Resonant gravity-wave interactions in a shear flow

Among a triad of gravity waves in a uniform shear flow, a remarkably powerful second-order resonant interaction may take place. This interaction is characterized by large growth rates of waves which propagate in directions oblique to that of the primary flow, and by a systematic transfer of energy from the primary flow to such waves. Most of the energy transfer takes place in the vicinity of a ‘critical layer’, where viscous forces are dominant.Provided the resonance condition may be satisfied, a uniform shear flow which is perturbed by a two-dimensional wave of small but finite amplitude may be unstable, owing to the growth of two initially infinitesimal oblique waves which complete the resonant triad.

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Transient and asymptotic stability of granular shear flow

Journal of Fluid Mechanics ◽

10.1017/s0022112094000650 ◽

1994 ◽

Vol 264 ◽

pp. 255-275 ◽

Cited By ~ 44

Author(s):

P. J. Schmid ◽

H. K. Kytömaa

Keyword(s):

Shear Flow ◽

Linear Stability ◽

Equations Of Motion ◽

Wave Structure ◽

Finite Amplitude ◽

Particulate Flows ◽

Uniform Shear ◽

Uniform Shear Flow ◽

The Stability ◽

Fast Mechanism

The linear stability of granular material in an unbounded uniform shear flow is considered. Linearized equations of motion derived from kinetic theories are used to arrive at a linear initial-value problem for the perturbation quantities. Two cases are investigated: (a) wavelike disturbances with time constant wavenumber vector, and (b) disturbances that will change their wave structure in time owing to a shear-induced tilting of the wavenumber vector. In both cases, the stability analysis is based on the solution operator whose norm represents the maximum possible amplification of initial perturbations. Significant transient growth is observed which has its origin in the non-normality of the involved linear operator. For case (a), regions of asymptotic instability are found in the two-dimensional wavenumber plane, whereas case (b) is found to be asymptotically stable for all physically meaningful parameter combinations. Transient linear stability phenomena may provide a viable and fast mechanism to trigger finite-amplitude effects, and therefore constitute an important part of pattern formation in rapid particulate flows.

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Formation of Vortex Street in Laminar Boundary Layer

Journal of Applied Mechanics ◽

10.1115/1.3153647 ◽

1980 ◽

Vol 47 (2) ◽

pp. 227-233 ◽

Cited By ~ 4

Author(s):

M. Kiya ◽

M. Arie

Keyword(s):

Boundary Layer ◽

Shear Flow ◽

Laminar Boundary Layer ◽

Solid Wall ◽

Vortex Sheet ◽

Vortex Street ◽

Bluff Bodies ◽

Uniform Shear ◽

Uniform Shear Flow ◽

Vortex Patterns

Main features of the formation of vortex street from free shear layers emanating from two-dimensional bluff bodies placed in uniform shear flow which is a model of a laminar boundary layer along a solid wall. This problem is concerned with the mechanism governing transition induced by small bluff bodies suspended in a laminar boundary layer. Calculations show that the background vorticity of shear flow promotes the rolling up of the vortex sheet of the same sign whereas it decelerates that of the vortex sheet of the opposite sign. The steady configuration of the conventional Karman vortex street is not possible in shear flow. Theoretical vortex patterns are experimentally examined by a flow-visualization technique.

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Rheology of Two- and Three-dimensional Granular Mixtures Under Uniform Shear Flow: Enskog Kinetic Theory Versus Molecular Dynamics Simulations

Granular Matter ◽

10.1007/s10035-006-0001-7 ◽

2006 ◽

Vol 8 (2) ◽

pp. 103-115 ◽

Cited By ~ 22

Author(s):

José María Montanero ◽

Vicente Garzó ◽

Meheboob Alam ◽

Stefan Luding

Keyword(s):

Molecular Dynamics ◽

Shear Flow ◽

Kinetic Theory ◽

Molecular Dynamics Simulations ◽

Three Dimensional ◽

Uniform Shear ◽

Uniform Shear Flow ◽

Granular Mixtures ◽

Theory Versus ◽

Dynamics Simulations

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The formation mechanism and shedding frequency of vortices from a sphere in uniform shear flow

Journal of Fluid Mechanics ◽

10.1017/s0022112095000905 ◽

1995 ◽

Vol 287 ◽

pp. 151-171 ◽

Cited By ~ 93

Author(s):

Hiroshi Sakamoto ◽

Hiroyuki Haniu

Keyword(s):

Reynolds Number ◽

Shear Flow ◽

Formation Mechanism ◽

Vortex Shedding ◽

Uniform Flow ◽

Sphere Diameter ◽

Uniform Shear ◽

Uniform Shear Flow ◽

Vortex Loops ◽

Shear Parameter

Experiments to investigate the formation mechanism and frequency of vortex shedding from a sphere in uniform shear flow were conducted in a water channel using flow visualization and velocity measurement. The Reynolds number, defined in terms of the sphere diameter and approach velocity at its centre, ranged from 200 to 3000. The shear parameter K, defined as the transverse velocity gradient of the shear flow non-dimensionalized by the above two parameters, was varied from 0 to 0.25. The critical Reynolds number beyond which vortex shedding from the sphere occurred was found to be lower than that for uniform flow and decreased approximately linearly with increasing shear parameter. Also, the Strouhal number of the hairpin-shaped vortex loops became larger than that for uniform flow and increased as the shear parameter increased.The formation mechanism and the structure of vortex shedding were examined on the basis of series of photographs and subsequent image processing using computer graphics. The range of Reynolds number in the present investigation, extending up to 3000, could be classified into three regions on the basis of this study, and it was observed that the wake configuration did not differ substantially from that for uniform flow. Also, unlike the detachment point of vortex loops in uniform flow, which was irregularly located along the circumference of the sphere, the detachment point in shear flow was always on the high-velocity side.

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The heat/mass transfer to a finite strip at small Péclet numbers

Journal of Fluid Mechanics ◽

10.1017/s0022112078001007 ◽

1978 ◽

Vol 86 (1) ◽

pp. 49-65 ◽

Cited By ~ 45

Author(s):

R. C. Ackerberg ◽

R. D. Patel ◽

S. K. Gupta

Keyword(s):

Heat Transfer ◽

Mass Transfer ◽

Shear Flow ◽

Sodium Hydroxide Solution ◽

Flow Direction ◽

Mathematical Problem ◽

Limiting Current ◽

Transfer Rates ◽

Uniform Shear ◽

Uniform Shear Flow

The problem of heat transfer (or mass transfer at low transfer rates) to a strip of finite length in a uniform shear flow is considered. For small values of the Péclet number (based on wall shear rate and strip length), diffusion in the flow direction cannot be neglected as in the classical Leveque solution. The mathematical problem is solved by the method of matched asymptotic expansions and expressions for the local and overall dimensionless heat-transfer rate from the strip are found. Experimental data on wall mass-transfer rates in a tube at small Péclet numbers have been obtained by the well-known limiting-current method using potassium ferrocyanide and potassium ferricyanide in sodium hydroxide solution. The Schmidt number is large, so that a uniform shear flow can be assumed near the wall. Experimental results are compared with our theoretical predictions and the work of others, and the agreement is found to be excellent.

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