Energy integral description of the development of KelvinHelmholtz billows
Abstract
The nonlinear development of KelvinHelmholtz instabilities in a stratified shear flow with a sufficiently small Richardson number is investigated using an analytical model in which the flow is separated into meanflow and instabilitywave components. Vertically integrated energyflux equations are employed to represent the mean flow and the wave; it is assumed that the timedependent waveamplitude is determined by the simultaneous solution of the wave's energy equation and that of the mean flow. The evolution of the wave's kinetic energy is analyzed along with the development of velocity shears, potential temperature layers, and vertical momentum as well as heat fluxes. Numerical results for the wave's lifetime and the thickness of the mean shear layer during this time are presented which show moderately good agreement with observational data.
 Publication:

Tellus
 Pub Date:
 January 1976
 DOI:
 10.3402/tellusa.v28i3.10281
 Bibcode:
 1976Tell...28..197L
 Keywords:

 Atmospheric Turbulence;
 KelvinHelmholtz Instability;
 Shear Flow;
 Stratified Flow;
 Atmospheric Temperature;
 Energy Transfer;
 Flow Equations;
 Flow Velocity;
 Integral Equations;
 Kinetic Energy;
 Richardson Number;
 Separated Flow;
 Vertical Distribution;
 Wave Equations;
 Geophysics