bubble plume in the ocean

Effects of Wind-induced Near-surface BubblePlumes on the Performance of Distributed

Underwater Acoustic Sensor Networks

Abstract—This paper analyzes the effect of the presence ofnear-surface oceanic bubble plumes on the overall performanceof distributed Underwater Wireless Acoustic Sensor Networks(UWASNs). The existence of bubble plumes in surface and sub-surface ocean water columns is inevitable in most windy oceanicenvironments. There exists studies reporting the degradationof acoustic signal propagating through oceanic bubble plumes.However, most of the existing network protocols designed foruse in underwater sensor networks are ignorant of these effects.In this paper, we study these effects and observe how bubbleplumes have impact on the overall performance of UWASNs,with respect to different parameters such as the bit error rate(BER), delay, and signal-to-interference-plus-noise-ratio (SINR).Simulation studies show that in the presence of bubble plumes,SINR decreases by approximately 29 %, BER increases by 71 %,and delay increases by 56 %, approximately.

Keywords-Shallow-water, acoustics signal, multipath-reflection, acoustic sensor network, bubble plumes

I. INTRODUCTION

This paper presents an analysis of the effect of oceanicbubble plumes on the performance of distributed UWASNs.UWASNs are envisioned to enable applications such asoceanographic data collection, pollution monitoring, offshoreexploration, disaster prevention, and assisted navigation [1][2].

Large volume of research literature (e.g., [3], [4], [5], [6],[7]) exists on UWASNs. However, most studies ignored theeffect of bubble plumes on the overall network performance,despite the fact that the existence of near-surface bubbleplumes is inevitable in most windy oceanic environments. Thiswork is an attempt towards addressing this important researchlacuna.

A UWASN consists of variable number of sensor nodes,which are capable of sensing, processing, and communicating,and are deployed over a given area of interest to performapplication-centric collaborative monitoring tasks [8]. Underthe surface of water, electromagnetic signals (RF) cannot beused efficiently, primarily due to the absorption by the conduc-tive sea water. Similarly, optical signals cannot be used in theunderwater column, as they suffer from increased scatteringeffects. Additionally, the precision for sending optical signalshould be high. On the contrary, in an underwater column,acoustic signal can traverse significant distance without atten-uation. So, for reliable communication in such an environment,acoustic signal is normally used.

Unlike terrestrial wireless sensor networks, UWASNs suffer

from multiple challenges. Some of the key inherent character-istics [9] in designing a UWASN are listed below.

• The available acoustic bandwidth under the surface of wa-ter depends on the transmission range [10] and frequency.Due to high environmental noise at low frequency [11],communication quality also degrades.

• UWASNs are highly dynamic in nature. Except for thenodes anchored with surface buoys, the other nodes havemobilities ranging from minimum to a finite value. Therelative mobility between the source and receiver nodesleads to Doppler spread. Additionally, node’s mobilityleads to deformation in architecture of a sensor network,which, in turn, affects its communication performance.

• In UWASNs, internode communication is affected for theacoustic signal fluctuation caused by many factors suchas path loss, noise, and multi-path fading [12].

• End-to-end delay in underwater environments is veryhigh [13]. The acoustic signal propagation speed in suchenvironments is five orders of magnitude higher than thepropagation speed in terrestrial environment. Propagationspeed of wireless acoustic signal in underwater environ-ment is about 1500 m/s, which is five orders of magnitudelower than propagation speed of signal used in terrestrialsensor network.

• Due to the adverse channel condition, there is a probabil-ity of having high Bit Error Rate (BER) and temporarylosses of connectivity, thereby affecting the overall net-work performance.

• Battery power of sensor nodes is limited and remotereplenishment of power source is nearly impossible. Also,solar power cannot be exploited as an energy source underwater. Therefore, energy consumption per node in thenetwork is crucial aspect of study to increase the overallnetwork lifetime.

• Power attenuation of the signal depends primarily onfrequency and distance.

• There is a probability of hardware failure due to foul-ing and corrosion. Failure rate of nodes in underwaterenvironments is more than that in the terrestrial sensornetwork.

An ocean column is typically segmented into three lay-ers –– mixed, thermocline, and deep isothermal. Among allthese layers, the mixed layer is normally the most turbu-lent. The upper surface of this layer is directly subjected

to tangential stress due to surface winds. In other words,transfer of momentum takes place from wind to the watersurface, which often results in splashing/breaking of the waves.This phenomenon creates concentrated layers of micro-bubblesunderlying the ocean surface, typically up to a depth of 10meters [14]. The layers of bubble plumes have been observedto vary not only in depth, but also in range and time [15].Their evolution in density, radius, and spatial distribution hasprofound influence on the quality of acoustic communication[16].

A. Contribution

As mentioned above, the communication performance ofdistributed UWASN systems is very sensitive to the presenceof near-surface bubble plumes. Again, wind has an importantrole on the nature and intensity of plumes at subsurface region.So, it is also important to study the effect of wind velocity onthe overall performance of distributed UWASN.

In sum, the contributions of this work is cataloged as below.• We have analyzed the variation of plume depth with the

variation of wind speeds.• We have also studied how the spatial distribution of

bubble plumes varies as a function of wind velocity.• We have analyzed the effect of individual bubble, as

well as the combined effect of bubble plumes, on thepropagation characteristics of the acoustic signal.

• Finally, we have analyzed the performance of the networkin terms of three metrics: SINR, BER, and delay.

II. RELATED WORK

The unique characteristics of acoustic signal propagation inunderwater environment makes UWASNs distinct from thoseof the terrestrial wireless sensor networks. There exist studieson the performance analysis of UWASNs in the physicallayer. Most of these studies are focused on the physicalcharacteristics of acoustic signal. There is deficiency of workanalyzing the performance of UWASNs by considering theinteraction of wireless acoustic signals in realistic physicalphenomena occurring in the ocean, especially in the surfaceand subsurface regions.

Ismail et al. [17] analyzed the performance of UWASNs interms of propagation loss by considering the acoustic signal tobe propagated through underwater ocean channel. The authorsconsidered only the inherent characteristics of the underwaterchannel from the communication point of view. Stefanovand Stojanovic [18] analyzed the performance of underwateracoustic ad-hoc networks in the presence of interference.They have assumed the uniform distribution of nodes in theentire channel. They have modeled path loss in inter-nodecommunication to be frequency dependent, and have assumedRician distribution of acoustic fading.

Fox et al. [19] proposed a methodology for predictingthe underwater acoustic communication performance. Theyshowed how performance varies with respect to the variationin relative locations of source and receiver nodes in the per-spective of acoustic speed profile in the channel. The authors

have taken parameters such as variable sound speed profilesas a function of environment variables between the sourceand the receiver nodes. These parameters help in assessingthe overall communication performance of UWASNs. Llorand Malumbes [20] studied how physical layer modelingaffects the performance of higher layer protocols. Zhang etal. [21] considered a linear multihop communication architec-ture to model acoustic propagation. They took into accountfrequency-dependent signal attenuation, interhop interference,and propagation delay.

A synthesis from the review of existing works reveals thatthe effect of near-surface bubble plumes on overall networkperformance needs investigation.

Fig. 1: Architecture profile of UWASN

Fig. 2: Link establishment between any two nodes in thenetwork

III. COMMUNICATION ARCHITECTURE

We have considered a 3-D architecture where large numberof nodes are randomly distributed in space in the oceancolumn, as shown in Figure 1. Due to the several advantagesof single-hop communication over multi-hop [22], we haveconsidered the multi-hop communication architecture betweenthe source and the surface sink node. We have neglected thevertical movement of nodes, as their deviation with respect totheir equilibrium position is very small.

Typically, nodes in UWASN are equipped with acoustictransceivers, whereas the surface sink nodes are equippedwith both acoustic and electromagnetic transceivers. The nodesplaced in between the source and surface sink nodes act asthe relay nodes. The relay nodes help in routing informa-tion from the source node to the surface sink. The nodescommunicate with one another in the wireless medium usingacoustic signal. In this paper, we have not considered inter-sink communication. Nodes are assumed to be homogeneousin nature with respect to their transmission capability. One ofthe challenging aspects of network modeling is establishingconnectivity amongst the sensor nodes. Connectivity betweenany two nodes is established when they come in the transmis-sion range of each other. In this paper, the network model ispresented in terms of a graph

G = (N,Cl) (1)

In Equation (1), N = N1, N2, ...., Nn is the number of nodesdeployed over the particular region of interest, and Cl is thelink established between two nodes. The term, ‘Cl’, can beexpressed as:

(ni, nj) ∈ Cl (2)

The scenario is depicted in Figure 2.

IV. CHARACTERIZATION OF NEAR-SURFACE WINDINDUCED BUBBLE PLUMES

A. Categorization of bubble plumes

The physical unit formed by the combination of manydiscrete bubbles is termed as bubble plume or bubble clouds[23]. Based on Thorp’s measurements and observations [23],Monohan [24] classified bubble plumes into three categories:α, β, and γ. These plumes bear their names on the basis oftheir individual lifetime during active bubble generation pro-cess induced by wind action on the ocean surface. Whitecaps[15] are associated with two stages, Stage-A and Stage-B,due to wave breaking. Stage-A is involved with the crestof spilling breaker and Stage-B with the foam patch. Theα−plume is the subsurface extension of Stage-A whitecap[15], and it contains the highest void fraction ranging from10−1 to 10−2. They have very short lifetime, typically in theorder of 1 second. Due to the dissipation of momentum ofdownward moving jets that originate due to wave-breaking,α−plumes decay into β−plumes. The β−plumes have lessvoid fraction (ranging from 10−4 to 10−3 ) than α−plumes,and they remain attached with the Stage-B foam patch. They,typically, persist only upto 4 seconds. In course of time,the β−plumes evolve into γ−plumes, and gradually becomedetached from the originating whitecap. Among the threeplume categories, γ−plumes have the lowest void fractionranging from 10−6 to 10−7 with a time span 10-100 timesgreater than β−plumes. Due to their high longevity and size,the γ−plumes are affected by the local circulation process,and finally decay to a weak-stratified background layer.

B. Physical characterization of bubble plumes

This section discusses the spatial distribution of bubbleplumes and the quantification of their population. Monahan[24] extensively studied the characteristics of oceanic bubbles,and their importance in the gas exchange between air-seainterface. As proposed by Hall [25], the Bubble PopulationSpectral Density (BPSD), ζ, for any level of bubble plume ismathematically expressed in the functional form as:

ζ(r, z, w10) = N0Ψ(r, z)Z(z, w10)W (w10) (3)

In Equation (3), r is the bubble radius, z is the depth fromocean surface, w10 is the wind speed 10 m above the seasurface, W is a wind-dependent factor, and N0 is a constanthaving value corresponding to a particular value of ζ, which isobtained for particular values of radius (r), depth (z), and windvelocity (w10). The term Ψ(r, z) denotes the spectral shapefunction, Z(z) is the depth dependent function signifying thee-folding depth [26] for each level of bubble plumes. The e-folding depth is normalized with respect to the reference depthz = 0. Thus, the general form of Equation (3) is written as:

ζ(r, z, w10) = N0Ψ(r)Z(z)W (w10) (4)

C. Wind dependent factor

As observed by Monahan [24], the rate of generation ofbubble plumes is equal to the rate of formation of whitecaps.The study of the relation between the fraction of whitecapson the sea surface and the wind velocity was undertaken byMonahan and Muircheartaigh [27]. After a couple of decades,Andreas and Monahan [28] presented a premier work, whichstates that the fraction of whitecaps present on the sea surfacecan be approximated to be proportional to the third powerof wind speed. Hall [25] undertook an integrated study onseveral research works done on the dependence of BPSD onwind velocity (w10). Finally, the author proposed a functionalrelation, which is given below [15]:

W (w10) = (w10

13)3 (5)

In Equation (5), w10 is the wind velocity 10 m above thesurface. As it is assumed that wind is the main factor toinduce the formation of all bubbles, the function W (w10)is regarded the same for all stages of plume development,including the last stage, i.e., the background layer at anyinstant of time.

D. Nature of spectral shape function

Based on the analysis of several experimental data usingmultiple measuring techniques, Hall [25] postulated that thespectral shape function follows power law with an exponentclose to -4. It has been observed that this power law is validfor bubbles having radii in the range 20-30 µm upto 50-80 µm.Again, on the basis of the report presented by Hall [25], it canbe stated that the power law for spectral shape function holdsgood for small and intermediate shaped bubbles. Therefore,power law of spectral shape function is invariant for small

and intermediate shaped bubbles, except for the changes inpopulation size. Therefore, the generalized form of the spectralshape function for β−plumes, γ−plumes, and the backgroundlayer is expressed as [25]:

Ψ(r) =

0, for rref = rmin

(rrefr1

)3, for rmin ≤ rref < r1

1.0, for r1 ≤ rref ≥ r2( r2rref

)4, for r2 > rref ≤ r3

(6)

In Equation (6), rmin = 10µm, r1 = 15µm, r2 = 20µm, r3= 54.4 + (1.984)zµm, and z is in meter. In the subsequentsections, BPSD for different types of bubble plumes isdiscussed.

1) Form of BPSD for β−Plume: From the previoussection, it has been observed that the spectral slope ofthe power law is a function of bubble size. Higher slopescorrespond to bubbles of larger radii. As the lifetime of aβ−plume is comparatively shorter than that of γ−plume,the spectral slope for a β−plume is set as -4, whereas forγ−plume and background layer a slightly higher value of -2.6is taken. Again, in our study it has been assumed that bubblesof larger radii exist near to the surface, and with increasingdepth, the population density decreases. Considering allthe aspects stated above, the functional form of BPSD forβ−plumes is expressed as follows [15].

ζβ(r, z, w10) = N0βΨβ(r)Zβ(z)W (w10) (7)

In Equation (7), the value of the constant, N0β , is taken tobe 2.0×107 m−3µm−1 [26]. The functional form for spectralshape function, Ψβ(r), for β−plume can be expressed as:

Ψβ(r) =

0, for rref > rmin

(rrefr1

)3, for rmin ≤ rref < r1


)4, for r2 < rref ≥ r3( r2r3 )4( r3

rref)2.6, for rref > r3

(8)

Following the work by Monahan and Lu [29], which considersuniform distribution of β−plume as a function of e-foldingdepth, the general form of depth dependent function is math-ematically expressed as:

Zβ(z) =

{1.0, for zref ≤ zβmax0, for z > zβmax

(9)

In Equation (9), the parameter, Zβmax, refers to the maximumpenetration depth of a β−plume, and it is related to orbitalmotion of breaking wave. Therefore, it controls the verticalaxis of β−plume. Normally, the penetration depth ofβ−plume extends to one half of the significant wave height[26]. The expression of maximum penetration depth forβ−plume, Zβmax, is presented as [15]:

Zβmax = (1.23× 102)w210 (10)

2) BPSD for γ−plume: Mathematically, bubble densityspectrum for γ−plume can be expressed in a manner similarto that in Equation (7) for β−plume. Therefore, consideringvarious parameters associated with the γ−plume, the densityspectrum is expressed as:

ζγ(r, z, w10) = N0γΨγ(r)Zγ(z)W (w10) (11)

As γ−plumes are the transformed products of β−plumes, thespectral shape function of γ−plumes, Ψγ(r), for small and in-termediate shaped bubbles remains unchanged. However, theirconcentration gets weaker. During the transformation phasefrom β−plume to γ−plume, a significant change is observedin bubble population size. The spectral shape function forγ−plume is expressed as:

Ψβ(r) =

0, for rref < rmin

(rrefr1

), for rmin ≤ rref < r1


)4, for r2 < rref ≤ r3( r2r3 )4( r3

rref)p(z), for rref > r3

(12)

In Equation (12), p(z) is the spectral slope, which has a steepervalue for the bubbles having radius larger than 60µm, and itis expressed as:

p(z) = 4.37 + (z

2.55)2 (13)

The representative values for r1, r2, and r3 are taken the sameas in Equation (7). Majority of the experimental observationsshow that the depth dependent function Zγ(z) in Equation(12) is expressed as:

Zγ(z) = exp(−z/dγ) (14)

In Equation (14), dγ is the the e-folding depth for γ−plume.The e-folding depth as a function of wind speed, w10, isexpressed as:

dγ(w10) =davg(w10)

ln(Mv(atz=0)Mn

)(15)

In Equation (15), davg is the average penetration depth, Mv

is the back-scattering cross-section per unit volume, and Mn

is the average noise level. The parameter, davg , is expressedas:

davg(w10) = 0.6(w10 − 5) + 3.5 (16)

Equation (16) is valid for any value of w10 greater than 5 m/s.The parameter, Mv , used in Equation (15) is expressed as:

∞∫0

nγ(r)Πbsdr (17)

In the Equation (17), Πbs is the back scattering cross-sectionfor a single bubble.

(a) BPSD for small and intermediate bubbles (b) BPSD for near-large bubbles

(c) BPSD for large bubbles

Fig. 3: Distribution of BPSD for β− and γ−plumes

Fig. 4: Variation of penetration depths of plumes with the variation in wind speed

0

50

100

150

200

250

10 15 20 25 30 35 40

(Cef

f) γ [m

/s]

Frequency [kHz]

w10 = 11m/sw10 = 12m/sw10 = 13m/s

(a) Effective speed, (Ceff )γ , of acoustic signal throughGamma plume

0

20

40

60

80

100

120

10 15 20 25 30 35 40

((C

eff) β

+(C

eff) γ

) avg

[m/s

]

Frequency [kHz]

w10 = 11m/sw10 = 12m/sw10 = 13m/s

(b) Effective speed of acoustic signal through Beta as well asGamma-plume

Fig. 5: Acoustic signal propagation through Beta and Gamma plume induced region

0

0.05

0.1

0.15

0.2

0.25

0.3

10 15 20 25 30 35 40

(αs)

γ [d

B/m

]

Frequency [kHz]

w10 = 11m/sw10 = 12m/sw10 = 13m/s

(a) Attenuation, (αs)γ of acoustic signal through Gammaplume

0

0.1

0.2

0.3

0.4

0.5

0.6

10 15 20 25 30 35 40

(αs)

β+γ

[dB

/m]

Frequency [kHz]

w10 = 11m/sw10 = 12m/sw10 = 13m/s

(b) Attenuation of acoustic signal due to combined effect ofBeta and Gamma plume

Fig. 6: Attenuation of acoustics signal through Beta and Gamma plume

Figures 3 (a), (b), (c) depict the distribution of BPSDfor both the plumes. From the figures, we observe that thedistribution curves get shifted upward for β−plume withrespect to the γ−plume.

E. Nature of penetration of β− and γ−PlumesWind velocity is an important factor in deciding the pen-

etration depth of a particular type of plume. It is usuallyseen that the penetration depth of β−plume is lower than thatof the γ−plume for a particular wind velocity. Variation ofpenetration depth for both types of aforementioned plumesis shown in Figure 4. From Figure 4, we infer that in thenear-surface bubble-induced region, wireless acoustic signalpropagates partly through the γ−plume induced region andpartly through the β− and γ−plume induced regions, together.Figure 7 shows the bubble induced regions under differentwind speeds.

V. ANOMALOUS BEHAVIOR OF ACOUSTIC SIGNAL IN THEPRESENCE OF BUBBLE PLUMES

During propagation through oscillating bubble clouds,acoustic signal gets attenuated. To calculate the attenuation

0

2

4

6

8

10

11 12 13

Pen

etar

tion

Dep

th (

m)

Wind speed w10 (m/s)

β- and γ-plume induced regionγ-plume induced region

Fig. 7: Bubble induced regions under different wind speed

and perturbation caused by the bubble plumes, we followedthe approach used by Norton and Novarini [15] and Hall [25].The assumptions made in this approach are as follows:

• The compressional speed of acoustic signal is assumedto be approximately constant throughout the medium.

• There is no interaction between any pair of bubbles.• Due to the oscillation mechanism, the medium becomes

dispersive.• Multiple scattering among the bubbles is negligible.

The steps to be followed to calculate the sound perturbationare:

• Compressibility is first calculated for a single bubble.• Total change in compressibility (∆K) is calculated by

integrating the result obtained for a single bubble, forsizes of bubbles ranging in radius from maximum (rmax)to minimum (rmin).

• Then, the effective speed of acoustic signal (Ceff ) isexpressed in terms of ∆K.

Under the condition when typical square distance betweenbubbles is larger than the scattering strength, the effectivecompressibility, Keff , of the bubble mixture is expressed asfollows:

Keff = (1− Vfrac)K0 + ∆K (18)

In Equation (18), K0 is the compressibility of ocean waterin the absence of bubbles, and Vfrac is the fractional volumeoccupied by the bubbles. Assuming kr < 1, where k is thepropagation vector of acoustic signal, ∆K is expressed as:

∆K(f, z) =N

ρ0πf2r

( frf − 1 + iδ)(19)

For a distribution of plumes, the expression is written as:

∆K(f, z) =1

ρ0πf2

rmax∫rmin

[rζ(r)

(( frf )2 − 1 + iδ)] dr (20)

In Equation (19), the physical parameter, fr, is the resonancefrequency. Under adiabatic oscillation and no viscous effect,for a spherical air-bubble in water, the resonance frequency isexpressed as:

fr = (1 +z

10)0.5(

3.25× 106

r) (21)

where, fr is expressed in Hz, and the radius r is in µm.The parameter, δ, in Equation (19), is the damping constant.Damping is observed in three forms––due to radiation, δr, dueto shear viscosity, δν , and due to thermal conductivity, δt.Damping constant, δ, in terms of these three components isexpressed as:

δ = δr + δν + δt (22)

Mathematical calculation shows that out of these three, damp-ing due to viscosity and temperature can be neglected ascompared to damping due to radiation. So, the effectivedamping is expressed as:

δ = δr =2πfr

C0(23)

where, C0 is the velocity of acoustic signal in the absence ofbubble plumes.

For low void fraction, the effective sound speed, Ceff , is

expressed as [15]:

1

C2eff

=1

C20

+1

πf2

rmax∫rmin

[rζ(r)

(( frf )2 − 1 + iδ)] dr (24)

Equating the numerator and the denominator of Equation (24),we have:

1

C2eff

=1

C20

+1

πf2

rmax∫rmin

rζ(r)[(( frf )2 − 1)− iδr][(( frf )2 − 1)2 + δ2r ]

dr (25)

By putting the value of δr from Equation (23) in Equation(25), and writing the real and imaginary part separately, wehave:

1

C2eff

=1

C20

+1

πf2

rmax∫rmin

rζ(r)[(( frf )2 − 1)]

[(( frf )2 − 1)2 + δ2r ]dr (26)

1

C2eff

=1

C20

+1

πf2

rmax∫rmin

rζ(r)(−δr)[(( frf )2 − 1)2 + δ2r ]

dr (27)

Equations (26) and (27), respectively, represent the real andimaginary parts. Next, we analyze the sound speed modifiedduring propagation through β− and γ−plumes.

A. Sound speed perturbation by β− and γ−plume

Sound perturbation due to bubble plume depends on thewind speed and the type of plume. In this section, we havecomputed the effective sound speed caused due to only theβ− and γ−plumes.

1) Perturbation by β−plume: On the basis of theirsizes, we classified the β−plumes into three subtypes:small-and-intermediate, near-large, and large. Contributionto the effective sound speed, Ceff , through β−plume comesfrom these three subtypes. Contribution by three types ofβ−plumes is given below.

Small and intermediate bubbles

Wind speed w10 = 11 m/sEffective sound speed, Ceff is expressed as:

1

C2eff

=1

C20

− Is (28)

In the Equation (28), the term Is is integrated over allpossible values of radii belonging to the small and intermediatebubbles, and it is expressed as:

Is = (1.51× 1016)f3×r1∫

rmin

r9

[((134.39× 106)2 − f2C0r2 × 106)2

+ (2πf3r3 × 109)2]

dr (29)

Wind speed w10 = 12 m/s

For wind speed 12 m/s, the term, Is, is expressed as:

Is = (2.52× 1016)f3×r1∫

rmin

r9

[((136.65× 106)2 − f2C0r2 × 106)2

+ (2πf3r3 × 109)2]

dr (30)


Is = (3.72× 1016)f3×r1∫

rmin

r9

[((138.65× 106)2 − f2C0r2 × 106)2

+ (2πf3r3 × 109)2]

dr (31)

Near large bubbles

Wind speed w10 = 11 m/sEffective sound speed, Ceff is expressed as:

1

C2eff

=1

C20

− In (32)

In Equation (32), the integration term, In, is expressed fordifferent wind speeds as follows.

Is = (5.1× 1019)f3×r2∫r1

r6

[((134.39× 106)2 − f2C0r2 × 106)2

+ (2πf3r3 × 109)2]

dr (33)

In Equation (33), r3 = 20 µm.Wind speed w10 = 12 m/s


Is = (8.49× 1016)f3×r2∫r1

r6

[((136.72× 106)2 − f2C0r2 × 106)2

+ (2πf3r3 × 109)2]

dr (34)


Is = (126× 1018)f3×r2∫r1

r6

[((138.65× 106)2 − f2C0r2 × 106)2

+ (2πf3r3 × 109)2]

dr (35)

Large bubbles

Wind speed w10 = 11 m/sEffective sound speed, Ceff , is expressed as:

1

C2eff

=1

C20

− Il (36)

In Equation (36), the integration term Il is expressed for

different wind speeds below.

Is = (8.13× 1024)f3×r3∫r2

r2

[((134.39× 106)2 − f2C0r2 × 106)2

+ (2πf3r3 × 109)2]

dr (37)

In the Equation (37), r3 is taken as 60 µm.Wind speed w10 = 12 m/s


Is = (1359× 1022)f3×r3∫r2

r2

[((136.72× 106)2 − f2C0r2 × 106)2

+ (2πf3r3 × 109)2]

dr (38)


Is = (20160× 1021)f3×r2∫r1

r2

[((138.65× 106)2 − f2C0r2 × 106)2

+ (2πf3r3 × 109)2]

dr (39)

2) Perturbation by γ−Plume: Like the β−plume,the γ−plume is further classified into three categories.Contribution to the effective sound speed under variable windspeed for each of these categories is given below.

Small and intermediate bubbles

Wind speed w10 = 11 m/sThe integration term, Is, is expressed as:

Is = (5.61× 1017)f3×r1∫

rmin

r7

[((164.60× 106)2 − f2C0r2 × 106)2

+ (2πf3r3 × 109)2]

dr (40)


Is = (7.26× 1017)f3×r1∫

rmin

r7

[((167.31× 106)2 − f2C0r2 × 106)2

+ (2πf3r3 × 109)2]

dr (41)

Wind speed w10 = 13 m/sFor w10 = 13 m/s,

Is = (9.96× 1017)f3×r1∫

rmin

r7

[((170.41× 106)2 − f2C0r2 × 106)2

+ (2πf3r3 × 109)2]

dr (42)

Near large bubbles


Is = (8.40× 1017)f3×r2∫r1

r6

[((164.60× 106)2 − f2C0r2 × 106)2

+ (2πf3r3 × 109)2]

dr (43)


Is = (10.89× 1018)f3×r2∫r1

r6

[((167.31× 106)2 − f2C0r2 × 106)2

+ (2πf3r3 × 109)2]

dr (44)


Is = (14.94× 1018)f3×r2∫r1

r6

[((170.41× 106)2 − f2C0r2 × 106)2

+ (2πf3r3 × 109)2]

dr (45)

Large bubbles


Is = (1.34× 1024)f3×r3∫r2

r2

[((164.60× 106)2 − f2C0r2 × 106)2

+ (2πf3r3 × 109)2]

dr (46)


Is = (17.43× 1023)f3×r3∫r2

r6

[((167.31× 106)2 − f2C0r2 × 106)2

+ (2πf3r3 × 109)2]

dr (47)


Is = (23.91× 1023)f3×r3∫r2

r6

[((170.41× 106)2 − f2C0r2 × 106)2

+ (2πf3r3 × 109)2]

dr (48)

B. Acoustic signal attenuation by near-surface bubble plumes

In Section A, we have the effective sound speed, Ceff , inthe presence of both types of plumes: β as well as γ. Theterm, Ceff , is expressed in terms of the real and imaginary

components as:Ceff = Cs + iαs (49)

In Equation (49), the real component, Cs, represents theacoustic phase speed, and the imaginary component, αs,represents the attenuation of the acoustic signal due to thepresence of bubble plumes. Equation (24) is derived underthe condition where multiple scattering among the bubbles isneglected. The two terms on the right side of Equation (49),can be, respectively, written as:

Cs = Re(Ceff ) (50)

αs(dB/m) =20

In(10)Im(

1

Ceff) (51)

In Figure 5, we have shown the variation of signal propagationthrough the β− and γ−plume induced underwater region.From the two figures, we can infer that with the sameincrement in frequency, the acoustic signal is subjected to lessresistance from the γ−plume induced region, compared to theregion induced by both the β− and γ−plumes. Alternatively,we can say that the acoustic signal propagates faster throughthe γ−plume induced region. In Figure 6, we show theacoustic signal attenuation during propagation through β− andγ−plume induced region. From the two figures, we infer thatthe attenuation rate of acoustic signal is higher in the β−and γ−plume induced region, than in the region with onlyγ−plume.

VI. PERFORMANCE EVALUATION

In this Section, we present the result of simulation-basedUWASN in terms of different metrics, which are explainedbelow.

A. Simulation settings

Settings of the simulation parameters are shown in TableI. We have used the NS-3 simulator for our work. We haveconsidered the network to be consisting of 150 nodes. In thenetwork, the nodes are deployed in a region of dimension100 m × 100 m × 100m. The nodes are deployed randomlyat different depths ranging from 0 to 100 m. The sink nodeis placed at the sea-surface. We have used the ‘Meandering-current mobility model’ [30]. Packets are transmitted from thesource node to the sink node via the intermediate relay nodes.We considered seven operating frequencies, namely, 10, 15,20, 25, 30, 35, and 40 kHz.

B. Performance metrics

The performance of UWASN is assessed using thefollowing metrics.

Signal-to-Interference-Plus-Noise-Ratio (SINR): In anycommunication system, signal gets affected due to thepresence of noise generated by system itself or injected fromoutside. Like the Signal-to-Noise-Ratio (SNR), SINR is animportant metric for estimating the link quality in wirelesscommunication among nodes. Interference occurs whensignals from transmitters, other than the desired source, arrive

TABLE I: Simulation Parameters

Parameters ValuesDeployment Region 100m× 100mm

Bubble’s Penetration Depth β−plume: 1.4m - 2.1m; γ−plume: 7.1m - 8.3mSignal frequencies 10 kHz, 15 kHz, 20 kHz, 25 kHz, 30 kHz, 35 kHz, 40 kHz

Data rate 500 bpsPacket interval 10 sec

Modulation scheme 64-QAMNumber of nodes (N) 150Spreading co-efficient 1.5

Wind Speed (w10) 11 m/s, 12 m/s, 13 m/s

0

10

20

30

40

50

60

70

80

10 15 20 25 30 35 40

SIN

R [d

B]

Frquency [kHz]

Bubble Plume, N = 30Bubble Plume, N = 90

Bubble Plume, N = 150

Thorpe, N = 30Thorpe, N = 90

Thorpe, N = 150

(a) SINR for wind speed 11 m/s

0

10

20

30

40

50

60

70

80

10 15 20 25 30 35 40

SIN

R [d

B]

Frquency [kHz]




Thorpe, N = 150

(b) SINR for wind speed 12 m/s

Fig. 8: SINR for bubble induced and bubble free channel

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

10 15 20 25 30 35 40

BE

R

Frquency [kHz]




Thorpe, N = 150

(a) BER for wind speed 11 m/s

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

10 15 20 25 30 35 40

BE

R

Frquency [kHz]




Thorpe, N = 150

(b) BER for wind speed 12 m/s

Fig. 9: BER for bubble induced and bubble free channel

at the receiver coincidentally with the desired signal [31].Mathematically, SINR is expressed as:

SINR =Si

I +N(52)

In Equation (52), Si indicates the signal from the ith source, Iindicates the interference between the signals at the receivingend, and N is noise in the channel.

Bit Error Rate (BER): In digital transmission, BERis defined as:

BER =Percentage of bits with errors

Total no of bits sent(53)

BER and SNR are interrelated with each other, but theyare distinct. In our experiment, we have used the 64-QAM

modulation scheme for evaluating BER. We have:

BER =7

12× (0.5× erfc(z)) (54)

Different topologies may exhibit different BER in the samesituation.

Delay (Latency):Delay is defined as the time taken by a packet to reach thedestination node from the source node [32]. In our work, wehave defined delay in terms of the propagation time, i.e., thetime for a message to reach the sink node from the sourcenode. Mathematically, it is expressed as:

Delay =Distance covered by the signal

Speed of acoustic signal through channel(55)

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

10 15 20 25 30 35 40

DE

LAY

[sec

]

Frquency [kHz]




Thorpe, N = 150

(a) Delay for wind speed 11 m/s

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

10 15 20 25 30 35 40

DE

LAY

[sec

]

Frquency [kHz]




Thorpe, N = 150

(b) Delay for wind speed 12 m/s

Fig. 10: Delay for bubble induced and bubble free channel

In propagating through the underwater channel, the acousticsignal traverses through bubble-free and bubble-induced en-vironments. Regarding speed, there will be combination ofideal channel propagation speed, which is C0 (1500 m/s), andanother, the effective speed, Ceff , through the bubble plume.

C. Benchmark

We have compared the simulated results with the existingThorp propagation [33] model in underwater environment.In Thorp model, internode communication is affected due toattenuation of acoustic signal by conductive and saline oceanwater. So, in this case, it is observed that the performanceof the network is solely dependent on the underwater oceanicchannel characteristics. In our study, part of the channel isinduced by bubble plume. So, in such a scenario, the perfor-mance of the network differs from that using the Thorp model.As the Thorp model includes the ideal channel scenario, wehave compared our simulation results with the results obtainedusing the Thorp model.

D. Result and discussion

The results obtained with respect to the three metrics definedin Section VI-B are discussed below.

1) SINR: Figure 8 shows how SINR varies with frequencyfor different number of nodes under variable wind speed. Wesee from the figure that for the same number of nodes at thesame frequency, SINR is higher using the Thorp model than inthe case where bubble plume is considered. Again, we observefrom the figure that towards the higher frequency region, SINRincreases with the increase in the number of nodes. In case ofThorp, we observe that the distribution of SINR is frequency-independent. This is due to the fact that even if signal and noisevalues are different, the ratio is the same for all the cases. Ourstudy reveals that the overall SINR for bubble plume decreasesby 28.80 % for wind speed 11 m/s and 29.80 % for wind speed12 m/s.

2) BER: Variation of BER with the variation in frequencyis shown in Figure 9. A close observation reveals that,compared to Thorp, BER is higher in the bubble-inducedchannel. Again, we see that BER gradually decreases withthe increase in frequency. Additionally, a comparative analysisdirects that as wind velocity shifts from 11 m/s to 12 m/s,

there is significant increase in the BER. This is due to thefact that as the wind velocity increases, the bubble plumespenetrate more deeper region. So, the signal traverses moredistance to reach the surface sink. As expected, the bubble-induced channel invokes more errors in bits than the bubble-free channel. In sum, we infer that compared to Thorp, BERincreases by 69.27 % for wind speed 11 m/s, and 71.72 % forthe wind speed 12 m/s.

3) Delay: Figure 10 shows the average time taken by apacket to reach the destination from the source node. As seenfrom the figure, in the bubble-induced channel, it takes longertime for a packet to reach the destination from the sourcenode than in the bubble-free channel. Again, we observethat with the increase in the number of nodes N, the delaydecreases. As the number of nodes increases, the number ofhops also increases. As a consequence, a packet takes lesserpropagation time. Another noticeable observation is that, withthe increase in wind speed, the delay also increases. As windspeed increases, bubble’s penetration depth also increases.Therefore, the depth of near-surface bubble-induced regionincreases, and the duration of interaction with bubbles alsoincreases. Simulation results show that delay for bubble plumeinduced region increases by 47.21 % for wind speed of 11 m/s,and 64.34 % for wind speed of 12 m/s.

VII. CONCLUSION

Increased wind speed near the ocean surface induces thegeneration of bubble plumes. Bubble plumes are importantphysical entities that persist near to the ocean surface. InUWASNs, we have studied the effect of near-surface bubble-induced region on network performance. Simulation-basednetwork performance was undertaken in terms of three per-formance metrics––SINR, BER, and delay. The simulationresults were compared with the results obtained using theThorp model. Performance comparison shows that there is anincrease in SINR by 29.3 %, whereas, for BER and delay, itis increased by 70.5 % and 55.78 % respectively.

In this work, bubble-plumes were considered to be station-ary. However, situations may arise where there is collectivemotion of bubble plumes. In future, we want to observe the

effect of near-surface moving bubble plumes on the perfor-mance of distributed UWASNs.

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bubble plume in the ocean

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