Internal Tide Generation Over a Continental Shelf

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Internal Tide Generation Over a Continental Shelf

• Summer 2008 internship
• Ga?lle Faivre
• Flavien Gouillon, Alexandra Bozec
• Pr. Eric P. Chassignet

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Biography

• Gaëlle Faivre
• Student from the Engineering School in Mathematic
  Modeling and Mechanics (MATMECA)
• Bordeaux, FRANCE
• Position at COAPS
• Internship from June 2 - Sept 16, 2008

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Outline

• Introduction
• Motivation
• Objective
• Approach
• - Analytical solution
• - Numerical experiment
• Results
• Conclusion

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I. Introduction

• Internal waves review
• Internal waves occur in stably stratified fluids
  when a water parcel is displaced by some external
  force and is restored by buoyancy forces. Then
  the restoration motion may overshoot the
  equilibrium position and set up an oscillation
  thereby forming an internal wave.
• Internal tide comes from the interaction between
  rough topography and the barotropic tide.
• Important internal wave generation occurs at the
  shelf break where the slope is abrupt.
• - Horizontal length scales of the order 1 to 100
  km
• - Horizontal Velocity of 0.05 to 0.5 m.s-1
• - Time scale of minutes to days

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Surface signature of an internal wave
An example of a surface signature of an internal
wave View from a boat
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II. Motivation

• Knowledge of internal wave generation and how
  they propagate is crucial to understand ocean
  mixing and the large scale ocean circulation.
• Internal waves generation at the shelf affects
• sediment transport
• biology
• oil production companies
• submarine navigation.
• At the shelf, the dynamic of internal wave is
  strongly non-hydrostatic and thus cannot be well
  resolved in Oceanic General Circulation Models
  that usually make the hydrostatic approximation

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III. Objectives

• Assess the HYbrid Coordinate Ocean Model (HYCOM)
  skills to simulate internal wave at an abrupt
  slope.
• Evaluate and document the limitation of HYCOM on
  representing these waves.

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IV. Approach

1. Compute an analytical solution for an idealized
   case of internal tide generation over a shelf
   break
2. Build the same configuration with HYCOM
3. Compare the dynamical properties as well as the
   energetic of the generated internal wave for both
   results.

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Analytical solution
Conditions for this analytic results - The
flow is two-dimensional - 2 layers ocean
- The interface between the 2 layers
needs to be smaller than the shelf depth

• Based on Griffiths and Grimshaw, (2004)
• 
  

• There is one baroclinic mode with the phase
  speed

Figure 1 schematic of the analytical model
Dimensions

• Wave speed at the shelf

• Wave speed in the deep ocean

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Analytical energy computation
The nondimensional depth-integrated energy fluxes
at the shelf are given by
JL
Semi-diurnal frequency
Steepness parameter
Prediction of the low energy flux

• Change in phase across the slope is given by

• Low energy fluxes located each ,
  where the slope accommodates an integer number of
  wavelengths of the internal wave

• High energy fluxes located each

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HYCOM

• HYCOM is run in fully isopycnal mode for this
  configuration.
• We used all the same parameters as the analytical
  configuration and vary the steepness parameter by
  changing the stratification, and the interface
  depth but keeping a constant shelf length/coast
  length ratio (Ls/Lc).
• Objectives Show that low energy fluxes are
  simulated in HYCOM and well located when Ls/Lc1.

Schematic of the Model Configuration
Analytical Energy Fluxes
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Results Energy fluxes comparison

• Energy fluxes as a function of the steepness
  parameter (function of the wave speed at the
  shelf) for

HYCOM
Analytical Solution
Energy fluxes (W.m-2)
Low energy fluxes expected at
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Discussion

• We obtain low energy fluxes just like the
  analytical solution predicted. However some of
  them seem to be not located correctly for a
  particular choice of parameters.
• What could cause this shift in the low energy
  location?
• Not enough sampling (because each point is a
  different configuration)
• Several approximations and truncations are made
  in the internal wave group speed and in the
  internal wave energy computations
• HYCOM does not represent the wave propagation
  correctly (wavelength, wave speed)

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Conclusion

• We have found an analytical solution for the
  internal wave generation at a shelf with a
  2-layers ocean idealized problem.
• We have conducted numerical simulations with
  HYCOM for the same configuration.
• Low energy fluxes are represented in HYCOM.
• For a particular choice of parameters, these some
  of the low energy fluxes seems to be shifted from
  where the analytical solution predicts.
• This could be due to our mistakes or HYCOM errors
  on the representing the propagation of the waves

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Future Work

• More simulations should be run in order to
  analyze the origin of the shift in the low energy
  fluxes
• From the small scale of s1?
• Computational errors in model?
• Human errors?
• Further analyses of the approximations in our
  computations should be made
• Additional model configurations
• Observe climatological density stratifications
  and adapt it to realistic continental shelves.
• Examine the effects of alongshore variability in
  shelf topography (application to 3 dimensions)
• Include nonlinear and nonhydrostatic terms

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Interface displacement of the internal waves
Fig2 Displacement of the interface for a
horizontal normalization
Fig3 Internal tide of two-layer fluid, with
,
at
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Baroclinic zonal velocities
Snapshot after 45 hours, (right after spin-up)
Velocity (ms-1)
The interface displacement is about 1 meter and
compares well with the analytical prediction
(difficult to see displacement from the scale of
the figure)