06.2007 S2

Field data were collected on 11 June 2007 from 10.00 a.m. till

2.00 p.m. (local time), in five stations, with a vertical resolution

of 1 m. The current speeds ranged from about 0.02 m/s to about

0.10 m/s and the wind data showed an average intensity equal to3 m/s and an average direction of N200E.

Fig. 11. Measured streamwise velocity distributions fitted by the log law, with error bars.



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Station B was the nearest to the coast, while stations A, C, D and

E are further from the coastline (Fig. 6). Their geographical coordi-

nates and depths are summed up inTable 2. InFig. 6the map of the

measured horizontal velocity is illustrated for some selected

depths in the range 4 m to 16 m starting from the sea surface.

On average a south-westward flow is observed in the target area,

so that the surface wind induced current seems to be strongly

influenced by the topography.

Fig. 7plots the vertical trends of measured Tand S and high-

lights that up to z/h 0.7 a reduction of temperature of 5% occurs

from the surface towards the bottom, while S is almost constant

and equal on average to 38.24 psu. In the most superficial layer,

for z/h> 0.7, the reduction of temperature with increasing depth

reaches 7%, while an increase of salinity of 2% occurs. Since this

thermohaline variation is less than 10%, also in this survey the flowwas still taken as homogeneous. In fact, also in this case, the calcu-

lated Richardson number resulted as less than 1.

3.2. Measurements acquisition by the rigidly mounted ADCP

During December 2013, as part of the RITMARE project, with

funds from PON R&C 20072013 provided by the Italian Ministry

of University, an oceanographic station was installed in the Mar

Grande basin. Its coordinates and depth are written in Table 2(sta-

tion O) and its placement is shown in Fig. 8. This station was pro-

vided with many instruments, including an ADCP and an

anemometer by Teledyne RD.

The shallow ADCP was on bottom tripods, looking verticallyupward with the transducer head about 0.50 m above the seafloor.

It was a four-beam ADCP, looking upward in a Janus configuration

with an angle relative to the vertical equal to h= 20, while the

beam width was 15(Fig. 2). It was rigidly mounted, so that the tilt

angles were constantly equal to 0during all the investigated per-

iod. Velocities were sampled along the water column with 0.50 m

vertical bin resolution and a 1.60 m blanking distance. The ADCP

instrument was operated in a standard dual profiling and wave-

burst sampling mode. Mean current velocity profiles were col-lected continuously at 1 h intervals, using an average of 60 mea-

surements acquired every 10 s. Instead, wave bursts of 2400

measurements at 0.5 s intervals (i.e. a 20-min-long record with a

frequency of 2 Hz) were collected each hour. The wave bursts sam-

pled five selected depth cells for all four beams. These selected

depth bins were distributed over the water column to examine

the data variation along the vertical. Burst samples were collected

at bins 1, 18, 36, 37 and 38 (counted starting from the transducer),

corresponding to heights above the seafloor of 1 m, 9.5 m, 18.5 m,

19 m and 19.5 m, respectively. The ADCP transducer head was

located approximately 0.50 m above the seabed. The ADCP config-

uration and setup are summarized in Table 3. The analysis carried

out with the field data measured by the rigidly mounted ADCP

focused on the estimates of the turbulent statistics of the flow (typ-

ically mean, root mean square and correlations of the velocity fluc-

tuations, whose calculations are possible thanks to the data

recording frequency). In fact, the acquisition frequency of 2 Hz,

which seems low in itself, is absolutely comparable with the

instrument acquisition frequency used by previous researchers in

other similar investigations[14,15,19,21].

4. Streamwise velocity profiles

In the present study, the log law was applied to the velocity

measurements acquired along the water column, starting from

the inner zone of the flow. The analysis of the vertical distributions

of the velocities assessed during surveys S1 and S2 was carried out

in the following way. For each measurement station the mean flow

direction along the vertical was detected, consequently the verticalprofiles were evaluated for the U velocity component along this

direction, the so-called streamwise velocity. This procedure could

be applied observing that the dispersion of the velocity with depth,

with respect to the mean flow direction, was generally slight

(Figs. 3and 6). Therefore, the flow was assumed as unidirectional

when the abovementioned dispersion was less than 15%, i.e. for

those stations where both the coast and the bathymetric lines pro-

vided a natural track for the current. The vertical distributions of

the streamwise velocity for these stations with unidirectional flow

are shown inFigs. 9and 10, respectively for S1 and S2.

Equation(1)was applied to the abovementioned vertical pro-

files, initially supposing that it may fit the observed data only in

the inner region, near the sea bed. Actually, it was observed that

the best matching between experimental data and log law profiles(i.e. maxima values of the correlation coefficient R2) was obtained

when the log law was applied to the whole water depth where

measurements were assessed. This expected result confirmed

recent studies[14,7],showing that the log law reproduces the ver-

tical trend of the streamwise current also outside the inner region

and up to the surface, if a stratification is absent, as seen in Figs. 5

and7. In this way it was possible to estimate both the shear veloc-

ity U and the coefficient B of Eq.(1) from the fitting line of each

graph plottingUas a function of log(z/m) (seeFig. 11). The deducedvalues ofU and B are summed inTable 4, together with R2. It is

worth noting that theB parameters are negative for all the vertical

streamwise profiles, confirming the results of Anwar[18]and De

Serio and Mossa [7]. Particularly, following research by De Serio

and Mossa [7], also in the present study the linear relation betweenB and the index number Ustr/U

was verified. Ustr represented the

Table 4

Calculated parameters of the log law.

Station u (m/s) B R2

5 0.018 26.787 0.76

6 0.028 25.925 0.87

7 0.012 16.844 0.73

8 0.013 23.473 0.73

10 0.024 25.409 0.73

A 0.032 30.775 0.76B 0.018 27.847 0.85

C 0.025 28.503 0.71

D 0.018 26.474 0.90

E 0.019 22.107 0.79

Fig. 12. ExperimentalB as function ofUstr/U, with error bars. The fitting line by De

Serio and Mossa[7](named DSM 2014) is shown, together with the new fitting line

derived also for data of the present experiment.



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streamwise velocity at the distance from the bottom where the

stratification started to affect the water. Therefore, in the present

case, it was the velocity assessed in the most superficial ADCP cell,

having considered the water homogeneous along the whole depth.

Adding the values ofB and Ustr/U derived for surveys S1 and S2 to

the data of De Serio and Mossa [7] and Anwar [18], the linear

behavior was proven again. It is worth noting that the coefficients

of the linear equation found in the present research differ slightly

(less than 4%) from those of De Serio and Mossa [7], as shown in

Fig. 12.

5. Analysis of the profiles of the turbulent estimates

5.1. Preliminary treatment of the data

A time period of ten days, from 10 to 20 February 2014, was

taken into consideration for the analysis of the fixed ADCP data.

This choice was suggested from the available anemometric data,

which guaranteed that in this period no strong wind episodes were

recorded. Hence also the wind-wave effect on the current could be

hypothesized as being slight.

Fig. 13. Time series ofHs (top) and Tp (bottom) of the significative wave during the observed period.

Fig. 14. Stick plot series of the measured wind during the analyzed period (1518.02.2014).



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Referring to this time period, Fig. 13 shows the time series of

the hourly recorded significative wave heights Hs (i.e. the average

of the highest 1/3 of the waves present) and peak periods Tp. The

fixed ADCP was located at so-called intermediate depth, resulting

1/20

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the large scales of the flow[15]. Applying Eqs.(12) and (13), the

Reynolds stress components, apart from q, that is u0w0 and v0w0,were calculated for each hour in the examined period. Succes-

sively, their vector sum provided the hourly Reynolds stress acting

in the horizontal plane. These values are plotted as an example for

day 17.02 at hours 00:02, 06:02, 12:02 and 18:02 in Fig. 16. A var-

iability with time in these vertical profiles up to z/h= 0.8 is evident,with a prevailing increasing trend of the absolute values for both

u0w0 and v0w0. Consequently, the Reynolds stress increases from

the bottom up toz/h= 0.8, while for z/h> 0.8 it decreases at hours

00:02 and at 18:00 and means a jet shape at hours 6:00 and 12:00.

Using Eq.(14)also the TKE was calculated and its vertical trend for

the same day is plotted inFig. 16every 6 h, showing an increasing

behavior from the bottom with increasing z. Daily-averaging over

the entire day 17.02 the Reynolds stress and the TKE, a resultingincreasing vertical trend towards the surface for both of them

Fig. 17. Vertical profiles of the daily averaged horizontal velocity, Reynolds stress and TKE, for day 17.02.2014, with error bars.





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was obtained, as shown inFig. 17. In the same figure also the ver-tical distribution of the daily-averaged horizontal velocity is plot-

ted, showing an increasing trend with increasing z and a jet

shape in the upper part of the water column.

The same approach was followed also for days 15.02, 16.02 and

18.02. Therefore, the daily averaged vertical profiles of the Rey-

nolds stress and the TKE were obtained, as illustrated in Figs. 18-

20, respectively. They confirm increasing values of both the Rey-

nolds stress and of the TKE from the bottom towards the surface.

These findings are in agreement with previous experimental

results by Nystrom et al. [15]and by De Serio et al. [22]in terms

of both order of magnitude and vertical behavior of the turbulent

estimates. Following Nezu and Nagakawa [4], the coefficient Rk,

which is the Reynolds stress normalized with 2TKE, is plotted

againstz/h in Fig. 21. Also data from De Serio and Mossa [7] wereadded to this graph.Rkincreases from the bottom towards the sur-

face and all the experimental data tend to collapse in a power law,

even if a larger scatter of data is present near the surface. This

trend is typical for the near-bottom and intermediate region of

open channel flows [4], while in their upper region the value of

Rk tends to reduce approaching the surface, as the turbulence

intensity is influenced by the damping effect of free surface. On

the contrary, in the present study, this damping effect did not

occur due to the presence of the surface waves, therefore an

increasing trend ofRk was observed also in the uppermost layer.

6. Estimation of the bottom drag and wind drag coefficients

The bottom stress sb, i.e. the drag exerted on the flow by theseabed, can be generally expressed as

sb qU2 15

when a log-layer is identified. In any case, also the following qua-

dratic form can be used, considering a reference velocity Ub

sb qCbU2b 16

where Cb is the non-dimensional bottom drag coefficient and Ub is

usually chosen to be either the depth-averaged velocity or a near

bottom velocity.

Comparing equations(15) and (16), the values for Cb could be

derived, as

Cb U

Ub

217

Firstly, using Eq.(17), theCbdrag coefficient was evaluated for

each measuring station of both surveys S1 and S2, where the log

law vertical distribution was verified. The used values ofU were

those reported inTable 4and theUb velocity was the streamwisevelocities measured in the point nearest to the bottom, for each

station.

Secondly, in correspondence of the rigidly mounted ADCP, Cbwas derived from Eq.(16)for all the examined hours of the inves-

tigated period 1518 February. It was deduced directly from the

Reynolds stress calculated in the bin nearest to the bottom. In this

case, the horizontal velocity measured in the bin nearest to the

bottom was used as the Ub comparing in Eq.(16).

Both forCbvalues coming from surveys S1 and S2 and for Cbval-

ues calculated in the fixed ADCP location, it is worth noting that

they are generally one order of magnitude greater than the typical

values in the range 24 103 reported in literature[23,24].This

result was expected, as also previous researches [7,6,9,25] noted

that wide ranges of the drag coefficient are possible and that theycan be attributed to mechanisms like wavecurrent interactions or

turbulent flow conditions or effects of small scale topography (i.e.

bed forms). Lueck and Lu [6] stated that the drag coefficient

related to form drag can be 410 times larger than that related

to skin friction, on the basis of some previous continental shelf

measurements. Also Apotsos et al. [26] wrote that observations

and theoretical calculations had shown that the bottom drag coef-

ficient can be large by an order of magnitude or more over rippled

sand beds, obtaining a value for Cbequal to 0.028 in the surf zone

from experimental data. The values of the bottom drag coefficients

Cbcalculated at all the examined stations during surveys S1 and S2

by means of Eq.(17)are in the range 2060 103. Therefore, they

seem to overestimate the classical bottom drag coefficients, but

could be considered consistent in any case with the presence ofbed forms, e.g. dunes. Greater values are detected in correspon-


Fig. 21. Ratio of daily averaged Reynolds stress to 2TKE plotted against z/hfor days

15.02, 16.02, 17.02 and 18.02 (open symbols) and for day 21.11.2010 and

25.11.2010 studied by De Serio and Mossa[7] (filled symbols).



http://-/?-http://-/?-https://www.researchgate.net/publication/259358067_Profile_Measurements_of_Turbulence_Properties_in_Coastal_Currents_Using_Acoustic_Doppler_Methods?el=1_x_8&enrichId=rgreq-2dc57f8e-8e6a-4df1-ad1c-e41d3d638672&enrichSource=Y292ZXJQYWdlOzI2ODY4OTcwNztBUzoxODUwODA5ODMwNzI3NzBAMTQyMTEzODE1MzU5MA==http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-https://www.researchgate.net/publication/228563180_Alongshore_momentum_balances_in_the_nearshore?el=1_x_8&enrichId=rgreq-2dc57f8e-8e6a-4df1-ad1c-e41d3d638672&enrichSource=Y292ZXJQYWdlOzI2ODY4OTcwNztBUzoxODUwODA5ODMwNzI3NzBAMTQyMTEzODE1MzU5MA==https://www.researchgate.net/publication/228563180_Alongshore_momentum_balances_in_the_nearshore?el=1_x_8&enrichId=rgreq-2dc57f8e-8e6a-4df1-ad1c-e41d3d638672&enrichSource=Y292ZXJQYWdlOzI2ODY4OTcwNztBUzoxODUwODA5ODMwNzI3NzBAMTQyMTEzODE1MzU5MA==https://www.researchgate.net/publication/258946122_Spectral_Scaling_in_a_Tidal_Boundary_Layer?el=1_x_8&enrichId=rgreq-2dc57f8e-8e6a-4df1-ad1c-e41d3d638672&enrichSource=Y292ZXJQYWdlOzI2ODY4OTcwNztBUzoxODUwODA5ODMwNzI3NzBAMTQyMTEzODE1MzU5MA==https://www.researchgate.net/publication/229092084_The_logarithmic_layer_in_a_tidal_channel?el=1_x_8&enrichId=rgreq-2dc57f8e-8e6a-4df1-ad1c-e41d3d638672&enrichSource=Y292ZXJQYWdlOzI2ODY4OTcwNztBUzoxODUwODA5ODMwNzI3NzBAMTQyMTEzODE1MzU5MA==https://www.researchgate.net/publication/33548495_Effects_of_wave_rollers_and_bottom_stress_on_wave_setup_J_Geophys_Res_112_C2?el=1_x_8&enrichId=rgreq-2dc57f8e-8e6a-4df1-ad1c-e41d3d638672&enrichSource=Y292ZXJQYWdlOzI2ODY4OTcwNztBUzoxODUwODA5ODMwNzI3NzBAMTQyMTEzODE1MzU5MA==http://-/?-http://-/?-http://dx.doi.org/10.1016/j.advwatres.2014.11.006https://www.researchgate.net/publication/258946122_Spectral_Scaling_in_a_Tidal_Boundary_Layer?el=1_x_8&enrichId=rgreq-2dc57f8e-8e6a-4df1-ad1c-e41d3d638672&enrichSource=Y292ZXJQYWdlOzI2ODY4OTcwNztBUzoxODUwODA5ODMwNzI3NzBAMTQyMTEzODE1MzU5MA==https://www.researchgate.net/publication/33548495_Effects_of_wave_rollers_and_bottom_stress_on_wave_setup_J_Geophys_Res_112_C2?el=1_x_8&enrichId=rgreq-2dc57f8e-8e6a-4df1-ad1c-e41d3d638672&enrichSource=Y292ZXJQYWdlOzI2ODY4OTcwNztBUzoxODUwODA5ODMwNzI3NzBAMTQyMTEzODE1MzU5MA==https://www.researchgate.net/publication/259358067_Profile_Measurements_of_Turbulence_Properties_in_Coastal_Currents_Using_Acoustic_Doppler_Methods?el=1_x_8&enrichId=rgreq-2dc57f8e-8e6a-4df1-ad1c-e41d3d638672&enrichSource=Y292ZXJQYWdlOzI2ODY4OTcwNztBUzoxODUwODA5ODMwNzI3NzBAMTQyMTEzODE1MzU5MA==https://www.researchgate.net/publication/228563180_Alongshore_momentum_balances_in_the_nearshore?el=1_x_8&enrichId=rgreq-2dc57f8e-8e6a-4df1-ad1c-e41d3d638672&enrichSource=Y292ZXJQYWdlOzI2ODY4OTcwNztBUzoxODUwODA5ODMwNzI3NzBAMTQyMTEzODE1MzU5MA==https://www.researchgate.net/publication/229092084_The_logarithmic_layer_in_a_tidal_channel?el=1_x_8&enrichId=rgreq-2dc57f8e-8e6a-4df1-ad1c-e41d3d638672&enrichSource=Y292ZXJQYWdlOzI2ODY4OTcwNztBUzoxODUwODA5ODMwNzI3NzBAMTQyMTEzODE1MzU5MA==https://www.researchgate.net/publication/229092084_The_logarithmic_layer_in_a_tidal_channel?el=1_x_8&enrichId=rgreq-2dc57f8e-8e6a-4df1-ad1c-e41d3d638672&enrichSource=Y292ZXJQYWdlOzI2ODY4OTcwNztBUzoxODUwODA5ODMwNzI3NzBAMTQyMTEzODE1MzU5MA==https://www.researchgate.net/publication/222415626_The_drag_coefficient_bottom_roughness_and_wave_breaking_in_the_nearshore_Coast_Eng?el=1_x_8&enrichId=rgreq-2dc57f8e-8e6a-4df1-ad1c-e41d3d638672&enrichSource=Y292ZXJQYWdlOzI2ODY4OTcwNztBUzoxODUwODA5ODMwNzI3NzBAMTQyMTEzODE1MzU5MA==http://dx.doi.org/10.1016/j.advwatres.2014.11.006http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-

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dence of the fixed ADCP, where the average value ofCbreaches 0.2.

Taking into account the complexity of the bottom nature and tex-

ture in the investigate region, the results could be considered reli-

able, even if more experimental confirmation is needed, being Cbaffected by many different factors. For example, Apotsos et al.

[26],also following Barrantes and Madsen[27],wrote that the ori-

entation of bedforms may influence cross-shore and along-shore

flows differently and that smaller drag coefficients may be esti-mated in alongshore flows.

An estimate of the non-dimensional wind drag coefficient Cwwas also attempted, using an expression for the wind stress sw atthe sea surface analogous to Eq.(16):

sw qaCwu2w 18

where uwis taken as the wind velocity and qa the air density.TheCwvalues were calculated only for the station O, taking into

account that in this position also wind measurements were

recorded (Fig. 14). An averaged wind drag coefficient Cw in the

range 670 103 was derived for wind intensities varying in

the range 0.56 m/s. These values overestimate typical literature

values ofCwwhich are on average around 0.001 [28].In any case,

it is worth to note that they are referred to a wind velocity mea-

sured by the instrument at the sea surface and not at 10 m above

the sea level, i.e. the distance at which usually uw of Eq. (18) is

referred. Hence, hypothesizing that the wind intensity can be

increased of 1015% at 10 m above the sea surface, the correspond-

ing values ofCwderived from Eq.(18)reduce by about one order of

magnitude and therefore better approximate the suggested values

present in literature.

7. Conclusions

The vertical structure of the coastal current in the inner part of

the Gulf of Taranto, in Southern Italy, is examined in the present

research. Both a vessel mounted ADCP and a bottom fixed ADCP

were used to measure the three velocity components along the

water column in some selected stationing points. The time-aver-

aged vertical profiles of the streamwise current were analyzed

from the VM-ADCP data, taking into account its low recording fre-

quency. It was proved that the classical log law well reproduced

the vertical profile of the experimental streamwise velocities up

to the surface, when the flow was mainly unidirectional along

the vertical and in absence of stratification. The velocities mea-

sured by the fixed ADCP at higher frequency were analyzed by

the variance method and were used to derive the vertical profiles

of the Reynolds stresses and turbulent kinetic energy TKE in this

location. These profiles showed an increasing trend toward the sur-

face, consistent with the presence of waves, thus confirming previ-

ous results in literature. Finally, starting from the experimental

Reynolds stresses derived near both the bed and the surface, the

estimates of the bottom drag coefficient Cb and of the wind dragcoefficientCw were respectively attempted. The derived values of

Cb generally overestimate the classical values proposed in litera-

ture, but they could be consistent with the presence of bed forms.

The estimates ofCw are comparable with classical suggested val-

ues, particularly when the experimental wind velocity is slightly

increased to resemble values at 10 m above the sea surface.

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