Accelerated diffusion in the centre of a vortex
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In this paper, an accelerated diffusion mechanism was proposed to destroy scalar fluctuations on a time scale of order P 1/3 times the turnover time, where P is a Peclet number.Abstract:
The spiral wind-up and diffusive decay of a passive scalar in circular streamlines is considered. An accelerated diffusion mechanism operates to destroy scalar fluctuations on a time scale of order P1/3 times the turn-over time, where P is a Peclet number. The mechanism relies on differential rotation, that is, a non-zero gradient of angular velocity. However if the flow is smooth, the gradient of angular velocity necessarily vanishes at the centre of the streamlines, and the time scale becomes greater. The behaviour at the centre is analysed and it is found that scalar there is only destroyed on a time scale of order P1/2. Related results are obtained for magnetic field and for weak vorticity, a scalar coupled to the stream function of the flow. Some exact solutions are presented.read more
Citations
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References
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Handbook of Mathematical Functions
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On steady laminar flow with closed streamlines at large Reynolds number
TL;DR: In this article, it is shown that if the motion is to be exactly steady there is an integral condition, arising from the existence of viscous forces, which must be satisfied by the vorticity distribution no matter how small the viscosity may be.
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Strained spiral vortex model for turbulent fine structure
TL;DR: In this paper, a model for the intermittent fine structure of high Reynolds number turbulence is proposed, consisting of slender axially strained spiral vortex solutions of the Navier-Stokes equation.
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Pseudospectra of linear operators
TL;DR: Ten examples of computed pseudospectra of thirteen highly nonnormal matrices arising in various applications are presented, each chosen to illustrate one or more mathematical or physical principles.
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Homogenization of potential vorticity in planetary gyres
Peter B. Rhines,William R. Young +1 more
TL;DR: In this paper, the Prandtl-Batchelor theorem is applied to non-rotating, steady two-dimensional flow and the results of the derivations given here can apply only where internal heating is negligible, upon the potential density surface under consideration.
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