An experimental study is made of the instability and transition of a laminar free shear layer by sound excitation. Primary emphasis is placed on the nonlinear stages of transition. Transition from laminar instability to turbulent breakdown covers approximately five wavelengths of downstream distance. The instability has six distinct regions of behaviour : a region of exponential growth described by linear theory; a nonlinear region where critical-layer effects are important, and harmonics and subharmonics are generated; a region of finite amplitude equilibration of the fundamental mode; a region of finite amplitude triggered sub-harmonic instabilities; a region of three-dimensional longitudinal vortex formation; and a final region of weak secondary instabilities and turbulent breakdown.

The relationship between nonlinear wave coupling and the properties of the bispectrum are investigated for the case of three-wave coupling. In particular, the dependence of the phase of the bispectrum, the direction of power flow between modes, and the sign of the skewness parameter, on the nonlinear amplitude variation and coupling coefficient, is analytically investigated and found to be in good agreement with experimental observations.

Articles you may be interested inContinuous wavelet transform based time-scale and multifractal analysis of the nonlinear oscillations in a hollow cathode glow discharge plasma Time-frequency analysis with the continuous wavelet transform Am.Time-series analysis of nonstationary plasma fluctuations using wavelet transforms Rev.The wavelet transform has emerged as an important tool for the analysis of intermittent and nonstationary signals. This article addresses implementation issues of a digital continuous wavelet transform that is sufficiently general that any continuous wavelet can be used. Working equations are derived for wavelet sampling, aliasing, and scale population by using the band-pass filter interpretation of wavelet functions. The implementation procedure is applied to the Morlet wavelet in detail as an example. Finally, the Morlet wavelet is applied to velocity fluctuations measured in a subsonic wake undergoing transition to turbulence.

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.