Mean flow distortion due to finite‐amplitude instability waves in a plane turbulent wake

1994 ◽  
Vol 6 (3) ◽  
pp. 1315-1322 ◽  
Author(s):  
B. Marasli ◽  
J. Cohen ◽  
V. Levinski
Keyword(s):  
Turbulent Wake ◽  
Finite Amplitude ◽  
Mean Flow ◽  
Flow Distortion ◽  
Instability Waves ◽  
Plane Turbulent Wake

scholarly journals Stability of zero-pressure-gradient boundary layer distorted by unsteady Klebanoff streaks

2011 ◽  
Vol 681 ◽  
pp. 116-153 ◽  
Author(s):  
NICHOLAS J. VAUGHAN ◽  
TAMER A. ZAKI
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Low Frequency ◽  
Finite Amplitude ◽  
Base Flow ◽  
Streamwise Vorticity ◽  
Mean Flow ◽  
S Wave ◽  
Flow Distortion ◽  
Tollmien Schlichting

The secondary instability of a zero-pressure-gradient boundary layer, distorted by unsteady Klebanoff streaks, is investigated. The base profiles for the analysis are computed using direct numerical simulation (DNS) of the boundary-layer response to forcing by individual free-stream modes, which are low frequency and dominated by streamwise vorticity. Therefore, the base profiles take into account the nonlinear development of the streaks and mean flow distortion, upstream of the location chosen for the stability analyses. The two most unstable modes were classified as an inner and an outer instability, with reference to the position of their respective critical layers inside the boundary layer. Their growth rates were reported for a range of frequencies and amplitudes of the base streaks. The inner mode has a connection to the Tollmien–Schlichting (T–S) wave in the limit of vanishing streak amplitude. It is stabilized by the mean flow distortion, but its growth rate is enhanced with increasing amplitude and frequency of the base streaks. The outer mode only exists in the presence of finite amplitude streaks. The analysis of the outer instability extends the results of Andersson et al. (J. Fluid Mech. vol. 428, 2001, p. 29) to unsteady base streaks. It is shown that base-flow unsteadiness promotes instability and, as a result, leads to a lower critical streak amplitude. The results of linear theory are complemented by DNS of the evolution of the inner and outer instabilities in a zero-pressure-gradient boundary layer. Both instabilities lead to breakdown to turbulence and, in the case of the inner mode, transition proceeds via the formation of wave packets with similar structure and wave speeds to those reported by Nagarajan, Lele & Ferziger (J. Fluid Mech., vol. 572, 2007, p. 471).

Local boundary-layer receptivity to a convected free-stream disturbance

1999 ◽  
Vol 378 ◽  
pp. 291-317 ◽  
Author(s):  
A. J. DIETZ
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Experimental Verification ◽  
Free Stream ◽  
Linear Stability Theory ◽  
Mean Flow ◽  
Flow Distortion ◽  
Instability Waves ◽  
Free Stream Turbulence ◽  
Local Boundary

An investigation of the local receptivity of a Blasius boundary layer to a harmonic vortical disturbance is presented as a step towards understanding boundary-layer receptivity to free-stream turbulence. Although there has been solid experimental verification of the linear theory describing acoustic receptivity of boundary layers, this was the first experimental verification of the mechanism behind local receptivity to a convected disturbance. The harmonic wake from a vibrating ribbon positioned upstream of a flat plate provided the free-stream disturbance. Two-dimensional roughness elements on the surface of the plate acted as a local receptivity site. Hot-wire measurements in the boundary layer downstream of the roughness confirmed the generation of Tollmien–Schlichting (TS) instability waves by an outer-layer interaction between the long-wavelength convected disturbance and the short-scale mean-flow distortion due to the roughness. The characteristics of the instability waves were carefully measured to ensure that their behaviour was correctly modelled by linear stability theory. This theory was then used to determine the immeasurably small initial wave amplitudes resulting from the receptivity process, from wave amplitudes measured downstream. Tests were performed to determine the range of validity of the linear assumptions made in current receptivity theories. Experimental data obtained in the linear regime were then compared to theoretical results of other authors by expressing the experimental data in the form of an efficiency function which is independent of the free-stream amplitude, roughness height and roughness geometry. Reasonable agreement between the experimental and theoretical efficiency functions was obtained over a range of frequencies and Reynolds numbers.

scholarly journals Interaction of oblique instability waves with weak streamwise vortices

1995 ◽  
Vol 284 ◽  
pp. 377-407 ◽  
Author(s):  
M. E. Goldstein ◽  
David W. Wundrow
Keyword(s):  
Streamwise Vortices ◽  
Rayleigh Instability ◽  
Mean Flow ◽  
Flow Distortion ◽  
Instability Waves ◽  
Instability Modes ◽  
Blasius Boundary Layer ◽  
The Common ◽  
Tollmien Schlichting ◽  
Streamwise Distance

This paper is concerned with the effect of a weak spanwise-variable mean-flow distortion on the growth of oblique instability waves in a Blasius boundary layer. The streamwise component of the distortion velocity initially grows linearly with increasing streamwise distance, reaches a maximum, and eventually decays through the action of viscosity. This decay occurs slowly and allows the distortion to destabilize the Blasius flow over a relatively large streamwise region. It is shown that even relatively weak distortions can cause certain oblique Rayleigh instability waves to grow much faster than the usual two-dimensional Tollmien–Schlichting waves that would be the dominant instability modes in the absence of the distortion. The oblique instability waves can then become large enough to interact nonlinearly within a common critical layer. It is shown that the common amplitude of the interacting oblique waves is governed by the amplitude evolution equation derived in Goldstein & Choi (1989). The implications of these results for Klebanoff-type transition are discussed.

scholarly journals Influence of the Atmospheric Surface Layer on a Turbulent Flow Downstream of a Ship Superstructure

2013 ◽  
Vol 30 (8) ◽  
pp. 1803-1819 ◽  
Author(s):  
Luksa Luznik ◽  
Cody J. Brownell ◽  
Murray R. Snyder ◽  
Hyung Suk Kang
Keyword(s):  
Surface Layer ◽  
Atmospheric Surface Layer ◽  
The United States ◽  
Naval Academy ◽  
Mean Flow ◽  
Flow Distortion ◽  
Turbulent Statistics ◽  
Sonic Anemometers ◽  
Flight Deck ◽  
Inflow Conditions

Abstract This paper describes a set of turbulence measurements at sea in the area of high flow distortion in the near-wake and recirculation zone behind a ship's superstructure that is similar in geometry to a helicopter hangar/flight deck arrangement found on many modern U.S. Navy ships. The instrumented ship is a 32-m-long training vessel operated by the United States Naval Academy that has been modified by adding a representative flight deck and hangar structure. The flight deck is instrumented with up to seven sonic anemometers/thermometers that are used to obtain simultaneous velocity measurements at various spatial locations on the flight deck, and one sonic anemometer at bow mast is used to characterize inflow atmospheric boundary conditions. Data characterizing wind over the deck at an incoming angle of 0° (head winds) and wind speeds from 2 to 10 m s−1 obtained in the Chesapeake Bay are presented and discussed. Turbulent statistics of inflow conditions are analyzed using the Kaimal universal turbulence spectral model for the atmospheric surface layer and show that for the present dataset this approach eliminates the need to account for platform motion in computing variances and covariances. Conditional sampling of mean flow and turbulence statistics at the flight deck indicate no statistically significant variations between unstable, stable, and neutral atmospheric inflow conditions, and the results agree with the published data for flows over the backward-facing step geometries.

Modal decomposition of velocity signals in a plane, turbulent wake

1989 ◽  
Vol 198 (-1) ◽  
pp. 255 ◽  
Author(s):  
B. Marasli ◽  
F. H. Champagne ◽  
I. J. Wygnanski
Keyword(s):  
Turbulent Wake ◽  
Modal Decomposition ◽  
Plane Turbulent Wake

scholarly journals Self-consistent triple decomposition of the turbulent flow over a backward-facing step under finite amplitude harmonic forcing

2019 ◽  
Vol 475 (2225) ◽  
pp. 20190018
Author(s):  
E. Yim ◽  
P. Meliga ◽  
F. Gallaire
Keyword(s):  
Turbulent Flow ◽  
Finite Amplitude ◽  
Navier Stokes ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Backward Facing Step ◽  
Eddy Viscosity Model ◽  
Coherent Interaction ◽  
Self Consistent ◽  
The Mean

We investigate the saturation of harmonically forced disturbances in the turbulent flow over a backward-facing step subjected to a finite amplitude forcing. The analysis relies on a triple decomposition of the unsteady flow into mean, coherent and incoherent components. The coherent–incoherent interaction is lumped into a Reynolds averaged Navier–Stokes (RANS) eddy viscosity model, and the mean–coherent interaction is analysed via a semi-linear resolvent analysis building on the laminar approach by Mantič-Lugo & Gallaire (2016 J. Fluid Mech. 793 , 777–797. ( doi:10.1017/jfm.2016.109 )). This provides a self-consistent modelling of the interaction between all three components, in the sense that the coherent perturbation structures selected by the resolvent analysis are those whose Reynolds stresses force the mean flow in such a way that the mean flow generates exactly the aforementioned perturbations, while also accounting for the effect of the incoherent scale. The model does not require any input from numerical or experimental data, and accurately predicts the saturation of the forced coherent disturbances, as established from comparison to time-averages of unsteady RANS simulation data.

On the stability of an inviscid shear layer which is periodic in space and time

1967 ◽  
Vol 27 (4) ◽  
pp. 657-689 ◽  
Author(s):  
R. E. Kelly
Keyword(s):  
Growth Rate ◽  
Shear Layer ◽  
Finite Amplitude ◽  
Periodic Component ◽  
Periodic Flow ◽  
Flow Profile ◽  
Mean Flow ◽  
Mean Velocity ◽  
The Mean ◽  
The Stability

In experiments concerning the instability of free shear layers, oscillations have been observed in the downstream flow which have a frequency exactly half that of the dominant oscillation closer to the origin of the layer. The present analysis indicates that the phenomenon is due to a secondary instability associated with the nearly periodic flow which arises from the finite-amplitude growth of the fundamental disturbance.At first, however, the stability of inviscid shear flows, consisting of a non-zero mean component, together with a component periodic in the direction of flow and with time, is investigated fairly generally. It is found that the periodic component can serve as a means by which waves with twice the wavelength of the periodic component can be reinforced. The dependence of the growth rate of the subharmonic wave upon the amplitude of the periodic component is found for the case when the mean flow profile is of the hyperbolic-tangent type. In order that the subharmonic growth rate may exceed that of the most unstable disturbance associated with the mean flow, the amplitude of the streamwise component of the periodic flow is required to be about 12 % of the mean velocity difference across the shear layer. This represents order-of-magnitude agreement with experiment.Other possibilities of interaction between disturbances and the periodic flow are discussed, and the concluding section contains a discussion of the interactions on the basis of the energy equation.

scholarly journals Why Are Stratospheric Sudden Warmings Sudden (and Intermittent)?

2020 ◽  
Vol 77 (3) ◽  
pp. 943-964 ◽  
Author(s):  
Noboru Nakamura ◽  
Jonathan Falk ◽  
Sandro W. Lubis
Keyword(s):  
Zonal Wind ◽  
Vortex Breakdown ◽  
Finite Amplitude ◽  
Wave Activity ◽  
Threshold Behavior ◽  
Mean Flow ◽  
Transient Wave ◽  
Wave Forcing ◽  
Stratospheric Sudden Warmings ◽  
Wave Activity Flux

Abstract This paper examines the role of wave–mean flow interaction in the onset and suddenness of stratospheric sudden warmings (SSWs). Evidence is presented that SSWs are, on average, a threshold behavior of finite-amplitude Rossby waves arising from the competition between an increasing wave activity A and a decreasing zonal-mean zonal wind u¯. The competition puts a limit to the wave activity flux that a stationary Rossby wave can transmit upward. A rapid, spontaneous vortex breakdown occurs once the upwelling wave activity flux reaches the limit, or equivalently, once u¯ drops below a certain fraction of uREF, a wave-free, reference-state wind inverted from the zonalized quasigeostrophic potential vorticity. This fraction is 0.5 in theory and about 0.3 in reanalyses. We propose r≡u¯/uREF as a local, instantaneous measure of the proximity to vortex breakdown (i.e., preconditioning). The ratio r generally stays above the threshold during strong-vortex winters until a pronounced final warming, whereas during weak-vortex winters it approaches the threshold early in the season, culminating in a precipitous drop in midwinter as SSWs form. The essence of the threshold behavior is captured by a semiempirical 1D model of SSWs, similar to the “traffic jam” model of Nakamura and Huang for atmospheric blocking. This model predicts salient features of SSWs including rapid vortex breakdown and downward migration of the wave activity/zonal wind anomalies, with analytical expressions for the respective time scales. The model’s response to a variety of transient wave forcing and damping is discussed.

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