The mixing layer: deterministic models of a turbulent flow. Part 2. The origin of the three-dimensional motion

Abstract

Experimental evidence suggests that in the turbulent mixing layer the fundamental mechanism of growth is two-dimensional and little affected by the presence of vigorous three-dimensional motion. To quantify this apparent property and study the growth of streamwise vorticity, we write for the velocity field \[ {\boldmath V}(x, t) = {\boldmath U}(x, z, t) + {\boldmath u}(x, y, z, t), \] where U is two-dimensional and u is three-dimensional. In a first version of the problem U is independent of u, while in the second U is the spanwise average of V. In both cases the equation for u is linearized around U. The equations for U and u are solved simultaneously by a finite-difference calculation starting with a slightly disturbed parallel shear layer.The solutions provide a detailed description of the growth of the three-dimensional motion. They show that its characteristics are dictated by the distribution of spanwise vorticity which results from roll-up and pairing. Pairing inhibits its growth. The solutions also demonstrate that even when the three-dimensional flow attains large amplitudes it has a negligible effect on the interaction of spanwise vortices and thus on the growth of the layer.

Effects of free-stream turbulence intensity on laminar separation bubbles

“…Subsequent merging events continue for large distances downstream [59], resulting in increasing streamwise spacing between vortices with increasing streamwise distance. Vortex merging results from the amplification of disturbances at the subharmmonic frequency of the initial Kelvin-Helmholtz instability [104,111,112]. The first merging event typically occurs at approximately twice the streamwise distance from the splitter plate as the location of initial roll-up [60,113].…”

Late-Time Mixing Sensitivity to Initial Broadband Surface Roughness in High-Energy-Density Shear Layers

“…We can see here that the smooth Al layer develops coherent structures, which are highly reminiscent of the traditional KH eddies, typically called rollers, seen in fluid hydrodynamic shear experiments [4][5][6][7]. These structures grow and can become quasisteady, and will strongly contribute to the growth of the mixing layer only after they saturate and energy begins to populate secondary instabilities which will merge the rollers and generate new eddies of smaller sizes [40][41][42] at later times. These secondary and tertiary mechanisms eventually populate the turbulent cascade, which will then finally speed up the mixing of materials across the layer [43].…”

Lift-up process in a heated-cylinder wake flow

“…26 It suggests that the occurrence of ⌳-shaped structures is a ubiquitous effect and seems to be the crucial step in the transition from laminar to turbulent flow. Although the legs of the ⌳-shaped structure seem to coincide with streamwise vorticity regions, the origin of the head is critical in understanding the formation of the ⌳-shaped structure.…”