Large- and small-scale stirring of vorticity and passive scalar in a 3-D temporal mixing layer

Abstract

We investigate, with the aid of a three-dimensional direct-numerical simulation at high resolution, the origin and topology of the longitudinal vortex filaments which appear in the temporally growing mixing layer. The basic velocity field is a hyperbolic-tangent profile U tanh(2y/δi), with a Reynolds number of Uδi/ν =100. The calculation uses pseudospectral methods, and is carried out at a resolution of 1283 grid points in a cubic box of size L containing four fundamental most-amplified wavelengths (L=4λa). The initial velocity field is the basic velocity, upon which is superposed a three-dimensional Gaussian perturbation of wide spectrum, peaking at ka=1/2πλa, with kinetic energy equal to 10−4U2, modulated by a Gaussian exp[−(y/δi)2] in the transverse direction. A passive-scalar transport equation is solved as well, with the same initial profile as the basic velocity profile. Isosurfaces of the passive scalar and three vorticity components are visualized, permitting the 3-D vortex structure of the flows to be revealed. Because of the initial spanwise decorrelation of the perturbation phase, the fundamental spanwise vortices that appear have strong spanwise oscillations which are not in phase, and hence cannot be interpreted in terms of the translative instability investigated by Pierrehumbert and Widnall.1 Pairings between the primary vortices exhibit the same spanwise decorrelation, and reconnections of the billows occur. Visualizations also show the generation of thin longitudinal vortices from the regions of reconnection. The vortex lines at the same moment indicate that the thin longitudinal vortices result from an intense longitudinal stretching of the spanwise vortex line when it is severely twisted in the reconnection region. Reconnected Kelvin–Helmholtz billows give rise to a three-dimensional Λ-shaped structure of the passive scalar. This behavior is in agreement with the theory developed by Lesieur et al., where it was proposed that the large-scale three-dimensionality of the temporal mixing layer perturbed randomly was governed by two-dimensional turbulence unpredictability mechanisms. It might explain the experimental findings of Breidenthal2 and Bernal and Roshko3 concerning a spatially-growing, unforced mixing layer. Notice also that the thin longitudinal filaments forming in our calculation do not seem to be explained by the mechanism proposed by Lasheras and Choi,4 where they originate from the straining by the big rollers of a spanwise vortex filament perturbed about the stagnation line.