Vorticity dynamics in a breaking internal gravity wave. Part 1. Initial instability evolution

1998 ◽  
Vol 367 ◽  
pp. 27-46 ◽  
Author(s):  
ØYVIND ANDREASSEN ◽  
PER ØYVIND HVIDSTEN ◽  
DAVID C. FRITTS ◽  
STEVE ARENDT
Keyword(s):  
Shear Flow ◽  
Gravity Wave ◽  
Three Dimensional ◽  
Internal Gravity Wave ◽  
Companion Paper ◽  
Vortex Sheets ◽  
Vortex Loops ◽  
Vorticity Dynamics ◽  
Spanwise Vorticity ◽  
Dimensional Simulation

A three-dimensional simulation of a breaking internal gravity wave in a stratified, compressible, sheared fluid is used to examine the vorticity dynamics accompanying the transition from laminar to turbulent flow. Our results show that baroclinic sources contribute preferentially to eddy vorticity generation during the initial convective instability of the wave field; the resulting counter-rotating vortices are aligned with the external shear flow. These vortices enhance the spanwise vorticity of the shear flow via stretching and distort the spanwise vorticity via advective tilting. The resulting vortex sheets undergo a dynamical (Kelvin–Helmholtz) instability which rolls the vortex sheets into tubes. These vortex tubes link with the original streamwise convective rolls to produce a collection of intertwined vortex loops. A companion paper (Part 2) describes the subsequent interactions among and the perturbations to these vortices that drive the evolution toward turbulence and smaller scales of motion.

Vorticity dynamics in a breaking internal gravity wave. Part 2. Vortex interactions and transition to turbulence

1998 ◽  
Vol 367 ◽  
pp. 47-65 ◽  
Author(s):  
DAVID C. FRITTS ◽  
STEVE ARENDT ◽  
ØYVIND ANDREASSEN
Keyword(s):  
Gravity Wave ◽  
Internal Gravity Wave ◽  
Companion Paper ◽  
Transition To Turbulence ◽  
Single Vortex ◽  
Vortex Sheets ◽  
Initial Formation ◽  
Vortex Interactions ◽  
Vorticity Dynamics ◽  
Vortex Tubes

A companion paper (Part 1) employed a three-dimensional numerical simulation to examine the vorticity dynamics of the initial instabilities of a breaking internal gravity wave in a stratified, sheared, compressible fluid. The present paper describes the vorticity dynamics that drive this flow to smaller-scale, increasingly isotropic motions at later times. Following the initial formation of discrete and intertwined vortex loops, the most important interactions are the self-interactions of single vortex tubes and the mutual interactions of multiple vortex tubes in close proximity. The initial formation of vortex tubes from the roll-up of localized vortex sheets gives the vortex tubes axial variations with both axisymmetric and azimuthal-wavenumber-2 components. The axisymmetric variations excite axisymmetric twist waves or Kelvin vortex waves which propagate along the tubes, drive axial flows, deplete the tubes' cores, and fragment the tubes. The azimuthal-wavenumber-2 variations excite m=2 twist waves on the vortex tubes, which undergo strong amplification and unravel single vortex tubes into pairs of intertwined helical tubes; the vortex tubes then burst or fragment. Reconnection often occurs among the remnants of such vortex fragmentation. A common mutual interaction is that of orthogonal vortex tubes, which causes mutual stretching and leads to long-lived structures. Such an interaction also sometimes creates an m=1 twist wave having an approximately steady helical form as well as a preferred sense of helicity. Interactions among parallel vortex tubes are less common, but include vortex pairing. Finally, the intensification and roll-up of weaker vortex sheets into new tubes occurs throughout the evolution. All of these vortex interactions result in a rapid cascade of energy and enstrophy toward smaller scales of motion.

scholarly journals Optimal perturbation growth on a breaking internal gravity wave

2021 ◽  
Vol 925 ◽  
Author(s):  
J.P. Parker ◽  
C.J. Howland ◽  
C.P. Caulfield ◽  
R.R. Kerswell
Keyword(s):  
Shear Flow ◽  
Gravity Wave ◽  
Three Dimensional ◽  
Internal Gravity Wave ◽  
Internal Gravity Waves ◽  
Mixing Efficiency ◽  
Two Dimensional ◽  
Systematic Analysis ◽  
Optimal Perturbation ◽  
Energy Growth

The breaking of internal gravity waves in the abyssal ocean is thought to be responsible for much of the mixing necessary to close oceanic buoyancy budgets. The exact mechanism by which these waves break down into turbulence remains an active area of research and can have significant implications on the mixing efficiency. Recent evidence has suggested that both shear instabilities and convective instabilities play a significant role in the breaking of an internal gravity wave in a high Richardson number mean shear flow. We perform a systematic analysis of the stability of a configuration of an internal gravity wave superimposed on a background shear flow first considered by Howland et al. (J. Fluid Mech., vol. 921, 2021, A24), using direct–adjoint looping to find the perturbation giving maximal energy growth on this evolving flow. We find that three-dimensional, convective mechanisms produce greater energy growth than their two-dimensional counterparts. In particular, we find close agreement with the direct numerical simulations of Howland et al. (J. Fluid Mech., 2021, in press), which demonstrated a clear three-dimensional mechanism causing breakdown to turbulence. The results are shown to hold at realistic Prandtl numbers. At low mean Richardson numbers, two-dimensional, shear-driven mechanisms produce greater energy growth.

scholarly journals The vorticity dynamics of instability and turbulence in a breaking internal gravity wave

1999 ◽  
Vol 51 (7-8) ◽  
pp. 457-473 ◽  
Author(s):  
David C. Fritts ◽  
Steve Arendt ◽  
Øyvind Andreassen
Keyword(s):  
Gravity Wave ◽  
Internal Gravity Wave ◽  
Vorticity Dynamics

Mean flows induced by internal gravity wave packets propagating in a shear flow

1979 ◽  
Vol 292 (1393) ◽  
pp. 391-417 ◽  
Keyword(s):  
Shear Flow ◽  
Gravity Wave ◽  
Internal Gravity Wave ◽  
Basic Flow ◽  
Channel Depth ◽  
Amplitude Wave ◽  
Generalized Lagrangian ◽  
Basic Shear ◽  
Wave Induced ◽  
The Waves

An inviscid, incompressible, stably stratified fluid occupies a horizontal channel, along which an internal gravity wave packet is propagating in the presence of a basic shear flow. By using a generalized Lagrangian mean formulation, the equation for wave action conservation is derived to describe the manner in which the basic flow affects the waves. Equations describing the second-order (in amplitude) wave-induced Lagrangian mean flows are obtained. Two kinds of applications are discussed: (i) steady mean flows, due to waves encountering an inhomogeneity in their environment, such as a varying channel depth; (ii) mean flows induced by modulations in the wave amplitude.

On three-dimensional internal gravity wave beams and induced large-scale mean flows

2015 ◽  
Vol 769 ◽  
pp. 621-634 ◽  
Author(s):  
T. Kataoka ◽  
T. R. Akylas
Keyword(s):  
Gravity Wave ◽  
Large Scale ◽  
Evolution Equations ◽  
Three Dimensional ◽  
Internal Gravity Wave ◽  
Nonlinear Effects ◽  
Beam Width ◽  
Finite Amplitude ◽  
Horizontal Line ◽  
Mean Flow

The three-dimensional propagation of internal gravity wave beams in a uniformly stratified Boussinesq fluid is discussed, assuming that variations in the along-beam and transverse directions are of long length scale relative to the beam width. This situation applies, for instance, to the far-field behaviour of a wave beam generated by a horizontal line source with weak transverse dependence. In contrast to the two-dimensional case of purely along-beam variations, where nonlinear effects are minor even for beams of finite amplitude, three-dimensional nonlinear interactions trigger the transfer of energy to a circulating horizontal time-mean flow. This resonant beam–mean-flow coupling is analysed, and a system of two evolution equations is derived for the propagation of a small-amplitude beam along with the induced mean flow. This model explains the salient features of the experimental observations of Bordes et al. (Phys. Fluids, vol. 24, 2012, 086602).

scholarly journals Linear Spectral Numerical Model for Internal Gravity Wave Propagation

2010 ◽  
Vol 67 (5) ◽  
pp. 1632-1642 ◽  
Author(s):  
J. Marty ◽  
F. Dalaudier
Keyword(s):  
Numerical Model ◽  
Gravity Wave ◽  
Gravity Waves ◽  
Three Dimensional ◽  
Internal Gravity Wave ◽  
Temporal Variations ◽  
Buoyancy Frequency ◽  
Background Wind ◽  
First Order ◽  
Good Agreement

Abstract A three-dimensional linear spectral numerical model is proposed to simulate the propagation of internal gravity wave fluctuations in a stably stratified atmosphere. The model is developed to get first-order estimations of gravity wave fluctuations produced by identified sources. It is based on the solutions of the linearized fundamental fluid equations and uses the fully compressible dispersion relation for inertia–gravity waves. The spectral implementation excludes situations involving spatial variations of buoyancy frequency or background wind. However, density stratification variations are taken into account in the calculation of fluctuation amplitudes. In addition to gravity wave packet free propagation, the model handles both impulsive and continuous sources. It can account for spatial and temporal variations of the sources, encompassing a broad range of physical situations. The method is validated with a monochromatic pressure monopole, which is known to generate St. Andrew’s cross–shaped waves. It is then applied to the case of the ozone layer cooling during a total solar eclipse. The asymptotic response to a Gaussian thermal forcing traveling at constant velocity and the transient response to the 4 December 2002 eclipse show good agreement with previous numerical simulations. Further applications for the model are discussed.

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