Amplitude Bounds for Nonlinear Internal Waves

2003 ◽  
Author(s):  
Nikolai I. Makarenko ◽  
Janna L. Maltseva
Keyword(s):  
Internal Waves ◽  
Gravity Waves ◽  
Density Profile ◽  
Analytical Methods ◽  
Internal Gravity Waves ◽  
Stratified Flows ◽  
Fine Scale ◽  
Critical Amplitude ◽  
The Mean

Amplitude bounds imposed by the conservation of mass, momentum and energy for internal gravity waves are considered. We discuss the theoretical schemes intended for a description of permanent waves just up to the broadening limit. Analytical methods which allow to determine the critical amplitude values for the current with a given density profile are considered. Attention is focused on the continuously stratified flows having multiple broadening limits. The role of the mean density profile and the influence of fine-scale stratification are analysed.

scholarly journals Conjugate flows and amplitude bounds for internal solitary waves

2009 ◽  
Vol 16 (2) ◽  
pp. 169-178 ◽  
Author(s):  
N. I. Makarenko ◽  
J. L. Maltseva ◽  
A. Yu. Kazakov
Keyword(s):  
Solitary Waves ◽  
Density Profile ◽  
Nonlinear Waves ◽  
Stratified Flows ◽  
Internal Solitary Waves ◽  
Fine Scale ◽  
Strongly Nonlinear ◽  
The Mean ◽  
Conjugate Flows

Abstract. Amplitude bounds imposed by the conservation of mass, momentum and energy for strongly nonlinear waves in stratified fluid are considered. We discuss the theoretical scheme which allows to determine broadening limits for solitary waves in the terms of a given upstream density profile. Attention is focused on the continuously stratified flows having multiple broadening limits. The role of the mean density profile and the influence of fine-scale stratification are analyzed.

On the role of density jumps in the reflexion and breaking of internal gravity waves

1975 ◽  
Vol 69 (3) ◽  
pp. 445-464 ◽  
Author(s):  
Donald P. Delisi ◽  
Isidoro Orlanski
Keyword(s):  
Gravity Waves ◽  
Gravitational Instability ◽  
Internal Gravity Waves ◽  
Basic Flow ◽  
Density Jump ◽  
Critical Amplitude ◽  
Horizontal Advection ◽  
Reflected Wave ◽  
Good Agreement

A laboratory experiment is presented which examines the role of density jumps in the reflexion and breaking of internal gravity waves. It is found that the measured phase shift of the reflected wave and the measured amplitude of the density jump are in good agreement with linear theory. Local overturning occurs when wave amplitude becomes large, and there appears to be a critical amplitude above which overturning will occur and below which it will not. The overturning seems to be due to local gravitational instability, caused by the horizontal advection of density. Overturning changes the basic flow field in the region of interaction; and it results in smaller-scale motions.

Internal waves and turbulence in a stable stratified jet

2010 ◽  
Vol 648 ◽  
pp. 297-324 ◽  
Author(s):  
HIEU T. PHAM ◽  
SUTANU SARKAR
Keyword(s):  
Shear Layer ◽  
Wave Field ◽  
Internal Waves ◽  
Gravity Waves ◽  
Internal Gravity Waves ◽  
Direct Numerical Simulations ◽  
The Other ◽  
Mean Velocity ◽  
Horseshoe Vortices ◽  
The Mean

Direct numerical simulations are performed to investigate the interaction between a stably stratified jet and internal gravity waves from an adjacent shear layer with mild stratification. Results from two simulations are presented: one with the jet located far from the shear layer (far jet) and the other with the shear layer right on top of the jet (near jet). The near jet problem is motivated by velocity and stratification profiles observed in equatorial undercurrents. In the far case, internal waves excited by the Kelvin–Helmholtz (K-H) rollers do not penetrate the jet. They are reflected and trapped in the region between the shear layer and the jet and lead to little dissipation. In the near case, internal waves with wavelength larger than that of the K-H rollers are found in and below the jet. Pockets of hot fluid, associated with horseshoe vortices that originate from the shear layer, penetrate into the jet region, initiate turbulence and disrupt the internal wave field. Coherent patches of enhanced dissipation moving with the mean velocity are observed. The dissipation in the stably stratified near jet is large, up to three orders of magnitude stronger than that in the propagating wave field or the jet of the far case.

A conservation law for internal gravity waves

1976 ◽  
Vol 78 (2) ◽  
pp. 209-216 ◽  
Author(s):  
Michael Milder
Keyword(s):  
Internal Wave ◽  
Group Velocity ◽  
Internal Waves ◽  
Gravity Waves ◽  
Conservation Law ◽  
Short Wavelength ◽  
Internal Gravity Waves ◽  
Volume Integral ◽  
Weak Density ◽  
Progressive Waves

The scaled vorticity Ω/N and strain ∇ ζ associated with internal waves in a weak density gradient of arbitrary depth dependence together comprise a quantity that is conserved in the usual linearized approximation. This quantity I is the volume integral of the dimensionless density DI = ½[Ω2/N2 + (∇ ζ)2]. For progressive waves the ‘kinetic’ and ‘potential’ parts are equal, and in the short-wavelength limit the density DI and flux FI are related by the ordinary group velocity: FI = DIcg. The properties of DI suggest that it may be a useful measure of local internal-wave saturation.

scholarly journals Interaction Features of Internal Wave Breathers in a Stratified Ocean

Fluids ◽  
2020 ◽  
Vol 5 (4) ◽  
pp. 205
Author(s):  
Ekaterina Didenkulova ◽  
Efim Pelinovsky
Keyword(s):  
Internal Wave ◽  
Internal Waves ◽  
Gravity Waves ◽  
Fourth Order ◽  
Numerical Experiments ◽  
Vries Equation ◽  
Internal Gravity Waves ◽  
Wave Fields ◽  
Tidal Waves ◽  
Stratified Ocean

Oscillating wave packets (breathers) are a significant part of the dynamics of internal gravity waves in a stratified ocean. The formation of these waves can be provoked, in particular, by the decay of long internal tidal waves. Breather interactions can significantly change the dynamics of the wave fields. In the present study, a series of numerical experiments on the interaction of breathers in the frameworks of the etalon equation of internal waves—the modified Korteweg–de Vries equation (mKdV)—were conducted. Wave field extrema, spectra, and statistical moments up to the fourth order were calculated.

Application of the IDEMIX Concept for Internal Gravity Waves in the Atmosphere

2020 ◽  
Vol 77 (10) ◽  
pp. 3601-3618
Author(s):  
B. Quinn ◽  
C. Eden ◽  
D. Olbers
Keyword(s):  
Energy Balance ◽  
Wave Field ◽  
Gravity Wave ◽  
Gravity Waves ◽  
Momentum Flux ◽  
Middle Atmosphere ◽  
Internal Gravity Waves ◽  
Wave Drag ◽  
Mean Flow ◽  
The Mean

AbstractThe model Internal Wave Dissipation, Energy and Mixing (IDEMIX) presents a novel way of parameterizing internal gravity waves in the atmosphere. IDEMIX is based on the spectral energy balance of the wave field and has previously been successfully developed as a model for diapycnal diffusivity, induced by internal gravity wave breaking in oceans. Applied here for the first time to atmospheric gravity waves, integration of the energy balance equation for a continuous wave field of a given spectrum, results in prognostic equations for the energy density of eastward and westward gravity waves. It includes their interaction with the mean flow, allowing for an evolving and local description of momentum flux and gravity wave drag. A saturation mechanism maintains the wave field within convective stability limits, and a closure for critical-layer effects controls how much wave flux propagates from the troposphere into the middle atmosphere. Offline comparisons to a traditional parameterization reveal increases in the wave momentum flux in the middle atmosphere due to the mean-flow interaction, resulting in a greater gravity wave drag at lower altitudes. Preliminary validation against observational data show good agreement with momentum fluxes.

The effect of viscosity and heat conduction on internal gravity waves at a critical level

1967 ◽  
Vol 30 (4) ◽  
pp. 775-783 ◽  
Author(s):  
Philip Hazel
Keyword(s):  
Differential Equation ◽  
Heat Conduction ◽  
Gravity Waves ◽  
Order Differential Equation ◽  
Fluid Velocity ◽  
Attenuation Factor ◽  
Internal Gravity Waves ◽  
Constant Factor ◽  
The Mean ◽  
The Waves

The differential equation for the vertical velocity of a gravity wave in an inviscid shear flow is singular at a level where the mean fluid velocity is equal to the horizontal phase velocity of the waves. It has been shown that a wave travelling through such a layer has its amplitude attenuated by a constant factor dependent on the local Richardson number. In this paper the results obtained by solving numerically the full sixth order differential equation, which is derived by including viscosity and heat conduction in the problem, (and is not singular) are discussed, and the same attenuation factor is found. Some experiments which confirm certain aspects of the theory are described in an appendix.

scholarly journals Parametrization of momentum and energy depositions from gravity waves generated by tropospheric hydrodynamic sources

1997 ◽  
Vol 15 (12) ◽  
pp. 1570-1580 ◽  
Author(s):  
N. M. Gavrilov
Keyword(s):  
Gravity Waves ◽  
Wave Energy ◽  
Internal Gravity Waves ◽  
Mean Flow ◽  
Energy Fluxes ◽  
The Mean ◽  
Turbulence Production

Abstract. The mechanism of generation of internal gravity waves (IGW) by mesoscale turbulence in the troposphere is considered. The equations that describe the generation of waves by hydrodynamic sources of momentum, heat and mass are derived. Calculations of amplitudes, wave energy fluxes, turbulent viscosities, and accelerations of the mean flow caused by IGWs generated in the troposphere are made. A comparison of different mechanisms of turbulence production in the atmosphere by IGWs shows that the nonlinear destruction of a primary IGW into a spectrum of secondary waves may provide additional dissipation of nonsaturated stable waves. The mean wind increases both the effectiveness of generation and dissipation of IGWs propagating in the direction of the wind. Competition of both effects may lead to the dominance of IGWs propagating upstream at long distances from tropospheric wave sources, and to the formation of eastward wave accelerations in summer and westward accelerations in winter near the mesopause.

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