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.