P.V.Lukyanov Vortex diffusion in the layer of stable stratified fluid |
Applied hydromechanics, Vol. 8 (80) ¹ 3, (2006) |
| This paper contains analytical solution for turbulent diffusion of an axisymmetric quasihorizontal isolated vortex. Quasihorizontality means small vertical velocities, and slow changing in time means also small radial velocities. The situations when these restrictions are broken are discussed in the section on secondary flows. On the base of made assumptions, the problem is reduced to an linear diffusion equation for vertical component of vorticity. The horizontal and vertical diffusions are different. The vertical diffusion is considered to be constant [1] that is only typical for stable stratification. Horizontal diffusion is calculated by Richardson Low of "four thirds'' that is approximately true for vortex scales range from 10 to 1000 m [2, 3]. The problem's boundary conditions are typical. The deformation of free surface for the problem is negligible in comparison with the thickness of the layer. So boundary conditions at free surface may be formulated at the surface of still fluid. For simulation of initial vorticity distribution on vertical coordinate, the special distribution that strictly meets boundary conditions is used. This distribution also affords to set vortex of various thickness and positions in the layer. On radial coordinate the distribution is taken as isolated Gaussian [4-6]. The solution of the linear problem affords splitting into two ones that correspond to horizontal and vertical diffusion processes. For the horizontal diffusion, the self-similar solution has been found. For certain radial distribution, this solution corresponds to conservation of vorticity third momentum. It is shown that linear model is valid when Froud number is significantly less than 1. |
|
KEY WORDS: *** |
| TEXT LANGUAGE: Russian |