Vorticity dynamics in an oscillatory flow over a rippled bed

1991 ◽  
Vol 226 ◽  
pp. 257-289 ◽  
Author(s):  
P. Blondeaux ◽  
G. Vittori
Keyword(s):  
Shear Layer ◽  
Flow Separation ◽  
Vortex Structure ◽  
Oscillatory Flow ◽  
Vortex Pair ◽  
Numerical Approach ◽  
Time Development ◽  
Half Cycle ◽  
Free Shear Layer ◽  
Viscous Effects

In the present paper we determine the oscillatory flow generated by surface gravity waves near a sea bottom covered with large-amplitude ripples. The vorticity equation and Poisson equation for the stream function are solved by means of a numerical approach based on spectral methods and finite-difference approximations. In order to test the numerical algorithm and in particular the numerical scheme used to generate vorticity along the ripple profile, we also perform an asymptotic analysis, which holds as the timettends to zero. The main features of the time development of vorticity are analysed and particular attention is paid to the dynamics of the large vortices generated by flow separation at the ripple crests and along the ripple profile. Some of the results obtained by Longuet-Higgins (1981) are recovered; in particular, the present results show a vortex pair shed from the ripple crest every half-cycle. The determination of flow separation along the ripple profile induced by the pressure gradient and the inclusion of viscous effects allows us to obtain accurate quantitative results and detect some important phenomena never observed before.In particular it is shown that: (i) Whenever a vortex structure moves towards the bottom, a secondary vortex is generated near the ripple profile, which interacts with the primary vortex and causes it to move away from the bottom, (ii) Depending on the values of the parameters, the time development of the free shear layer shed from the ripple crest may produce two or even more vortex structures, (iii) Occasionally vortices generated previously may coalesce with the free shear layer shed from the ripple crest, generating a unique vortex structure.

Shear-layers in magnetohydrodynamic spherical Couette flow with conducting walls

2010 ◽  
Vol 645 ◽  
pp. 145-185 ◽  
Author(s):  
A. M. SOWARD ◽  
E. DORMY
Keyword(s):  
Magnetic Field ◽  
Shear Layer ◽  
Electric Current ◽  
Current Flow ◽  
Outer Boundary ◽  
Free Shear Layer ◽  
Viscous Effects ◽  
Current Leakage ◽  
Axisymmetric Motion ◽  
Relative Conductance

We consider the steady axisymmetric motion of an electrically conducting fluid contained within a spherical shell and permeated by a centred axial dipole magnetic field, which is strong as measured by the Hartmann number M. Slow axisymmetric motion is driven by rotating the inner boundary relative to the stationary outer boundary. For M ≫ 1, viscous effects are only important in Hartmann boundary layers adjacent to the inner and outer boundaries and a free shear-layer on the magnetic field line that is tangent to the outer boundary on the equatorial plane of symmetry. We measure the ability to leak electric current into the solid boundaries by the size of their relative conductance ɛ. Since the Hartmann layers are sustained by the electric current flow along them, the current inflow from the fluid mainstream needed to feed them increases in concert with the relative conductance, because of the increasing fraction ℒ of the current inflow leaked directly into the solids. Therefore the nature of the flow is sensitive to the relative sizes of ɛ−1 and M.The current work extends an earlier study of the case of a conducting inner boundary and an insulating outer boundary with conductance ɛo = 0 (Dormy, Jault & Soward, J. Fluid Mech., vol. 452, 2002, pp. 263–291) to other values of the outer boundary conductance. Firstly, analytic results are presented for the case of perfectly conducting inner and outer boundaries, which predict super-rotation rates Ωmax of order M1/2 in the free shear-layer. Successful comparisons are made with numerical results for both perfectly and finitely conducting boundaries. Secondly, in the case of a finitely conducting outer boundary our analytic results show that Ωmax is O(M1/2) for ɛo−1 ≪ 1 ≪ M3/4, O(ɛo2/3M1/2) for 1 ≪ ɛo−1 ≪ M3/4 and O(1) for 1 ≪ M3/4 ≪ ɛo−1. On increasing ɛo−1 from zero, substantial electric current leakage into the outer boundary, ℒo ≈ 1, occurs for ɛo−1 ≪ M3/4 with the shear-layer possessing the character appropriate to a perfectly conducting outer boundary. When ɛo−1 = O(M3/4) the current leakage is blocked near the equator, and the nature of the shear-layer changes. So, when M3/4 ≪ ɛo−1, the shear-layer has the character appropriate to an insulating outer boundary. More precisely, over the range M3/4 ≪ ɛo−1 ≪ M the blockage spreads outwards, reaching the pole when ɛo−1 = O(M). For M ≪ ɛo−1 current flow into the outer boundary is completely blocked, ℒo ≪ 1.

The nonlinear stability of a free shear layer in the viscous critical layer régime

1980 ◽  
Vol 293 (1408) ◽  
pp. 643-672 ◽  
Keyword(s):  
Shear Layer ◽  
Critical Layer ◽  
Reynolds Stresses ◽  
Free Shear Layer ◽  
Mean Flow ◽  
Viscous Effects ◽  
Flow Distortion ◽  
Threshold Amplitude ◽  
The Mean ◽  
Valid Solution

The nonlinear evolution of weakly amplified waves in a hyperbolic tangent free shear layer is described for spatially and temporally growing waves when the shear layer Reynolds number is large and the critical layer viscous. An artificial body force is introduced in order to keep the mean flow parallel. Jump conditions on the perturbation velocity and mean vorticity are derived across the critical layer by applying the method of matched asymptotic expansions and it is shown that viscous effects outside the critical layer have to be taken into account in order to obtain a uniformly valid solution. Consequently the true neutral wavenumber and frequency are lower than their inviscid counterparts. When only the harmonic fluctuations are considered, it is known that the Landau constant is negative so that linearly amplified disturbances reach an equilibrium amplitude. It is shown that when the mean flow distortion generated by Reynolds stresses is also included, the Landau constant becomes positive. Thus, in both the spatial and temporal case, linearly amplified waves are further destabilized and damped waves are unstable above a threshold amplitude.

The Taylor column problem

1964 ◽  
Vol 20 (4) ◽  
pp. 581-591 ◽  
Author(s):  
S.J. Jacobs
Keyword(s):  
Shear Layer ◽  
Vertical Cylinder ◽  
Relative Vorticity ◽  
Solid Surfaces ◽  
Main Body ◽  
Free Shear Layer ◽  
Viscous Effects ◽  
Continuous Transition ◽  
Ekman Layers ◽  
Taylor Column

We consider here flow past an obstacle on the lower of two rotating horizontal planes which bound a viscous fluid. It is found that when the Taylor number is large viscous effects are confined to Ekman boundary layers on the solid surfaces and to a free shear layer coincident with the vertical cylinder circumscribing the bottom obstacle. The flow in the main body of the fluid outside the cylinder proves to be two-dimensional with zero relative vorticity, while inside the cylinder the fluid is stagnant in the rotating frame. The shear layer provides a continuous transition between the exterior and interior of the cylinder, and in addition provides a means by which fluid from the Ekman layers on the horizontal planes is exchanged with fluid outside the Ekman layers and exterior to the circumscribing cylinder. The predicted flow proves to be in agreement with many of the experimental results.

scholarly journals The approach of a vortex pair to a plane surface in inviscid fluid

1979 ◽  
Vol 92 (3) ◽  
pp. 497-503 ◽  
Author(s):  
P. G. Saffman
Keyword(s):  
Approximate Calculation ◽  
Plane Surface ◽  
Vortex Pair ◽  
Plane Wall ◽  
Inviscid Fluid ◽  
Viscous Effects ◽  
Axis Ratio ◽  
Local Rate

It is shown that a symmetrical vortex pair consisting of equal and opposite vortices approaching a plane wall at right angles must approach the wall monotonically in the absence of viscous effects. An approximate calculation is carried out for uniform vortices in which the vortices are assumed to be deformed into ellipses whose axis ratio is determined by the local rate of strain according to the results of Moore & Saffman (1971).

Three-dimensional wake transition

1996 ◽  
Vol 328 ◽  
pp. 345-407 ◽  
Author(s):  
C. H. K. Williamson
Keyword(s):  
Shear Layer ◽  
Three Dimensional ◽  
Streamwise Vortex ◽  
Physical Structure ◽  
Small Scale ◽  
Half Cycle ◽  
Vortex Loops ◽  
Wake Transition ◽  
Mode A ◽  
Flow States

It is now well-known that the wake transition regime for a circular cylinder involves two modes of small-scale three-dimensional instability (modes A and B), depending on the regime of Reynolds number (Re), although almost no understanding of the physical origins of these instabilities, or indeed their effects on near-wake formation, have hitherto been made clear. We address these questions in this paper. In particular, it is found that the two different modes A and B scale on different physical features of the flow. Mode A has a larger spanwise wavelength of around 3–4 diameters, and scales on the larger physical structure in the flow, namely the primary vortex core. The wavelength for mode A is shown to be the result of an ‘elliptic instability’ in the nearwake vortex cores. The subsequent nonlinear growth of vortex loops is due to a feedback from one vortex to the next, involving spanwise-periodic deformation of core vorticity, which is then subject to streamwise stretching in the braid regios. This mode gives an out-of-phase streamwise vortex pattern.In contrast, mode-B instability has a distinctly smaller wavelength (1 diameter) which scales on the smaller physical structure in the flow, the braid shear layer. It is a manifestation of an instability in a region of hyperbolic flow. It is quite distinct from other shear flows, in that it depends on the reverse flow of the bluff-body wake; the presence of a fully formed streamwise vortex system, brought upstream from a previous half-cycle, in proximity to the newly evolving braid shear layer, leads to an in-phase stream-wise vortex array, in strong analogy with the ‘Mode 1’ of Meiburg & Lasheras (1988) for a forced unseparated wake. In mode B, we also observe amalgamation of streamwise vortices from a previous braid with like-sign vortices in the subsequent braid.It is deduced that the large scatter in previous measurements concerning mode A is due to the presence of vortex dislocations. Dislocations are triggered at the sites of some vortex loops of mode A, and represent a natural breakdown of the periodicity of mode A instability. By minimizing or avoiding the dislocations which occur from end contamination or which occur during wake transition, we find an excellent agreement of both critical Re and spanwise wavelength of mode A with the recent secondary stability analysis of Barkley & Henderson (1996).Wake transition is further characterized by velocity and pressure measurements. It is consistent that, when mode-A instability and large-scale dislocations appear, one finds a reduction of base suction, a reduction of (two-dimensional) Reynolds stress level, a growth in size of the formation region, and a corresponding drop in Strouhal frequency. Finally, the present work leads us to a new clarification of the possible flow states through transition. Right through this regime of Re, there exist two distinct and continuous Strouhal frequency curves: the upper one corresponds with purley small- scale instabilities (e.g. denoted as mode A), while the lower curve corresponds with a combination of small-scale plus dislocation structures (e.g. mode A*). However, some of the flow states are transient or ‘unstable’, and the natural transitioning wake appears to follow the scenario: (2D→A*→B).

Deformable bubbles in a free shear layer

1997 ◽  
Vol 23 (5) ◽  
pp. 977-1001 ◽  
Author(s):  
E. Loth ◽  
M. Taeibi-Rahni ◽  
G. Tryggvason
Keyword(s):  
Shear Layer ◽  
Free Shear Layer

Assessment of turbulence models using DNS data of compressible plane free shear layer flow

2021 ◽  
Vol 931 ◽  
Author(s):  
D. Li ◽  
J. Komperda ◽  
A. Peyvan ◽  
Z. Ghiasi ◽  
F. Mashayek
Keyword(s):  
Shear Layer ◽  
Compressible Flows ◽  
Eddy Viscosity ◽  
Turbulence Models ◽  
Correlation Coefficients ◽  
Free Shear Layer ◽  
Smagorinsky Model ◽  
Reynolds Analogy ◽  
Velocity Fluctuations ◽  
Scale Similarity

The present paper uses the detailed flow data produced by direct numerical simulation (DNS) of a three-dimensional, spatially developing plane free shear layer to assess several commonly used turbulence models in compressible flows. The free shear layer is generated by two parallel streams separated by a splitter plate, with a naturally developing inflow condition. The DNS is conducted using a high-order discontinuous spectral element method (DSEM) for various convective Mach numbers. The DNS results are employed to provide insights into turbulence modelling. The analyses show that with the knowledge of the Reynolds velocity fluctuations and averages, the considered strong Reynolds analogy models can accurately predict temperature fluctuations and Favre velocity averages, while the extended strong Reynolds analogy models can correctly estimate the Favre velocity fluctuations and the Favre shear stress. The pressure–dilatation correlation and dilatational dissipation models overestimate the corresponding DNS results, especially with high compressibility. The pressure–strain correlation models perform excellently for most pressure–strain correlation components, while the compressibility modification model gives poor predictions. The results of an a priori test for subgrid-scale (SGS) models are also reported. The scale similarity and gradient models, which are non-eddy viscosity models, can accurately reproduce SGS stresses in terms of structure and magnitude. The dynamic Smagorinsky model, an eddy viscosity model but based on the scale similarity concept, shows acceptable correlation coefficients between the DNS and modelled SGS stresses. Finally, the Smagorinsky model, a purely dissipative model, yields low correlation coefficients and unacceptable accumulated errors.

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