Experiments on nonlinear interactions in the transition of a free shear layer

Abstract

An experimental study is made of nonlinear interactions in a laminar free shear layer. Two disturbances ( f 1 and f 2 ), excited by sound, amplify and grow independently for small amplitudes. At larger amplitudes the disturbances interact to generate fluctuations of sum and difference frequencies ( f 2 ± f 1 ). Harmonics and subharmonics of f 1 and f 2 are also generated and all fluctuations interact to generate additional fluctuations of the form ( nf 2 / m ) ± ( pf 1 / q ); n, p = 1,2,3,…, m, q = 1,2. Nonlinear mode competition suppresses the growth of f 1 or f 2 , depending on their relative amplitudes, and contributes to finite amplitude equilibration. An upper bound on the modal integral of total u ′ r.m.s. 2 fluctuation energy is found. Fluctuation energy tends to be distributed among all possible frequency components, and its upper bound does not increase as the number of components increases.