Nonlinear Vortex Structures in Obliquely Rotating Fluid (original) (raw)
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It is known that two-dimensional vortices are subject to generic three-dimensional instabilities. This phenomenon is located near the core of vortices and depends on the eccentricity of their streamlines. In this paper we are concerned with the modification of this instability when stretching is applied to such vortices. We describe this instability by linearizing the Navier-Stokes equations around a basic state, which is an exact time-dependent solution. The complete system for the perturbations is reduced to a single equation for the perturbed velocity along the vortex span. In the limit of weak stretching, a perturbation theory can be performed and leads to a WKBJ approximation for the solution. This procedure demonstrates that a small amount of stretching is able to prevent the appearance of three-dimensional instabilities for vortices with a low enough eccentricity. Since most vortices are slightly elliptical in turbulent flows, the above computations are expected to cover a wide range of experimental cases. In particular, it is tentatively argued that this mechanism may explain recent experimental observations ͓Phys. Fluids 7, 630 ͑1995͔͒.
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Fluid Dynamics Research, 1997
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We present results from a new series of experiments on the geophysically important issue of the instability of anticyclonic columnar vortices in a rotating fluid in circumstances such that the Rossby number exceeds unity. The vortex pair consisting of a cyclonic and an anticyclonic vortex is induced by a rotating flap in a fluid which is itself initially in a state of solid-body rotation. The anticyclonic vortex is then subject to either centrifugal or elliptical instability, depending on whether its initial ellipticity is small or large, while the cyclone always remains stable. The experimental results demonstrate that the perturbations due to centrifugal instability have a typical form of toroidal vortices of alternating sign (rib vortices). The perturbations due to elliptical instability are of the form of sinuous deformation of the vortex filament in the plane of maximal stretching which corresponds to the plane of symmetry for the vortex pair. The initial perturbations in both cases are characterized by a definite wave number in the vertical direction. The characteristics of the unstable anticyclone are determined by the main nondimensional parameter of the flow -the Rossby number. The appearance of both centrifugal and elliptical instabilities are in accord with the predictions of theoretical criteria for these cases.
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We present the results of a combined experimental and numerical investigation into steady secondary vortex flows confined between two concentric right circular cylinders. When the flow is driven by the symmetric rotation of both end walls and the inner cylinder, toroidal vortex structures arise through the creation of stagnation points (in the meridional plane) at the inner bounding cylinder or on the mid-plane of symmetry. A detailed description of the flow regimes is presented, suggesting that a cascade of such vortices can be created. Experimental results are reported, which visualize some of the new states and confirm the prediction that they are stable to (mid-plane) symmetry-breaking perturbations. We also present some brief results for the flows driven by the rotation of a single end wall. Vortex structures may also be observed at low Reynolds numbers in this geometry. We show that standard flow visualization methods lead to some interesting non-axisymmetric particle paths in...
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