Propagation of internal gravity waves in fluids with shear flow and rotation

1967 ◽  
Vol 30 (3) ◽  
pp. 439-448 ◽  
Author(s):  
Walter L. Jones
Keyword(s):  
Angular Momentum ◽  
Shear Flow ◽  
Gravity Waves ◽  
Shear Flows ◽  
Internal Gravity Waves ◽  
Vertical Transport ◽  
Wave Frequency ◽  
Slow Rotation ◽  
Critical Levels ◽  
Rotating System

In a rotating system, the vertical transport of angular momentum by internal gravity waves is independent of height, except at critical levels where the Doppler-shifted wave frequency is equal to plus or minus the Coriolis frequency. If slow rotation is ignored in studying the propagation of internal gravity waves through shear flows, the resulting solutions are in error only at levels where the Doppler-shifted and Coriolis frequencies are comparable.

Propagation of internal gravity waves in perfectly conducting fluids with shear flow, rotation and transverse magnetic field

1972 ◽  
Vol 52 (1) ◽  
pp. 193-206 ◽  
Author(s):  
N. Rudraiah ◽  
M. Venkatachalappa
Keyword(s):  
Magnetic Field ◽  
Angular Momentum ◽  
Shear Flow ◽  
Gravitational Waves ◽  
Transverse Magnetic Field ◽  
Internal Gravity Waves ◽  
Transverse Magnetic ◽  
Critical Levels ◽  
Mean Flow ◽  
The Waves

The propagation of internal Alfvén-inertio-gravitational waves in a Boussinesq inviscid adiabatic perfectly conducting shear flow with rotation is investigated in the presence of a transverse magnetic field. It is shown that the effect of the rotational nature of electromagnetic force and Coriolis force is that linear momentum is not conserved anywhere in the fluid even at critical levels, whereas the angular momentum flux is conserved everywhere in the fluid except at the critical levels at which the Doppler-shifted frequency Ωd = 0, + ΩA or ± Ω ± (Ω2 + Ω2A)½, where ΩA is the Alfvén frequency and Ω is the Coriolis frequency, and the angular momentum is transferred to the mean flow there by Alfvén-inertio-gravitational waves. Asymptotic solutions to the wave equation are obtained near the critical levels and it is shown that the effect of the Lorentz force on the waves at the critical levels is to increase the process of critical layer absorption. The condition for neglection of rotation for higher frequency waves is also obtained and is found to be the same in both hydrodynamic and hydro-magnetic flows.

Resonant wave interactions in a stratified shear flow

1988 ◽  
Vol 190 ◽  
pp. 357-374 ◽  
Author(s):  
R. Grimshaw
Keyword(s):  
Shear Flow ◽  
Gravity Waves ◽  
Critical Level ◽  
Internal Gravity Waves ◽  
Wave Interactions ◽  
Resonant Wave ◽  
Resonant Interactions ◽  
Stratified Shear Flow ◽  
Weak Resonance ◽  
Background Shear

Resonant interactions between triads of internal gravity waves propagating in a shear flow are considered for the case when the stratification and the background shear flow vary slowly with respect to typical wavelengths. If ωn, kn(n = 1, 2, 3) are the local frequencies and wavenumbers respectively then the resonance conditions are that ω1 + ω2 + ω3 = 0 and k1 + k2 + k3 = 0. If the medium is only weakly inhomogeneous, then there is a strong resonance and to leading order the resonance conditions are satisfied globally. The equations governing the wave amplitudes are then well known, and have been extensively discussed in the literature. However, if the medium is strongly inhomogeneous, then there is a weak resonance and the resonance conditions can only be satisfied locally on certain space-time resonance surfaces. The equations governing the wave amplitudes in this case are derived, and discussed briefly. Then the results are applied to a study of the hierarchy of wave interactions which can occur near a critical level, with the aim of determining to what extent a critical layer can reflect wave energy.

scholarly journals Momentum and Energy Transport by Gravity Waves in Stochastically Driven Stratified Flows. Part I: Radiation of Gravity Waves from a Shear Layer

2007 ◽  
Vol 64 (5) ◽  
pp. 1509-1529 ◽  
Author(s):  
Nikolaos A. Bakas ◽  
Petros J. Ioannou
Keyword(s):  
Shear Flow ◽  
Shear Layer ◽  
Gravity Wave ◽  
Gravity Waves ◽  
Wave Energy ◽  
Energy Transport ◽  
Wave Spectrum ◽  
Internal Gravity Waves ◽  
Wave Interference ◽  
Wide Range

Abstract In this paper, the emission of internal gravity waves from a local westerly shear layer is studied. Thermal and/or vorticity forcing of the shear layer with a wide range of frequencies and scales can lead to strong emission of gravity waves in the region exterior to the shear layer. The shear flow not only passively filters and refracts the emitted wave spectrum, but also actively participates in the gravity wave emission in conjunction with the distributed forcing. This interaction leads to enhanced radiated momentum fluxes but more importantly to enhanced gravity wave energy fluxes. This enhanced emission power can be traced to the nonnormal growth of the perturbations in the shear region, that is, to the transfer of the kinetic energy of the mean shear flow to the emitted gravity waves. The emitted wave energy flux increases with shear and can become as large as 30 times greater than the corresponding flux emitted in the absence of a localized shear region. Waves that have horizontal wavelengths larger than the depth of the shear layer radiate easterly momentum away, whereas the shorter waves are trapped in the shear region and deposit their momentum at their critical levels. The observed spectrum, as well as the physical mechanisms influencing the spectrum such as wave interference and Doppler shifting effects, is discussed. While for large Richardson numbers there is equipartition of momentum among a wide range of frequencies, most of the energy is found to be carried by waves having vertical wavelengths in a narrow band around the value of twice the depth of the region. It is shown that the waves that are emitted from the shear region have vertical wavelengths of the size of the shear region.

The breaking of transient inertio-gravity waves in a shear flow using the Gaussian beam approximation

2014 ◽  
Vol 759 ◽  
pp. 676-700 ◽  
Author(s):  
C. Rodas ◽  
M. Pulido
Keyword(s):  
Shear Flow ◽  
Gaussian Beam ◽  
Ray Tracing ◽  
Gravity Waves ◽  
Convective Instability ◽  
Shear Flows ◽  
Computational Cost ◽  
Dynamical Instability ◽  
Initial Time ◽  
Instability Criterion

AbstractThe propagation of transient inertio-gravity waves in a shear flow is examined using the Gaussian beam formulation. This formulation assumes Gaussian wavepackets in the spectral space and uses a second-order Taylor expansion of the phase of the wave field. In this sense, the Gaussian beam formulation is also an asymptotic approximation like spatial ray tracing; however, the first one is free of the singularities found in spatial ray tracing at caustics. Therefore, the Gaussian beam formulation permits the examination of the evolution of transient inertio-gravity wavepackets from the initial time up to the destabilization of the flow close to the critical levels. We show that the transience favours the development of the dynamical instability relative to the convective instability. In particular, there is a well-defined threshold for which small initial amplitude transient inertio-gravity waves never reach the convective instability criterion. This threshold does not exist for steady-state inertio-gravity waves for which the wave amplitude increases indefinitely towards the critical level. The Gaussian beam formulation is shown to be a powerful tool to treat analytically several aspects of inertio-gravity waves in simple shear flows. In more realistic shear flows, its numerical implementation is readily available and the required numerical calculations have a low computational cost.

Resonant amplification of internal gravity waves in shear flow

1989 ◽  
Vol 32 (10) ◽  
pp. 898-907
Author(s):  
Yu. I. Troitskaya ◽  
A. L. Fabrikant
Keyword(s):  
Shear Flow ◽  
Gravity Waves ◽  
Internal Gravity Waves

On the shape and breaking of finite amplitude internal gravity waves in a shear flow

1978 ◽  
Vol 85 (1) ◽  
pp. 7-31 ◽  
Author(s):  
S. A. Thorpe
Keyword(s):  
Shear Flow ◽  
Internal Waves ◽  
Gravity Waves ◽  
Second Harmonic ◽  
Mixing Layer ◽  
Phase Speed ◽  
Internal Gravity Waves ◽  
Finite Amplitude ◽  
Depth Interval ◽  
Plane Shear

This paper is concerned with two important aspects of nonlinear internal gravity waves in a stably stratified inviscid plane shear flow, their shape and their breaking, particularly in conditions which are frequently encountered in geophysical applications when the vertical gradients of the horizontal current and the density are concentrated in a fairly narrow depth interval (e.g. the thermocline in the ocean). The present theoretical and experimental study of the wave shape extends earlier work on waves in the absence of shear and shows that the shape may be significantly altered by shear, the second-harmonic terms which describe the wave profile changing sign when the shear is increased sufficiently in an appropriate sense.In the second part of the paper we show that the slope of internal waves at which breaking occurs (the particle speeds exceeding the phase speed of the waves) may be considerably reduced by the presence of shear. Internal waves on a thermocline which encounter an increasing shear, perhaps because of wind action accelerating the upper mixing layer of the ocean, may be prone to such breaking.This work may alternatively be regarded as a study of the stability of a parallel stratified shear flow in the presence of a particular finite disturbance which corresponds to internal gravity waves propagating horizontally in the plane of the flow.

Sign in / Sign up

Export Citation Format

Share Document