Pseudo-spectral and asymptotic sensitivity investigation of counter-rotating vortices

Dagan, A.; Carey, G. F.

doi:10.1016/0045-7930(89)90025-x

Cited by 6 publications

(3 citation statements)

References 10 publications

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“…(iv) Whereas in irrotational motion the choice of a sufficiently large initial depth 6 does not affect the solution, the initial depth in a viscous fluid does. The two vortices decay and their paths are not parallel as in the inviscid-flow case but diverge slightly (Dagan 1989). However, since a decreasing 6 has an effect similar to that of an increasing Re, as long as the assumption of an undisturbed surface at t = 0 is not violated, the value 6 = -3 has been chosen to keep the number of computer runs low.…”

Section: (Ii)mentioning

confidence: 99%

Interaction of a viscous vortex pair with a free surface

Ohring¹,

Lugt²

1991

J. Fluid Mech.

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A vortex pair in a viscous, incompressible fluid rises vertically toward a deformable free surface. The mathematical, description of this flow situation is a time-dependent nonlinear free-surface problem that has been solved numerically for a two-dimensional laminar flow with the aid of the Navier-Stokes equations by using boundary-fitted coordinates. For a number of selected flow parameters, results are presented on the decay of the primary vortices and their paths, the generation of surface vorticity and secondary vortices, the development and final stage of the disturbed free surface, and the influence of surface tension. High and low Froude numbers represent the two extremes of free-surface yielding and stiffness, respectively. For an intermediate Froude number, a special rebounding due to the presence of secondary vortices has been observed: the path of the primary vortex centre portrays a complete loop.

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Section: (Ii)mentioning

confidence: 99%

Interaction of a viscous vortex pair with a free surface

Ohring¹,

Lugt²

1991

J. Fluid Mech.

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“…TO' (14) and the vector v is written as where A is a diagonal matrix and contains the eigenvalue of the amplification matrix (13). The form of the last expression defines the fundamental matrix solution of Eq.…”

Section: Derivation Of the Equationsmentioning

confidence: 99%

“…A similar transformation has been used by Coddington et al,20 where a solution to Eq (14) for a small variation of the matrix E in time can be found. To further clarify the role of the transformation matrix T, we shall expand T in a Taylor series in the neighborhood of T 0'=0:…”

Section: Derivation Of the Equationsmentioning

confidence: 99%

Instability of strained counter-rotating vortices

Dagan¹

1994

Physics of Fluids

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The stability of counter-rotating vortices sUbjected to a uniform plane straining flow has been examined in this study. The straining flow field flattens the vortices in a way that the resulting slender shape can be considered as a double shear layer. The linear analysis based on this assumption has indicated two regions of instability: decreasing slenderness ratio and increasing slenderness ratio with time, where the Orr-Sommerfeld equation has been found to describe the phenomenon when the slenderness ratio is time independent. Decreasing slenderness ratio with time, coupled with an extension of the line vortex, is a stabilizing mechanism, where the rate of change of the slenderness ratio plays an important role in this process. On the other hand, in the case of a contracting line vortex with decreasing slenderness ratio, instability will not reach full growth and the vortex will undergo irreversible elongation. Increasing slenderness ratio is found to be an unconditionally destabilizing mechanism. The nonlinear phenomenon, computed by the numerical solution, indicates that in the case of an extending line vortex and decreasing slenderness ratio, the vortices will collapse to form a pair of vortices with finite cores. In some other cases, the vortex pair will undergo irreversible elongation, where increased slenderness ratio is found numerically to be a destabilizing mechanism.

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A Guide to Literature Related to the Taylor-Couette Problem

Tagg

1992

NATO ASI Series

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Pseudo-spectral and asymptotic sensitivity investigation of counter-rotating vortices

Cited by 6 publications

References 10 publications

Interaction of a viscous vortex pair with a free surface

Interaction of a viscous vortex pair with a free surface

Instability of strained counter-rotating vortices

A Guide to Literature Related to the Taylor-Couette Problem

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