non-hydrostatic effects on internal waves and mixing in the coastal ocean jiuxing xing and alan m....
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![Page 1: Non-hydrostatic effects on internal waves and mixing in the coastal ocean Jiuxing Xing and Alan M. Davies (Proudman Oceanographic Laboratory, Liverpool)](https://reader038.vdocument.in/reader038/viewer/2022110401/56649e055503460f94af14a1/html5/thumbnails/1.jpg)
Non-hydrostatic effects on internal waves and mixing in
the coastal ocean
Jiuxing Xing and Alan M. Davies
(Proudman Oceanographic Laboratory, Liverpool)
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Jonsmod 2006-Plymouth
Motivation
Understand small scale processes (e.g. solitary waves, convection)
Stratified (tidal) flows over the steep topography (e.g., lee waves, flow separation and eddies)
Are current coastal ocean models sufficient (e.g., is non-hydrostatic dynamics important)?
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Jonsmod 2006-Plymouth
Examples of small scale processes: ISWs of elevation on the Oregon shelf
Klymak and Moum (2003)
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Jonsmod 2006-Plymouth
ISWs in the Faeroe-Shetland Channel
Hosegood et al (2004)
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Jonsmod 2006-Plymouth
Stratified tidal flow over sills (Loch Etive, Inall et al, 2004)
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Jonsmod 2006-Plymouth
Models σ-following coordinate models (e.g.,
POLCOMS, POM, BOM) Z-coordinate models (e.g., MITgcm) The iterative method for non-hydrostatic
pressure:
• an elliptic equation for the non-hydrostatic pressure
0
0),,(),,(),(),(
zNH
tzxPzdtzxgtxgtxP
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Jonsmod 2006-Plymouth
Tests of the MIT model using Lab. exp. (Internal solitary waves over a slope (Michallet and Ivey 1999)
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Jonsmod 2006-Plymouth
Internal solitary waves (model results)
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Jonsmod 2006-Plymouth
Internal solitary waves (lab experiments vs model results)
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Jonsmod 2006-Plymouth
A dispersive ISW (small-amplitude)
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Jonsmod 2006-Plymouth
Large amplitude ISWs on a slope
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Jonsmod 2006-Plymouth
Tidal flow over a sill – lee wave generation and non-hydrostatic effects
Idealized model setup• M2 tide forced at the seaward boundary
• Closed landward boundary
• Resolution: dx=10 to 100m, dz=1m
• Minimum viscosity (Av=10-3 m2s-1, Ah=10-1 m2s-1, no explicit diffusivity)
• Initial zero velocity, N=0.01 s-1
Model domain
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Jonsmod 2006-Plymouth
Interaction of tidal waves with bottom topography: key non-dimensional parameters
The key physical parameters:
• U0, ω0, f, N, h0, L, H.
Non-dimensional parameters:
• U0 /(ω0L) the tidal excursion parameter;
• h0/H the relative height of the topography;
• [(ω02 - f 2 )/(N2- ω0
2)]1/2 the internal wave ray slope;
• h0 /L the topographic slope;
• U0 /(Nh0) the Froude number (or h’=Nh0 /U0);
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Jonsmod 2006-Plymouth
Snapshots of (T,u,w) at 23 mins (4,5,6,7/32 Tm2,non-hydro run)
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Jonsmod 2006-Plymouth
Snapshots of (T,u,w) at 23 mins (4,5,6,7/32 Tm2,non-hydro run)
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Jonsmod 2006-Plymouth
Snapshots of Ri number at 4,5,6,7/32T (non-hydrostatic run)
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Jonsmod 2006-Plymouth
Snapshots of temp & velocity at 4,5,6,7/32T (hydrostatic run)
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Jonsmod 2006-Plymouth
Temp & velocity at t=2/8T, 3/8T, 4/8T, 5/8T (non-hydrostatic run)
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Jonsmod 2006-Plymouth
Temp & velocity at t=2/8T, 3/8T, 4/8T, 5/8T (hydrostatic run)
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Jonsmod 2006-Plymouth
Vertical averaged internal wave energy flux (non-hydrostatic (left) and hydrostatic (right) )
01d
pdzuH
F
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Jonsmod 2006-Plymouth
Non-hydrostatic (top) and hydrostatic pressure
PPhh and P and Pnhnh have a 180 have a 180oo phase shift phase shift
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Jonsmod 2006-Plymouth
In a linear system, Ph & Pnh out phase
,00z
pb
z
p
t
wnh
,02
wNtb
)(nhhppp
)/(0
gb
,0
bz
ph
,0
bz
ph
0)( 2
2
2
z
pN
z
p
tnhh
)cos(
),cos(
2
2
tANz
p
thentAz
pif
nh
h
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Jonsmod 2006-Plymouth
indirect estimate of hydrostatic pressure by matching isopycnals to streamlines
nonhydrostatic pressure
seafloor value
seafloor value
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Jonsmod 2006-Plymouth
Power spectral density (w) at two locations, non-hydrostatic (left) vs hydrostatic (right) (N=0.01)
At lower frequency, as predicted by Khatiwala (2003), but not higher frequency.
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Jonsmod 2006-Plymouth
Power spectral density (w) for a steeper topography (N=0.01), non-hydrostatic (left) vs hydrostatic (right) (N=0.01)
Significant departure from recent theory at both lower & higher frequency.
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Jonsmod 2006-Plymouth
Summary
Including non-hydrostatic dynamics in the coastal ocean models is feasible.
Model results are encouraging comparing to the laboratory data.
Importance of non-hydrostatic dynamics to lee wave generation and breaking;
Strong kinetic energy spectral peak at higher (lee wave) frequency near the sill - a challenge to observationlists;
Enhanced mixing due to the smaller-scale ripple topography - a challenge to modellers;
More work is needed to assess the model quantitatively and quantify wave drag effects on mixing and circulation (3D effects may be important) .