Abstract
Direct numerical simulations of turbulence resulting from Kelvin–Helmholtz
instability in stratified shear flow are used to examine the geometry of the dissipation
range in a variety of flow regimes. As the buoyancy and shear Reynolds numbers that
quantify the degree of isotropy in the dissipation range increase, alignment statistics
evolve from those characteristic of parallel shear flow to those found previously in
studies of stationary, isotropic, homogeneous turbulence (e.g. Ashurst et al. 1987;
She et al. 1991; Tsinober et al. 1992). The analysis yields a limiting value for the
mean compression rate of scalar gradients that is expected to be characteristic of all
turbulent flows at sufficiently high Reynolds number.My main focus is the value of the constant q that appears in both the Batchelor
(1959) and Kraichnan (1968) theoretical forms for the passive scalar spectrum. Taking
account of the effects of time-dependent strain, I propose a revised estimate of q,
denoted qe, which appears to agree with spectral shapes derived from simulations
and observations better than do previous theoretical estimates. The revised estimate
is qe = 7.3±4, and is expected to be valid whenever the buoyancy Reynolds number
exceeds O(102). The Kraichnan (1968) spectral form, in which effects of intermittency
are accounted for, provides a better fit to the DNS results than does the Batchelor
(1959) form.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
64 articles.
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