Three-dimensional-mode resonance in far wakes

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Abstract
This work is aimed at understanding mechanisms which govern the growth of secondary three-dimensional modes of a particular type which feed from a resonant energy exchange with the primary Kármán instability in two-dimensional wakes. Our approach was to introduce controlled time-periodic three-dimensional (oblique) wave pairs of equal but opposite sign, simultaneously with a two-dimensional wave. The waves were introduced by an array of v-component-producing elements on the top and bottom surfaces of the body. These were formed by metallized electrodes which were vapour deposited onto a piezoelectrically active polymer wrapped around the surface. The amplitudes, streamwise and spanwise wavenumbers, and initial phase difference are all individually controllable. The initial work focused on a fundamental/subharmonic interaction, and the dependence on spanwise wave-number. The results include mode eigenfunction modulus and phase distributions in space, and stream functions for the phase-reconstructed flow field. Analysis of these shows that such a resonance mechanism exists and its features can account for characteristic changes associated with the growth of three-dimensional structures in the wake of two-dimensional bodies.