Nonlinear evolution analysis of T-S disturbance wave at finite amplitude in nonparallel boundary layers

The nonlinear evolution of wavepackets in a laminar boundary layer has been studied experimentally. The packets were generated by acoustic excitations injected into the boundary layer through a small hole in the plate. Various packets with different phases relative to the envelope were studied. It was found that for all the packets the nonlinearity involved the appearance of oblique modes of frequency close to the subharmonic of the dominant two-dimensional wave. Moreover, the results confirmed that the phase had a strong influence on the strength of the nonlinear interaction. The experimental observations also indicated that although a subharmonic resonance appeared to be present in the process, it alone could not explain the nonlinear behaviour. The experiment demonstrated that the process must also involve a mechanism that generates oblique waves of frequency lower than the Tollmien–Schlichting band.

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Studying turbulence using direct numerical simulation: 1987 Center for Turbulence Research NASA Ames/Stanford Summer Programme

Journal of Fluid Mechanics ◽

10.1017/s0022112088001363 ◽

1988 ◽

Vol 190 ◽

pp. 375-392 ◽

Cited By ~ 18

Author(s):

J. C. R. Hunt

Keyword(s):

Boundary Layers ◽

Turbulent Flows ◽

Large Scale ◽

Isotropic Turbulence ◽

Stokes Equations ◽

Turbulent Boundary Layers ◽

Finite Amplitude ◽

Wall Layer ◽

Navier Stokes ◽

Scale Motion

This paper is an account of a summer programme for the study of the ideas and models of turbulent flows, using the results of direct numerical stimulations of the Navier-Stokes equations. These results had been obtained on the computers and stored as accessible databases at the Center for Turbulence Research (CTR) of NASA Ames Research Center and Stanford University. At this first summer programme, some 32 visiting researchers joined those at the CTR to test hypotheses and models in five aspects of turbulence research: turbulence decomposition, bifurcation and chaos; two-point closure (or k-space) modelling; structure of turbulent boundary layers; Reynolds-stress modelling; scalar transport and reacting flows.A number of new results emerged including: computation of space and space-time correlations in isotropic turbulence can be related to each other and modelled in terms of the advection of small scales by large-scale motion; the wall layer in turbulent boundary layers is dominated by shear layers which protrude into the outer layers, and have long lifetimes; some aspects of the ejection mechanism for these layers can be described in terms of the two-dimensional finite-amplitude Navier-Stokes solutions; a self-similar form of the two-point, cross-correlation data of the turbulence in boundary layers (when normalized by the r.m.s. value at the furthest point from the wall) shows how both the blocking of eddies by the wall and straining by the mean shear control the lengthscales; the intercomponent transfer (pressure-strain) is highly localized in space, usually in regions of concentrated vorticity; conditioned pressure gradients are linear in the conditioning of velocity and independent of vorticity in homogeneous shear flow; some features of coherent structures in the boundary layer are similar to experimental measurements of structures in mixing-layers, jets and wakes.The availability of comprehensive velocity and pressure data certainly helps the investigation of concepts and models. But a striking feature of the summer programme was the diversity of interpretation of the same computed velocity fields. There are few signs of any convergence in turbulence research! But with new computational facilities the divergent approaches can at least be related to each other.

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The evolution of a localized vortex disturbance in external shear flows. Part 1. Theoretical considerations and preliminary experimental results

Journal of Fluid Mechanics ◽

10.1017/s0022112095001285 ◽

1995 ◽

Vol 289 ◽

pp. 159-177 ◽

Cited By ~ 13

Author(s):

Vladimir Levinski ◽

Jacob Cohen

Keyword(s):

Boundary Layers ◽

Shear Flows ◽

Flow Direction ◽

Linear Equations ◽

Three Dimensional ◽

Finite Amplitude ◽

Experimental Results ◽

Instability Criterion ◽

Hairpin Vortices ◽

Plane Normal

The evolution of a finite-amplitude three-dimensional localized disturbance embedded in external shear flows is addressed. Using the fluid impulse integral as a characteristic of such a disturbance, the Euler vorticity equation is integrated analytically, and a system of linear equations describing the temporal evolution of the three components of the fluid impulse is obtained. Analysis of this system of equations shows that inviscid plane parallel flows as well as high Reynolds number two-dimensional boundary layers are always unstable to small localized disturbances, a typical dimension of which is much smaller than a dimensional length scale corresponding to an O(1) change of the external velocity. Since the integral character of the fluid impulse is insensitive to the details of the flow, universal properties are obtained. The analysis predicts that the growing vortex disturbance will be inclined at 45° to the external flow direction, in a plane normal to the transverse axis. This prediction agrees with previous experimental observations concerning the growth of hairpin vortices in laminar and turbulent boundary layers. In order to demonstrate the potential of this approach, it is applied to Taylor-Couette flow, which has additional dynamical effects owing to rotation. Accordingly, a new instability criterion associated with three-dimensional localized disturbances is found. The validity of this criterion is supported by our experimental results.

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Nonlinear Evolution of Multiple-Finite Amplitude Resonant Loss-Cone Modes

The Physics of Fluids ◽

10.1063/1.1693213 ◽

1970 ◽

Vol 13 (8) ◽

pp. 2147 ◽

Cited By ~ 10

Author(s):

R. E. Aamodt

Keyword(s):

Nonlinear Evolution ◽

Finite Amplitude ◽

Loss Cone

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Nonlinear disturbance growth during sedimentation in dilute fibre suspensions

Journal of Fluid Mechanics ◽

10.1017/jfm.2013.4 ◽

2013 ◽

Vol 719 ◽

pp. 268-294 ◽

Cited By ~ 5

Author(s):

Feng Zhang ◽

Anders A. Dahlkild ◽

Fredrik Lundell

Keyword(s):

Reynolds Number ◽

Nonlinear Evolution ◽

Finite Amplitude ◽

Long Time Behaviour ◽

Bulk Motion ◽

Fibre Suspensions ◽

Fibre Suspension ◽

Long Time ◽

Induced Flow ◽

Selection For

AbstractDisturbances in a dilute fibre suspension are studied with an Eulerian approach. Based on a linear stability analysis, it is shown that inertia and hydrodynamic diffusion damp perturbations at long wavelengths and short wavelengths, respectively, leading to a wavenumber selection. For small but finite Reynolds number of the fluid bulk motion, the most unstable wavenumber is a finite value, which increases with Reynolds number. Furthermore, the diffusion narrows the range of unstable wavenumbers. Numerical simulations of the full nonlinear evolution in time of a normal-mode perturbation show that the induced flow may either die out or saturate on a finite amplitude. The character of this long-time behaviour is dictated by the wavenumber and the presence or absence, as well as nature, of the translational and rotational diffusivities.

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