An experiment on the stability of small disturbances in a stratified free shear layer

1972 ◽  
Vol 52 (3) ◽  
pp. 499-528 ◽  
Author(s):  
R. S. Scotti ◽  
G. M. Corcos
Keyword(s):  
Reynolds Number ◽  
Shear Layer ◽  
Test Section ◽  
Richardson Number ◽  
Molecular Diffusion ◽  
Free Shear Layer ◽  
Horizontal Beam ◽  
Theoretical Predictions ◽  
Critical Richardson Number ◽  
The Stability

A statically stable stratified free shear layer was formed within the test section of a wind tunnel by merging two uniform streams of air after uniformly heating the top stream. The two streams were accelerated side by side in a contraction section. The resulting sheared thermocline thickened gradually as a result of molecular diffusion and was characterized by nearly self-similar temperature (odd), velocity (odd) and Richardson number (even) profiles. The minimum Richardson numberJ0could be adjusted over the range 0·07 ≥J0≥ 0·76; the Reynolds number Re varied between 30 and 70. Small periodic disturbances were introduced upstream of the test section by a fine wire oscillating in the thermocline. The wire generated a narrow horizontal beam of internal waves, which propagated downstream and remained confined within the thermocline. The growth or decay of these waves was observed in the test section. The results confirm the existence of a critical Richardson number the value of which is in plausible agreement with theoretical predictions (J0≅ 0·22 for the Reynolds number of the experiment). The growth rate is a function of the wavenumber and is somewhat different from that computed for the same Reynolds and Richardson numbers, but the calculation assumed velocity and density profiles which were also somewhat different.

Hydromagnetic instability of a free shear layer at small magnetic Reynolds numbers

1971 ◽  
Vol 49 (1) ◽  
pp. 21-31 ◽  
Author(s):  
Kanefusa Gotoh
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Shear Layer ◽  
Critical Reynolds Number ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Free Shear Layer ◽  
Electrically Conducting ◽  
The Stability ◽  
The Magnetic Field

The effect of a uniform and parallel magnetic field upon the stability of a free shear layer of an electrically conducting fluid is investigated. The equations of the velocity and the magnetic disturbances are solved numerically and it is shown that the flow is stabilized with increasing magnetic field. When the magnetic field is expressed in terms of the parameter N (= M2/R2), where M is the Hartmann number and R is the Reynolds number, the lowest critical Reynolds number is caused by the two-dimensional disturbances. So long as 0 [les ] N [les ] 0·0092 the flow is unstable at all R. For 0·0092 < N [les ] 0·0233 the flow is unstable at 0 < R < Ruc where Ruc decreases as N increases. For 0·0233 < N < 0·0295 the flow is unstable at Rlc < R < Ruc where Rlc increases with N. Lastly for N > 0·0295 the flow is stable at all R. When the magnetic field is measured by M, the lowest critical Reynolds number is still due to the two-dimensional disturbances provided 0 [les ] M [les ] 0·52, and Rc is given by the corresponding Rlc. For M > 0·52, Rc is expressed as Rc = 5·8M, and the responsible disturbance is the three-dimensional one which propagates at angle cos−1(0·52/M) to the direction of the basic flow.

The stability of a thermally radiating stratified shear layer, including self-absorption

1974 ◽  
Vol 64 (1) ◽  
pp. 65-83 ◽  
Author(s):  
Joseph J. Dudis
Keyword(s):  
Shear Layer ◽  
Optical Depth ◽  
Richardson Number ◽  
Stability Boundary ◽  
Lower Troposphere ◽  
Neutral Stability ◽  
Viscous Effects ◽  
The Earth ◽  
Critical Richardson Number ◽  
The Stability

A linear stability analysis is applied to a stably stratified, thermally radiating shear layer. The grey Milne–Eddington approximation is employed as a radiation model. In contrast to a previously reported optically thin analysis, no inviscid instability exists, in the limit of vanishing horizontal wavenumber, for this selfabsorbing model. The inviscid neutral-stability boundary (Richardson number us. dimensionless wavenumber) for the Milne–Eddington approximation converges to the optically thick limit as the optical depth of the shear layer is increased. As the optical depth of the shear layer is decreased, the inviscid Milne–Eddington neutral-stability boundary approaches the optically thin limit, although not uniformly in the wavenumber. For fixed mean velocity gradient and fluid properties, the inviscid critical Richardson number approaches infinity as the optical depth of the shear layer approaches zero. Viscous effects neutralize this radiative destabilization, and the critical Richardson number eventually returns to zero as the optical depth continues to decrease. A shearlayer thickness exists for which the viscous critical Richardson number is a maximum. For shear depths greater than this thickness, self-absorption effects increase the stability; and for shear depths less than this thickness, viscous effects increase the stability. Results of the analysis are applied to the atmospheres of Venus and the earth. A critical Richardson number somewhat above the non-radiating value of 3 (although below the previously reported optically thin value) is found for the lower troposphere of the earth. No substantial effect is found for the earth's lower stratosphere or for the 100 km level above Venus.

On the stability of a heterogeneous shear layer subject to a body force

1961 ◽  
Vol 11 (2) ◽  
pp. 284-290 ◽  
Author(s):  
J. Menkes
Keyword(s):  
Shear Layer ◽  
Richardson Number ◽  
Body Force ◽  
Density Variation ◽  
The Body ◽  
Neutral Stability ◽  
Horizontal Shear ◽  
Critical Richardson Number ◽  
The Stability ◽  
Small Disturbances

The effects of density variation and body force on the stability of a heterogeneous horizontal shear layer are investigated. The density is assumed to decrease exponentially with height, and the body force is assumed to be derivable from a potential; the velocity distribution in the shear layer is taken to be U(y) = tanh y. The method of small disturbances is employed to obtain a family of neutral stability curves depending on the choice of the Richardson number. It is demonstrated, furthermore, that the value of the critical Richardson number depends on the magnitude of the non-dimensional density gradient.

An experimental study of the instability of a stably stratified free shear layer

1975 ◽  
Vol 71 (3) ◽  
pp. 563-575 ◽  
Author(s):  
Yu-Hwa Wang
Keyword(s):  
Flow Field ◽  
Shear Layer ◽  
Richardson Number ◽  
Open Channel ◽  
Salt Water ◽  
Stability Boundary ◽  
Water Channel ◽  
Free Shear Layer ◽  
Circulating Water ◽  
The Stability

A stably stratified free shear layer is created in a continuously circulating water channel in the laboratory. Two streams of salt water of different concentrations are brought together at the entrance to the open channel and a layered uniform flow field with a distinct sharp interface is produced in the test section. The maximum density difference between the two layers is Δρx = 0·0065ρw, where ρw is the density of water. The velocity of each layer can be adjusted at will to create free shear across the interface. At the end of the open channel, a mechanical device to separate the layers for recirculation is provided. The resulting flow field has a viscous region approximately 15 times larger than the scale of the salinity diffusion layer. Visual observations are made with hydrogen bubbles and dye traces. Interfacial waves are initiated by artificial excitation. The perturbation frequencies range from 0·476 to 10·40Hz. The measured wavelengths range from 0·46 to 3·02 cm. Damped waves as well as growing waves are observed at various exciting frequencies. Velocity profiles and instantaneous velocities are measured by a hot-film anemometer designed for use in salt water. Experimental values of the Richardson number, the dominant parameter characterizing the instability process, range from 1·23 to 14·45. The stability boundary is determined experimentally. Comparisons with Hazel's numerical results and the earlier results of Scotti & Corcos for low values of the Richardson number are also made.

Large Eddy Simulations of a Stratified Shear Layer

2014 ◽  
Vol 136 (6) ◽  
Author(s):  
Hieu T. Pham ◽  
Sutanu Sarkar
Keyword(s):  
Reynolds Number ◽  
Shear Layer ◽  
Richardson Number ◽  
Scalar Dissipation ◽  
Momentum Thickness ◽  
Bulk Richardson Number ◽  
Scalar Flux ◽  
Linear Evolution ◽  
Eddy Simulation ◽  
Large Eddy

The performance of the large eddy simulation (LES) approach in predicting the evolution of a shear layer in the presence of stratification is evaluated. The LES uses a dynamic procedure to compute subgrid model coefficients based on filtered velocity and density fields. Two simulations at different Reynolds numbers are simulated on the same computational grid. The fine LES simulated at a low Reynolds number produces excellent agreement with direct numerical simulations (DNS): the linear evolution of momentum thickness and bulk Richardson number followed by an asymptotic approach to constant values is correctly represented and the evolution of the integrated turbulent kinetic energy budget is well captured. The model coefficients computed from the velocity and the density fields are similar and have a value in range of 0.01-0.02. The coarse LES simulated at a higher Reynolds number Re = 50,000 shows acceptable results in terms of the bulk characteristics of the shear layer, such as momentum thickness and bulk Richardson number. Analysis of the turbulent budgets shows that, while the subgrid stress is able to remove sufficient energy from the resolved velocity fields, the subgrid scalar flux and thereby the subgrid scalar dissipation are underestimated by the model.

Asynchronous Instability of a Rotating Centrifuge Partially Filled With Fluid

1985 ◽  
Vol 52 (4) ◽  
pp. 777-782 ◽  
Author(s):  
C. A. Cheng ◽  
A. S. Berman ◽  
T. S. Lundgren
Keyword(s):  
Experimental Investigation ◽  
Reynolds Number ◽  
Support System ◽  
Linear Analysis ◽  
Elastic Support ◽  
Mass Ratio ◽  
Stability Boundaries ◽  
Fill Ratio ◽  
Theoretical Predictions ◽  
The Stability

An experimental investigation of the asynchronous whirl motion of a partially filled rotating centrifuge on an elastic support system has been performed. Whirl runout amplitudes are measured and the data are used to deduce the stability boundaries of the asynchronous whirl. The effects of various parameters on the stability boundaries are studied systematically. These parameters are the fill ratio, mass ratio, Reynolds number, and the damping of the elastic support system. The experimental results are compared with theoretical predictions based on a linear analysis. Free surface shapes are compared with results of nonlinear analysis.

scholarly journals Direct numerical simulation of turbulent flow over a backward-facing step

1997 ◽  
Vol 330 ◽  
pp. 349-374 ◽  
Author(s):  
HUNG LE ◽  
PARVIZ MOIN ◽  
JOHN KIM
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Shear Layer ◽  
Stokes Equations ◽  
Recirculation Region ◽  
Wall Region ◽  
Free Shear Layer ◽  
Backward Facing Step ◽  
Temporal Behaviour ◽  
Log Law

Turbulent flow over a backward-facing step is studied by direct numerical solution of the Navier–Stokes equations. The simulation was conducted at a Reynolds number of 5100 based on the step height h and inlet free-stream velocity, and an expansion ratio of 1.20. Temporal behaviour of spanwise-averaged pressure fluctuation contours and reattachment length show evidence of an approximate periodic behaviour of the free shear layer with a Strouhal number of 0.06. The instantaneous velocity fields indicate that the reattachment location varies in the spanwise direction, and oscillates about a mean value of 6.28h. Statistical results show excellent agreement with experimental data by Jovic & Driver (1994). Of interest are two observations not previously reported for the backward-facing step flow: (a) at the relatively low Reynolds number considered, large negative skin friction is seen in the recirculation region; the peak |Cf| is about 2.5 times the value measured in experiments at high Reynolds numbers; (b) the velocity profiles in the recovery region fall below the universal log-law. The deviation of the velocity profile from the log-law indicates that the turbulent boundary layer is not fully recovered at 20 step heights behind the separation.The budgets of all Reynolds stress components have been computed. The turbulent kinetic energy budget in the recirculation region is similar to that of a turbulent mixing layer. The turbulent transport term makes a significant contribution to the budget and the peak dissipation is about 60% of the peak production. The velocity–pressure gradient correlation and viscous diffusion are negligible in the shear layer, but both are significant in the near-wall region. This trend is seen throughout the recirculation and reattachment region. In the recovery region, the budgets show that effects of the free shear layer are still present.

Sign in / Sign up

Export Citation Format

Share Document