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 (f1 and f2), excited by sound, amplify and grow independently for small amplitudes. At larger amplitudes the disturbances interact to generate fluctuations of sum and difference frequencies (f2 ± f1). Harmonics and subharmonics of f1 and f2 are also generated and all fluctuations interact to generate additional fluctuations of the form (nf2/m) ± (pf1/q); n, p = 1,2,3,…, m, q = 1,2. Nonlinear mode competition suppresses the growth of f1 or f2, 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.