The late stages of transition induced by a low-amplitude wavepacket in a laminar boundary layer

1997 ◽  
Vol 340 ◽  
pp. 395-411 ◽  
Author(s):  
KENNETH S. BREUER ◽  
JACOB COHEN ◽  
JOSEPH H. HARITONIDIS
Keyword(s):  
Boundary Layer ◽  
Laminar Boundary Layer ◽  
Wavelet Transforms ◽  
Random Phase ◽  
Low Frequency ◽  
Small Scale ◽  
Frequency Spectra ◽  
Weakly Nonlinear ◽  
Lower Amplitude ◽  
Low Amplitude

The evolution of a wavepacket in a laminar boundary layer is studied experimentally, paying particular attention to the stage just prior to the formation of a turbulent spot. The initial stages of development are found to be in very good agreement with previous results and indicate a stage in which the disturbance grows according to linear theory followed by a weakly nonlinear stage in which the subharmonic grows, apparently through a parametric resonance mechanism. In a third stage, strong non-linear interactions are observed in which the disturbance develops a streaky structure and the corresponding wavenumber–frequency spectra exhibit an organized cascade mechanism in which spectral peaks appear with increasing spanwise wavenumber and with frequencies which alternate between zero and the subharmonic frequency. Higher harmonics are also observed, although with lower amplitude than the low-frequency peaks. The final (breakdown) stage is characterized by the appearance of high-frequency oscillations with random phase, located at low-speed ‘spike’ regions of the primary disturbance. Wavelet transforms are used to analyse the structure of both coherent and random small-scale structure of the disturbance. In particular, the breakdown oscillations are also observed to have a wavepacket character riding on the large-amplitude primary disturbance.

Diapycnal Transport and Mixing Efficiency in Stratified Boundary Layers near Sloping Topography

2011 ◽  
Vol 41 (2) ◽  
pp. 329-345 ◽  
Author(s):  
Lars Umlauf ◽  
Hans Burchard
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Slope Angle ◽  
Low Frequency ◽  
Moment Closure ◽  
Mixing Efficiency ◽  
Small Scale ◽  
Second Moment Closure ◽  
Steep Slopes ◽  
Sloping Topography

Abstract The interaction of shear, stratification, and turbulence in boundary layers on sloping topography is investigated with the help of an idealized theoretical model, assuming uniform bottom slope and homogeneity in the upslope direction. It is shown theoretically that the irreversible vertical buoyancy flux generated in the boundary layer is directly proportional to the molecular destruction rate of small-scale buoyancy variance, which can be inferred, for example, from microstructure observations. Dimensional analysis of the equations shows that, for harmonic boundary layer forcing and no rotation, the problem is governed by three nondimensional parameters (slope angle, roughness number, and ratio of forcing and buoyancy frequencies). Solution of the equations with a second-moment closure model for the turbulent fluxes reveals the periodic generation of gravitationally unstable boundary layers during upslope flow, consistent with available observations. Investigation of the nondimensional parameter space with the help of this model illustrates a systematic increase of the bulk mixing efficiencies for (i) steep slopes and (ii) low-frequency forcing. Except for very steep slopes, mixing efficiencies are substantially smaller than the classical value of Γ = 0.2.

Receptivity, instability and breakdown of Görtler flow

2011 ◽  
Vol 682 ◽  
pp. 362-396 ◽  
Author(s):  
LARS-UVE SCHRADER ◽  
LUCA BRANDT ◽  
TAMER A. ZAKI
Keyword(s):  
Boundary Layer ◽  
Free Stream ◽  
Low Frequency ◽  
Boundary Layer Transition ◽  
Transition To Turbulence ◽  
Flat Plates ◽  
Frequency Spectra ◽  
Free Stream Turbulence ◽  
Görtler Vortices ◽  
Gortler Vortices

Receptivity, disturbance growth and breakdown to turbulence in Görtler flow are studied by spatial direct numerical simulation (DNS). The boundary layer is exposed to free-stream vortical modes and localized wall roughness. We propose a normalization of the roughness-induced receptivity coefficient by the square root of the Görtler number. This scaling removes the dependence of the receptivity coefficient on wall curvature. It is found that vortical modes are more efficient at generating Görtler vortices than localized roughness. The boundary layer is most receptive to zero- and low-frequency free-stream vortices, exciting steady and slowly travelling Görtler modes. The associated receptivity mechanism is linear and involves the generation of boundary-layer streaks, which soon evolve into unstable Görtler vortices. This connection between transient and exponential amplification is absent on flat plates and promotes transition to turbulence on curved walls. We demonstrate that the Görtler boundary layer is also receptive to high-frequency free-stream vorticity, which triggers steady Görtler rolls via a nonlinear receptivity mechanism. In addition to the receptivity study, we have carried out DNS of boundary-layer transition due to broadband free-stream turbulence with different intensities and frequency spectra. It is found that nonlinear receptivity dominates over the linear mechanism unless the free-stream fluctuations are concentrated in the low-frequency range. In the latter case, transition is accelerated due to the presence of travelling Görtler modes.

Simulations of bypass transition

2001 ◽  
Vol 428 ◽  
pp. 185-212 ◽  
Author(s):  
R. G. JACOBS ◽  
P. A. DURBIN
Keyword(s):  
Boundary Layer ◽  
Laminar Boundary Layer ◽  
Free Stream ◽  
Low Frequency ◽  
Numerical Data ◽  
Bypass Transition ◽  
Mean Velocity ◽  
Free Stream Turbulence ◽  
Turbulent Inflow ◽  
Irregular Motion

Bypass transition in an initially laminar boundary layer beneath free-stream turbulence is simulated numerically. New perspectives on this phenomenon are obtained from the numerical flow fields. Transition precursors consist of long backward jets contained in the fluctuating u-velocity field; they flow backwards relative to the local mean velocity. The jets extend into the upper portion of the boundary layer, where they interact with free-stream eddies. In some locations a free-stream perturbation to the jet shear layer develops into a patch of irregular motion – a sort of turbulent spot. The spot spreads longitudinally and laterally, and ultimately merges into the downstream turbulent boundary layer. Merging spots maintain the upstream edge of the turbulent region. The jets, themselves, are produced by low-frequency components of the free-stream turbulence that penetrate into the laminar boundary layer. Backward jets are a component of laminar region streaks.A method to construct turbulent inflow from Orr–Sommerfeld continuous modes is described. The free-stream turbulent intensity was chosen to correspond with the experiment by Roach & Brierly (1990). Ensemble-averaged numerical data are shown to be in good agreement with laboratory measurements.

Calculation of the primary trajectories of spores ejected into still air and laminar flow

1988 ◽  
Vol 233 (1273) ◽  
pp. 477-486 ◽  
Keyword(s):  
Boundary Layer ◽  
Gravitational Field ◽  
Laminar Flow ◽  
Laminar Boundary Layer ◽  
Low Frequency ◽  
Viscous Friction ◽  
Spherical Particles ◽  
Horizontal Wind ◽  
Boundary Layer Flows ◽  
Family Of Curves

The plane ballistic trajectories followed by small spherical particles representing a variety of spores ejected into still air are determined for motion in a constant gravitational field and resisted according to the Stokes law of viscous friction. These trajectories are presented in terms of a universal one-parameter formula together with a family of curves defining the ground ranges likely to be achieved in a majority of practical cases. Consideration is also given to the movement of spores ejected into linear laminar boundary-layer flows that are both steady and periodic in time in the downstream velocity. The solutions show that projection to the largest possible vertical and downstream altitude, and also the presence of temporal periodic horizontal wind motion of low frequency and favourable phasing, are both factors of significance in augmenting the ground range achieved.

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