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

Abstract

This work is devoted to an experimental investigation of the initial nonlinear stages of laminar–turbulent transition of a self-similar boundary layer with an adverse pressure gradient (Hartree parameter β _H  = −0.115). All experiments 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 (this paper), part 2 (Borodulin V I, Kachanov Y S, Koptsev D B and Roschektayev A P 2002 J. Turbulence 3 063), and 3 (Borodulin V I, Kachanov Y S and Koptsev D B 2002 J. Turbulence 3 064). This paper (part 1) describes the experimental procedure, the basic flow characteristics, all regimes of measurements (related to all parts of the study), and the results of measurements obtained in cases of tuned resonant interactions of instability waves in comparison with non-resonant (linear) development of the involved Tollmien–Schlichting (TS) modes. Part 2 is devoted to investigation of resonant interactions in the presence of frequency and spanwise-wavenumber detunings of the quasi-subharmonic modes, while part 3 describes the results of investigation of resonant amplification of broadband, continuous-spectrum instability waves, which simulate some background perturbations (a ‘noise’ of TS waves).

In the main resonant regime described in this paper (part 1) the disturbances excited in the flow represent symmetric triplets consisting of three TS waves: (i) a 2D fundamental wave with relatively large initial amplitude and (ii) a pair of 3D subharmonic waves of rather small initial amplitudes with the most favourable (for the resonance) spanwise wavenumbers. The influence of initial fundamental and subharmonic amplitudes, as well as the phase relationship between them, was investigated in several other regimes. The results obtained in resonant regimes were compared with those measured in non-resonant regimes when the fundamental and subharmonic modes were excited separately. It is found that the resonant interaction leads to a rapid, double-exponential growth of the subharmonics. A variation of the phase shift between the subharmonic pair and the fundamental wave dramatically influences the subharmonic growth. When this shift is orthogonal to the resonant one the interaction leads to a resonant suppression of the subharmonics. The double-exponential growth of the subharmonics is observed at a parametric stage of the interaction where the subharmonic modes do not influence the exponential growth of the fundamental wave. This stage ends when the transition process enters the essentially nonlinear region. In this region a formation of coherent vortex structures is observed; the spectrum becomes very rich and the growth of the fundamental and subharmonic modes 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).