Experimental study of resonant interactions of instability waves in self-similar boundary layer with an adverse pressure gradient: III. Broadband disturbances

Abstract

These experiments are devoted to the investigation of initial nonlinear stages of laminar–turbulent transition in a self-similar boundary layer with an adverse pressure gradient (APG) at Hartree parameter β _H  = −0.115. The measurements are performed at controlled disturbance conditions at very large variation of initial spectra of excited 3D (in general) Tollmien–Schlichting (TS) 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 (Borodulin V I, Kachanov Y S, Koptsev D B and Roschektayev A P 2002 J. Turbulence 3 063), and part 3 (this paper). The experimental procedure, the basic flow characteristics, the disturbance generator, all regimes of measurements, and the results obtained in the cases of tuned resonant interactions of TS waves are presented in part 1. The investigation of resonant interactions in the presence of frequency and spanwise-wavenumber detunings of quasi-subharmonic modes is presented in part 2.

This paper (part 3) is devoted to the study of resonant (and non-resonant) interaction and amplification of broadband low-amplitude 3D instability waves in the presence (and absence) of a primary 2D Tollmien–Schlichting (TS) wave, harmonic in time. The broadband, noise-like TS waves represent controlled perturbations, pseudo-random in time and space, with a continuous frequency–wavenumber spectrum. These perturbations simulate some background disturbances usually observed at ‘natural’ conditions. The deterministic primary TS wave simulates a ‘natural’ instability mode, which has been formed by the linear instability mechanism. In contrast to the study of deterministic resonant regimes in parts 1 and 2, no specific (preinstalled) disturbance frequencies or spanwise wavenumbers were excited in the boundary layer (except for the primary wave). So, the flow was free to amplify almost any mode by means of any available mechanisms of TS wave interaction. Two main regimes of excitation were studied: (i) the broadband disturbances only and (ii) the broadband disturbances together with the 2D primary TS wave.

It is found that in case (i) the perturbations develop downstream in agreement with the linear stability mechanism, while in case (ii) a strong resonant interaction between the broadband perturbations and the primary TS wave is observed in a wide frequency range. In the latter case the amplification is double-exponential (exponent in exponent), similar to that found in tuned and detuned resonances of deterministic modes (parts 1 and 2). The phase synchronism conditions are found to be satisfied for the resonantly interacting disturbances. Based on results obtained in all three parts of this study (for 59 initial TS wave spectra), a main conclusion is drawn about the dominant role of the resonant TS wave interactions in the APG boundary layer transition.

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).