Control of free shear layers

The fundamental aspects of controlled multiple coherent mode presence in turbulent shear flows is first discussed, including the supplementary averaging procedures in addition to the Reynolds average and the nonlinear energy transfer mechanisms coupling the coherent modes, mean flow and fine-grained turbulence. Then the problem of a fundamental mode and its subharmonic in a developing mixing layer, the prototype problem of subharmonic cascade, is examined. An integral method is presented which allows the determination of the coherent wave envelope or amplitude simultaneously with the mean flow growth rate and turbulence energy. This is then generalized to the presence of multiple subharmonics using a binary-frequency interaction argument. Free shear layer control is discussed in terms of initial coherent mode amplitudes, dimensionless initial frequencies, phase angle between the modes and fine-grained turbulence levels, in particular, how these parameters could enhance or suppress the shear layer spreading rate and the levels of fine-grained turbulence.