Examining the Validity of Approximations to Fully Three-Dimensional Shallow-Water Acoustic Propagation through Nonlinear Internal Gravity Waves

2007 ◽  
Author(s):  
Timothy F. Duda
Keyword(s):  
Shallow Water ◽  
Gravity Waves ◽  
Three Dimensional ◽  
Internal Gravity Waves ◽  
Acoustic Propagation

scholarly journals Observations of Near-Inertial Internal Gravity Waves Radiating from a Frontal Jet

2013 ◽  
Vol 43 (6) ◽  
pp. 1225-1239 ◽  
Author(s):  
Matthew H. Alford ◽  
Andrey Y. Shcherbina ◽  
Michael C. Gregg
Keyword(s):  
Gravity Waves ◽  
Three Dimensional ◽  
Internal Gravity Wave ◽  
Internal Gravity Waves ◽  
Shear Layers ◽  
Adjustment Process ◽  
Vertical Wavelength ◽  
The North ◽  
Inertial Wave ◽  
The North Pacific

Abstract Shipboard ADCP and towed CTD measurements are presented of a near-inertial internal gravity wave radiating away from a zonal jet associated with the Subtropical Front in the North Pacific. Three-dimensional spatial surveys indicate persistent alternating shear layers sloping downward and equatorward from the front. As a result, depth-integrated ageostrophic shear increases sharply equatorward of the front. The layers have a vertical wavelength of about 250 m and a slope consistent with a wave of frequency 1.01f. They extend at least 100 km south of the front. Time series confirm that the shear is associated with a downward-propagating near-inertial wave with frequency within 20% of f. A slab mixed layer model forced with shipboard and NCEP reanalysis winds suggests that wind forcing was too weak to generate the wave. Likewise, trapping of the near-inertial motions at the low-vorticity edge of the front can be ruled out because of the extension of the features well south of it. Instead, the authors suggest that the wave arises from an adjustment process of the frontal flow, which has a Rossby number about 0.2–0.3.

scholarly journals Momentum Flux Spectrum of Convectively Forced Internal Gravity Waves and Its Application to Gravity Wave Drag Parameterization. Part I: Theory

2005 ◽  
Vol 62 (1) ◽  
pp. 107-124 ◽  
Author(s):  
In-Sun Song ◽  
Hye-Yeong Chun
Keyword(s):  
Gravity Waves ◽  
Momentum Flux ◽  
Three Dimensional ◽  
Internal Gravity Waves ◽  
Buoyancy Frequency ◽  
Spectral Structure ◽  
Two Dimensional ◽  
Resonance Factor ◽  
Flux Spectrum ◽  
Wave Momentum

Abstract The phase-speed spectrum of momentum flux by convectively forced internal gravity waves is analytically formulated in two- and three-dimensional frameworks. For this, a three-layer atmosphere that has a constant vertical wind shear in the lowest layer, a uniform wind above, and piecewise constant buoyancy frequency in a forcing region and above is considered. The wave momentum flux at cloud top is determined by the spectral combination of a wave-filtering and resonance factor and diabatic forcing. The wave-filtering and resonance factor that is determined by the basic-state wind and stability and the vertical configuration of forcing restricts the effectiveness of the forcing, and thus only a part of the forcing spectrum can be used for generating gravity waves that propagate above cumulus clouds. The spectral distribution of the wave momentum flux is largely determined by the wave-filtering and resonance factor, but the magnitude of the momentum flux varies significantly according to spatial and time scales and moving speed of the forcing. The wave momentum flux formulation in the two-dimensional framework is extended to the three-dimensional framework. The three-dimensional momentum flux formulation is similar to the two-dimensional one except that the wave propagation in various horizontal directions and the three-dimensionality of forcing are allowed. The wave momentum flux spectrum formulated in this study is validated using mesoscale numerical model results and can reproduce the overall spectral structure and magnitude of the wave momentum flux spectra induced by numerically simulated mesoscale convective systems reasonably well.

scholarly journals Oceanic tides from Earth-like to ocean planets

2018 ◽  
Vol 615 ◽  
pp. A23 ◽  
Author(s):  
P. Auclair-Desrotour ◽  
S. Mathis ◽  
J. Laskar ◽  
J. Leconte
Keyword(s):  
Gravity Waves ◽  
Three Dimensional ◽  
Stable Stratification ◽  
Internal Gravity Waves ◽  
Tidal Dissipation ◽  
Planetary Rotation ◽  
Wide Range ◽  
Oceanic Tides ◽  
3D Effects ◽  
Tidal Response

Context. Oceanic tides are a major source of tidal dissipation. They drive the evolution of planetary systems and the rotational dynamics of planets. However, two-dimensional (2D) models commonly used for the Earth cannot be applied to extrasolar telluric planets hosting potentially deep oceans because they ignore the three-dimensional (3D) effects related to the ocean’s vertical structure. Aims. Our goal is to investigate, in a consistant way, the importance of the contribution of internal gravity waves in the oceanic tidal response and to propose a modelling that allows one to treat a wide range of cases from shallow to deep oceans. Methods. A 3D ab initio model is developed to study the dynamics of a global planetary ocean. This model takes into account compressibility, stratification, and sphericity terms, which are usually ignored in 2D approaches. An analytic solution is computed and used to study the dependence of the tidal response on the tidal frequency and on the ocean depth and stratification. Results. In the 2D asymptotic limit, we recover the frequency-resonant behaviour due to surface inertial-gravity waves identified by early studies. As the ocean depth and Brunt–Väisälä frequency increase, the contribution of internal gravity waves grows in importance and the tidal response becomes 3D. In the case of deep oceans, the stable stratification induces resonances that can increase the tidal dissipation rate by several orders of magnitude. It is thus able to significantly affect the evolution time scale of the planetary rotation.

On the mean motion induced by internal gravity waves

1969 ◽  
Vol 36 (4) ◽  
pp. 785-803 ◽  
Author(s):  
Francis P. Bretherton
Keyword(s):  
Gravity Waves ◽  
Wave Energy ◽  
Wave Train ◽  
Three Dimensional ◽  
Internal Gravity Waves ◽  
Wave Number ◽  
Mean Flow ◽  
Mean Velocity ◽  
Mean Motion ◽  
The Mean

A train of internal gravity waves in a stratified liquid exerts a stress on the liquid and induces changes in the mean motion of second order in the wave amplitude. In those circumstances in which the concept of a slowly varying quasi-sinusoidal wave train is consistent, the mean velocity is almost horizontal and is determined to a first approximation irrespective of the vertical forces exerted by the waves. The sum of the mean flow kinetic energy and the wave energy is then conserved. The circulation around a horizontal circuit moving with the mean velocity is increased in the presence of waves according to a simple formula. The flow pattern is obtained around two- and three-dimensional wave packets propagating into a liquid at rest and the results are generalized for any basic state of motion in which the internal Froude number is small. Momentum can be associated with a wave packet equal to the horizontal wave-number times the wave energy divided by the intrinsic frequency.

Acoustic mode beam effects of nonlinear internal gravity waves in shallow water

2008 ◽  
Vol 123 (5) ◽  
pp. 3943-3943
Author(s):  
Timothy Duda ◽  
Ying‐Tsong Lin ◽  
James F. Lynch
Keyword(s):  
Shallow Water ◽  
Gravity Waves ◽  
Internal Gravity Waves ◽  
Acoustic Mode ◽  
Mode Beam

Energy transfer between external and internal gravity waves

1964 ◽  
Vol 19 (3) ◽  
pp. 465-478 ◽  
Author(s):  
F. K. Ball
Keyword(s):  
Energy Transfer ◽  
Internal Wave ◽  
Surface Waves ◽  
Shallow Water ◽  
Gravity Waves ◽  
External Surface ◽  
Internal Gravity Waves ◽  
Liquid System ◽  
Resonant Interactions ◽  
Non Linear

In a two-layer liquid system non-linear resonant interactions between a pair of external (surface) waves can result in transfer of energy to an internal wave when appropriate resonance conditions are satisfied. This energy transfer is likely to be more powerful than similar transfers between external waves. The shallow water case is discussed in detail.

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