scholarly journals A two‐wave‐number description of shallow water ocean acoustics

1993 ◽  
Vol 93 (4) ◽  
pp. 2271-2271
Author(s):  
Robert M. Kennedy
Keyword(s):  
Shallow Water ◽  
Wave Number ◽  
Ocean Acoustics

scholarly journals Propagation properties of Rossby waves for latitudinal β-plane variations of <I>f</I> and zonal variations of the shallow water speed

2012 ◽  
Vol 30 (5) ◽  
pp. 849-855 ◽  
Author(s):  
C. T. Duba ◽  
J. F. McKenzie
Keyword(s):  
Shallow Water ◽  
Group Velocity ◽  
Rossby Wave ◽  
Rossby Waves ◽  
Low Frequency ◽  
Wave Number ◽  
Coriolis Parameter ◽  
Propagation Properties ◽  
Wave Normal ◽  
Water Speed

Abstract. Using the shallow water equations for a rotating layer of fluid, the wave and dispersion equations for Rossby waves are developed for the cases of both the standard β-plane approximation for the latitudinal variation of the Coriolis parameter f and a zonal variation of the shallow water speed. It is well known that the wave normal diagram for the standard (mid-latitude) Rossby wave on a β-plane is a circle in wave number (ky,kx) space, whose centre is displaced −β/2 ω units along the negative kx axis, and whose radius is less than this displacement, which means that phase propagation is entirely westward. This form of anisotropy (arising from the latitudinal y variation of f), combined with the highly dispersive nature of the wave, gives rise to a group velocity diagram which permits eastward as well as westward propagation. It is shown that the group velocity diagram is an ellipse, whose centre is displaced westward, and whose major and minor axes give the maximum westward, eastward and northward (southward) group speeds as functions of the frequency and a parameter m which measures the ratio of the low frequency-long wavelength Rossby wave speed to the shallow water speed. We believe these properties of group velocity diagram have not been elucidated in this way before. We present a similar derivation of the wave normal diagram and its associated group velocity curve for the case of a zonal (x) variation of the shallow water speed, which may arise when the depth of an ocean varies zonally from a continental shelf.

Supercritical Group Velocity for Dissipative Waves in Shallow Water

2012 ◽  
Author(s):  
Tae-Hwa Jung ◽  
Changhoon Lee
Keyword(s):  
Energy Dissipation ◽  
Phase Velocity ◽  
Shallow Water ◽  
Group Velocity ◽  
Water Depth ◽  
Numerical Experiments ◽  
Angular Frequency ◽  
Wave Number ◽  
Geometric Optics ◽  
Complex Valued

The group velocity for waves with energy dissipation in shallow water was investigated. In the Eulerian viewpoint, the geometric optics approach was used to get, at the first order, complex-valued wave numbers from given real-valued angular frequency, water depth, and damping coefficient. The phase velocity was obtained as the ratio of angular frequency to realvalued wave number. Then, at the second order, we obtained the energy transport equation which gives the group velocity. We also used the Lagrangian geometric optics approach which gives complex-valued angular frequencies from real-valued wave number, water depth, and damping coefficient. A noticeable thing was found that the group velocity is always greater than the phase velocity (i.e., supercritical group velocity) in the presence of energy dissipation which is opposite to the conventional theory for non-dissipative waves. The theory was proved through numerical experiments for dissipative bichromatic waves which propagate on a horizontal bed. Both the wave length and wave energy decrease for waves with energy dissipation. As a result, wave transformation such as shoaling, refraction, and diffraction are all affected by the energy dissipation. This implies that the shoaling, refraction, and diffraction coefficients for dissipative waves are different from the corresponding coefficients for non-dissipative waves. The theory was proved through numerical experiments for dissipative monochromatic waves which propagate normally or obliquely on a planar slope.

scholarly journals A shallow-water ocean acoustics inverse problem

2005 ◽  
Vol 6 (4) ◽  
pp. 287-290 ◽  
Author(s):  
David Stickler
Keyword(s):  
Inverse Problem ◽  
Shallow Water ◽  
Ocean Acoustics

PARAMETER SENSITIVITIES IN TWO-LAYER ISOSPEED MODELS OF SHALLOW WATER CHANNELS

1993 ◽  
Vol 01 (04) ◽  
pp. 469-486 ◽  
Author(s):  
R. J. CEDERBERG ◽  
W. L. SIEGMANN ◽  
M. J. JACOBSON ◽  
W. M. CAREY
Keyword(s):  
Shallow Water ◽  
Low Frequency ◽  
Propagation Model ◽  
Wave Number ◽  
Parameter Uncertainties ◽  
Rates Of Change ◽  
Wave Numbers ◽  
Analytic Expressions ◽  
Horizontal Wave ◽  
Order Of Magnitude

Sensitivities of relative intensity, interference wavelength, and horizontal wave number predictions to input parameters in two-layer isospeed models of shallow-water, low-frequency (less than 100 Hz) acoustic propagation problems are examined. The investigation is directed toward environmental parameter values corresponding generally to those near the site of a recent New Jersey shelf experiment. Typical parameter uncertainties in the environment of the experiment site are used to determine effects of parameter sensitivities on the accuracy of propagation model predictions. Also, analytic expressions for rates of change of wave numbers with respect to parameters are used to compute wave number and interference wavelength changes caused by parameter variations corresponding to the uncertainties. It is found that channel depth variations cause the largest change in intensity, while water sound speed variations have the greatest effect on wave numbers. Variabilities of the parameter sensitivities in regions about the base parameter sets are also examined, with the rates of change generally staying of the same order of magnitude throughout the regions considered. However, wave numbers which are close to cutoff can produce rates of change which vary by as much as three orders of magnitude.

A shallow water ocean acoustics inverse problem

2004 ◽  
Vol 115 (5) ◽  
pp. 2407-2407
Author(s):  
David Stickler
Keyword(s):  
Inverse Problem ◽  
Shallow Water ◽  
Ocean Acoustics

Propagation of Fully Nonlinear Waves in Deepwater, Transition Zone and Shallow-Water

2007 ◽  
Author(s):  
Hoda M. El Safty ◽  
Alaa M. Mansour ◽  
A. G. Abul-Azm
Keyword(s):  
Shallow Water ◽  
Transition Zone ◽  
Nonlinear Waves ◽  
Wave Number ◽  
Numerical Wave Tank ◽  
Tank Model ◽  
Wave Tank ◽  
Fully Nonlinear ◽  
Nonlinear Solution ◽  
Numerical Wave

In this paper, a fully nonlinear numerical wave tank model has been used to simulate the propagation of fully nonlinear waves in different water depths. In the numerical wave tank model, the fully nonlinear dynamic and kinematic free-surface boundary conditions have been applied and the boundary integral equation (BIE) solution to the Laplacian problem has been obtained using the Mixed Eulerian-Lagrangian (MEL) approach. The model solution has been verified through the comparison with the available experimental data. A convergence and accuracy study has been carried out to examine the time stepping scheme and the required mesh density. The nonlinearity effects were evident in the solution by the asymmetrical wave profile around both vertical and horizontal axis along with sharp high crests and broad flat troughs. Fully nonlinear wave propagation in deepwater, in transition zone and in shallow water has been simulated. The nonlinear solution has been compared to the linear solution for various waves. Shoaling coefficient and wave-number have been derived based on the nonlinear solution and compared to the linear theory solution for various wave characteristics.

scholarly journals The Matsuno baroclinic wave test case

2018 ◽  
Author(s):  
Ofer Shamir ◽  
Itamar Yacoby ◽  
Nathan Paldor
Keyword(s):  
Shallow Water ◽  
Gravity Waves ◽  
Analytic Solutions ◽  
Wave Mode ◽  
Wave Number ◽  
Water Model ◽  
Test Case ◽  
Wave Solutions ◽  
Barotropic Vorticity ◽  
Spatial Spectra

Abstract. The analytic wave-solutions obtained by Matsuno (1966) in his seminal work on equatorial waves provide a simple and informative way of assessing atmospheric and oceanic models by measuring the accuracy with which they simulate these waves. These solutions approximate the solutions of the shallow water equations on the sphere for small speeds of gravity waves such as those of the baroclinic modes in the atmosphere and ocean. This is in contrast to the solutions of the non-divergent barotropic vorticity equation, used in the Rossby-Haurwitz test case, which are only accurate for large speeds of gravity waves such as those of the barotropic mode. The proposed test case assigns specific values to the wave-parameters (gravity wave speed, zonal wave-number, meridional wave-mode and amplitude) for both planetary and inertia gravity waves, and confirms the accuracy of the simulation by employing Hovmöller diagrams and temporal and spatial spectra. The proposed test case is successfully applied to a standard finite-difference, equatorial, non-linear, shallow water model in spherical coordinates, which demonstrates that Matsuno’s wave-solutions can be accurately simulated for at least 10 wave-periods, which for oceanic planetary waves is nearly 1300 days. In order to facilitate the use of the proposed test case, we provide Matlab, Python and Fortran codes for computing the analytic solutions at any time on arbitrary latitude-longitude grids.

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