On the Fourier space decomposition of free shear flow measurements and mode degeneration in the pairing process

Abstract

A two-dimensional shear layer perturbed by low level perturbation is studied experimentally. The driving signal is composed of two sine waves of fundamental and subharmonic modes of the most unstable natural frequency, with an adjustable phase angle. The flow is examined in a Fourier space and a phase measuring technique is employed to capture the disturbance field, including the subharmonic and its three higher harmonics. The flow field composed of the mean motion and the above-mentioned modes is reassembled. By this quantitative method the crucial connection between the evolution of superposed instability waves, based on hydrodynamic stability theory, and the experimentally observed large-scale orderly structures is made feasible. By considering the fundamental frequency field superimposed on the mean flow, two different Fourier mode structures, having two different phase speeds, are observed in the pairing region. This mode degeneration process is also observed in the fields of other higher harmonics of the subharmonic. Binary-mode as well as modal energy exchanges with the mean flow are discussed in this paper.