A numerical simulation of Kelvin-Helmholtz waves of finite amplitude

Abstract

A number of initial- and boundary-value problems for the Boussinesq equations are solved by a finite-difference technique, in an attempt to see how a stably-stratified horizontal shear layer rolls up into horizontally periodic billows of concentrated vorticity, such as are frequently observed in the atmosphere and oceans. This paper describes the methods, results and accuracy of the numerical simulations. The results are further analysed and approximately reproduced by a simple semi-analytic model in Corcos & Sherman (1976).

A simple model of mixing and chemical reaction in a turbulent shear layer

“…Coles (1981) conjectures, from results such as those in figure 1 (a) and from the numerical calculations of Patnaik, Sherman & Corcos (1976) and , that the mean particle paths in this system are as depicted in figure 5 . In this figure the upper stream carries a reactant A and the lower, a reactant B.…”

The plane mixing layer flow visualization results and three dimensional effects

“…In fact such a complementarity is suggested in the results obtained by Patnaik et al (1976) for the primary instability.…”

Nonlinear Instabilities and Large Scale Structures in Mixing Layers

“…show that significant variations of mean flow and maximum shear accompany the growth of instabilities even at modest amplitudes, we relinquish the classical asswnption of invariant eigenfunction shape (Stuart 1960) Miksad's "(1972) hot wire measurements in the nonlinear stages of free shear layer transition as well as with the predictions of a nonlinear model largely patterned after those of Zabusky and Deem (1971) and Patnaik et al (1976). Unfortunately,…”

“…In its support we note that the numerirr.al results of Miura and Sato (1978), who adopted the Fourier series approximation, and those of Zabusky and Deem (1971), who directly integrated the time-dependent incompressible Navier-Stokes efiuations, exhibit qualitatively identical saturation and post-saturation behaviors for finite amplitude instabilities in free shear flows. Thus, the departure of finite amplitude instabilities from an initially sinusoidal spatial shape (Patnaik et al 1976) seemingly plays a secondary role in their development. However, further scrutiny may be in order as to the influ,.nce af that de.parture on the onset arnd evolution of small scale secondary instabilities --e.g., those responsible for the skewness and apparent branching of the mixing layer structures --which are sensitive to the details of the flow pattern relative to those very struct",ies.…”