Experimental study of resonant interactions of instability waves in self-similar boundary layer with an adverse pressure gradient: II. Detuned resonances

Abstract

This experimental study is of the initial nonlinear stages of the laminar-turbulent transition of a self-similar boundary layer with an adverse pressure gradient (Hartree parameter β_H = −0.115). All measurements were performed at controlled disturbance conditions at various initial spectra of excited 3D (in general) instability waves. The results are presented in three papers: part 1 (Borodulin V I, Kachanov Y S and Koptsev D B 2002 J. Turbulence 3 062), part 2 (this paper), and part 3 (Borodulin V I, Kachanov Y S and Koptsev D B 2002 J. Turbulence 3 064). The experimental procedure, the basic flow characteristics, the disturbance generator, the regimes of measurements (related to all parts), and the results of measurements obtained in cases of tuned resonant interactions of Tollmien–Schlichting (TS) waves are presented in part 1. The results of investigation of resonant amplification of broadband, continuous-spectrum instability waves (random in time and space), which simulate some background perturbations, are described in part 3.

This paper (part 2) is devoted to detuned subharmonic resonances of deterministic waves. In total, 28 different initial spectra of instability waves were excited in the boundary layer and investigated. Similar to the main (tuned) resonance regime (see section 3.3 in part 1), the disturbances excited in the flow represented symmetric triplets consisting of three TS waves: (i) a 2D fundamental wave with relatively large initial amplitude and (ii) a pair of 3D subharmonic or quasi-subharmonic waves with rather small initial amplitudes. The disturbances (ii) represented either a pair of frequency-detuned quasi-subharmonics with resonant (tuned) spanwise wavenumbers or a pair of spanwise-wavenumber detuned subharmonics. The results obtained in the detuned resonant regimes were compared with those measured in the tuned resonance regime and in non-resonant regimes when the fundamental and subharmonic modes were excited separately.

It is found that the studied resonances have very large spectral width and are able to amplify quasi-subharmonic modes with very significant frequency and spanwise-wavenumber detunings. The amplification of the detuned subharmonics is double-exponential (exponent-in-exponent), similar to the tuned case. For modes with positive frequency detunings the growth rates are found to be even larger than those observed in tuned resonances. The wavenumber-detuned subharmonics are amplified less effectively than in the tuned case. In all studied cases the phase synchronism conditions are shown to be satisfied for resonantly interacting modes. At late stages of transition the growth of detuned subharmonics saturates.

This article was chosen from selected Proceedings of the Eighth European Turbulence Conference (Advances in Turbulence VIII (Barcelona, 27-30 June 2000) (Barcelona: CIMNE) ed C Dopazo. ISBN: 84-89925-65-8).