Inviscid instabilities in two-dimensional spatially periodic flows

1993 ◽  
Vol 51 (1-2) ◽  
pp. 79-84
Author(s):  
A. Thess
Keyword(s):  
Two Dimensional ◽  
Periodic Flows ◽  
Spatially Periodic

Mixing by chaotic advection in a class of spatially periodic flows

1992 ◽  
Vol 236 ◽  
pp. 1-26 ◽  
Author(s):  
Susan C. Ryrie
Keyword(s):  
Vortex Flow ◽  
Detailed Comparison ◽  
Laminar Flows ◽  
Basic Flow ◽  
Chaotic Advection ◽  
Taylor Vortex ◽  
Two Dimensional ◽  
Periodic Flows ◽  
Taylor Vortex Flow ◽  
Spatially Periodic

The paths followed by individual fluid particles can be extremely complicated even in smooth laminar flows. Such chaotic advection causes mixing of the fluid. This phenomenon is studied analytically for a class of spatially periodic flows comprising a basic flow of two-dimensional (or axisymmetric) counter-rotating vortices in a layer of fluid, and modulated by a perturbation which is periodic in time and/or space. Examples of this type of flow include Bénard convection just above the point of instability of two-dimensional roll cells, and Taylor vortex flow between concentric rotating cylinders. The transport of chaotically advected particles is modelled as a Markov process. This predicts diffusion-like mixing, and provides an expression for the diffusion coefficient. This expression explains some features of experimental results reported by Solomon & Gollub (1988): its accuracy is investigated through a detailed comparison with numerical results from a model of wavy Taylor vortex flow. The approximations used in the analysis are equivalent to those used to obtain the quasi-linear result for diffusion in the standard map.

A Lagrangian criterion of unsteady flow separation for two-dimensional periodic flows

2018 ◽  
Vol 39 (7) ◽  
pp. 1007-1018 ◽  
Author(s):  
Shuaibin Han ◽  
Shuhai Zhang ◽  
Hanxin Zhang
Keyword(s):  
Unsteady Flow ◽  
Flow Separation ◽  
Two Dimensional ◽  
Periodic Flows

The stability of spatially periodic flows

1981 ◽  
Vol 108 ◽  
pp. 461-474 ◽  
Author(s):  
D. N. Beaumont
Keyword(s):  
Velocity Profile ◽  
Phase Speed ◽  
Neutral Curve ◽  
Long Waves ◽  
Inviscid Fluid ◽  
Periodic Flows ◽  
A Value ◽  
Parallel Flows ◽  
Spatially Periodic ◽  
The Stability

The stability characteristics for spatially periodic parallel flows of an incompressible fluid (both inviscid and viscous) are studied. A general formula for the determination of the stability characteristics of periodic flows to long waves is obtained, and applied to approximate numerically the stability curves for the sinusoidal velocity profile. The neutral curve for the sinusoidal velocity profile is obtained analytically. The stability of two broken-line velocity profiles in an inviscid fluid is studied and the results are used to describe the overall pattern for the sinusoidal velocity profile in the case of long waves. In an inviscid fluid it is found that all periodic flows (other than the trivial flow in which the basic velocity is constant) are unstable to long waves with a value of the phase speed determined by simple integrals of the basic flow. In a viscous fluid it is found that the sinusoidal velocity profile is very unstable with the inviscid solution being a good approximation to the solution of the viscous problem when the value of the Reynolds number is greater than about 20.

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