Author:
BALMFORTH NEIL J.,YOUNG YUAN-NAN
Abstract
In this study we investigate the Kolmogorov flow (a shear flow with a sinusoidal
velocity profile) in a weakly stratified, two-dimensional fluid. We derive amplitude
equations for this system in the neighbourhood of the initial bifurcation to instability
for both low and high Péclet numbers (strong and weak thermal diffusion,
respectively). We solve amplitude equations numerically and find that, for low Péclet
number, the stratification halts the cascade of energy from small to large scales at an
intermediate wavenumber. For high Péclet number, we discover diffusively spreading,
thermal boundary layers in which the stratification temporarily impedes, but does not
saturate, the growth of the instability; the instability eventually mixes the temperature
inside the boundary layers, so releasing itself from the stabilizing stratification there,
and thereby grows more quickly. We solve the governing fluid equations numerically
to compare with the asymptotic results, and to extend the exploration well beyond
onset. We find that the arrest of the inverse cascade by stratification is a robust feature
of the system, occurring at higher Reynolds, Richards and Péclet numbers – the flow
patterns are invariably smaller than the domain size. At higher Péclet number, though
the system creates slender regions in which the temperature gradient is concentrated
within a more homogeneous background, there are no signs of the horizontally mixed
layers separated by diffusive interfaces familiar from doubly diffusive systems.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
53 articles.
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