Wave Packets In Boundary Layer Research Articles

The use of wavelet transform for the correlation analysis of boundary-layer pulsations

As a rule, experimental studies at hypersonic Mach numbers are carried out in short-duration wind tunnels. Under such conditions, data on boundary-layer pulsations are primarily measured by surface pressure sensors. There are many factors affecting the level of pulsations at model walls; that is why the cross-correlation analysis is often invoked to analyze the development of wave packets in boundary layer. However, the standard correlation analysis very often fails in providing the possibility to trace the evolution of wave packets. In the present publication, we propose a new method for obtaining cross-correlation data based on the wavelet transform.

Characteristics of nonlinear evolution of wavepackets in boundary layers

The nonlinear evolution of a finite-amplitude disturbance in a 3-D supersonic boundary layer over a cone was investigated recently by Liu et al. using direct numerical simulation (DNS). It was found that certain small-scale 3-D disturbances amplified rapidly. These disturbances exhibit the characteristics of second modes, and the most amplified components have a well-defined spanwise wavelength, indicating a clear selectivity of the amplification. In the case of a cone, the three-dimensionality of the base flow and the disturbances themselves may be responsible for the rapid amplification. In order to ascertain which of these two effects are essential, in this study we carried out DNS of the nonlinear evolution of a spanwise localized disturbance (wavepacket) in a flat-plate boundary layer. A similar amplification of small-scale disturbances was observed, suggesting that the direct reason for the rapid amplification is the three-dimensionality of the disturbances rather than the three-dimensional nature of the base flow, even though the latter does alter the spanwise distribution of the disturbance. The rapid growth of 3-D waves may be attributed to the secondary instability mechanism. Further simulations were performed for a wavepacket of first modes in a supersonic boundary layer and of Tollmien-Schlichting (T-S) waves in an incompressible boundary layer. The results show that the amplifying components are in the band centered at zero spanwise wavenumber rather than at a finite spanwise wavenumber. It is therefore concluded that the rapid growth of 3-D disturbances in a band centered at a preferred large spanwise wavenumber is the main characteristic of nonlinear evolution of second mode disturbances in supersonic boundary layers.

Influence of centrifugal forces on the development of wave packets in boundary layers with a uniformly valid model

The behavior of three-dimensional wave packets in the boundary layer on curved surfaces is analyzed in this study based on a modification of the triple-deck theory referred to as the “criss-cross” interaction model. The equations of the criss-cross interaction describe a particular type of boundary layer instability mode that possesses underlying properties of both the Tollmien–Schlichting waves and Taylor–Görtler vortices. Previous analysis of the criss-cross interaction regime suggests a possibility for upstream propagation of perturbations in the boundary layer and possible absolute instability of the flow. However, these results cannot be considered as conclusive because the initial-value problem for the criss-cross interaction equations is ill-posed. In a recent work [Turkyilmazoglu M, Ruban AI. A uniformly valid well-posed asymptotic approach to the inviscid–viscous interaction theory. Stud Appl Math 2002;108:161–85] a regularized non-asymptotic model to describe criss-cross interaction has been proposed. Whereas in the original version of the theory, perturbations have an unbounded growth rate as the longitudinal wave number ∣ k∣ → ∞, in the new model of [Turkyilmazoglu M, Ruban AI. A uniformly valid well-posed asymptotic approach to the inviscid–viscous interaction theory. Stud Appl Math 2002;108:161–85], as physically expected the amplification rate remains bounded for both spatially growing and temporally growing waves. A Fourier transform method is used in the present study to solve the linearized equations for the flow over concave roughness and humps and it is found that disturbances develop and are convected downstream as wave packets. The behavior of the wave packets is consistent with convective instability, and the upstream influence is no longer present at large times.

The influence of phase on the nonlinear evolution of wavepackets in boundary layers

The nonlinear evolution of wavepackets in a laminar boundary layer has been observed experimentally. The packets originated from disturbances generated by a loudspeaker coupled to the boundary layer by a small hole in the plate. In a preliminary experiment two types of short-duration acoustic pulses were used, one with a positive excitation and another with a negative excitation. The experiments indicated that the packet that originated from a positive pulse displayed nonlinear behaviour at considerably lower amplitudes than that from a negative pulse. However, the preliminary experiments suggested that at some distance from the source the packets were identical in shape with a relative phase shift of 180°. Using complex-amplitude pulses it was possible to extend the experiments to include packets with other phases. This more comprehensive experiment not only showed a strong influence of the phase on the evolution of the packet, but also demonstrated that this nonlinear behaviour is not determined by the local effects of the excitation process. The observations suggested that the important parameter is the phase of the packet relative to the modulation envelope.

The development of three-dimensional wave packets in a boundary layer

The formation and growth of three-dimensional wave packets in a laminar boundary layer is treated as a linear problem. The asymptotic form of the disturbed region developing from a point source is obtained in terms of parameters describing two-dimensional instabilities of the flow. It is shown that a wave caustic forms and limits the lateral spread of growing disturbances whenever the Reynolds number is √2 times the critical value. The analysis is applied to the boundary layer on a flat plate and shapes of the wave-envelope are calculated for various Reynolds numbers. These show that all growing disturbances are contained within a wedge-shaped region of approximately 10° semi-angle.