Flow structures and their evolution in turbulent shear layer

The flow structure and its evolution in a turbulent shear layer was analyzed. The turbulent motion of a fluid which involves excitation of many strongly interacting degrees of freedom is considered. This motion is neither perfectly random, accessible to simple statistical analysis, nor perfectly coherent, characterized by regular vortex clusters. The analysis is based on two other models, and the Helmholtz instability as the principal mechanism of flow structure evolution studied. The simpler model considers a vorticity distribution initially uniform over a thin boundary layer of a boundless nonviscous fluid. The corresponding Hamilton equations are formulated in the finite dimensional approximation of vorticity, with the total kinetic energy playing the role of internal energy in the Hamiltonian and with the dimensionless intermittence parameters characterizing the evolution process. The more intricate model is a linear array of identically oriented clusters, each consisting of substructures at equilibrium statistically and the number of the latter increasing from some minimum to some maximum in the evolution process. Recurrence relations are derived here, just as for the simpler model, but the influence of and merger with adjacent structures and non-conservative moment of momentum are considered. The evolution is demonstrated.