On the alignment and axisymmetrization of a vertically tilted geostrophic vortex

Abstract

We investigate the evolution of a vertically tilted geostrophic vortex of cylindrical shape and circular horizontal cross-section using the recently developed method of boundary surface dynamics. The vortex consists of a finite volume of constant potential vorticity immersed in a spatially unbounded fluid of uniform density stratification. The fully nonlinear three-dimensional problem is then reduced to the calculation of the Lagrangian evolution of the boundary surface of the vortex region, thus decreasing the dimensionality by one. In the numerical simulations presented here, the vortex shows a general tendency to attain vertical alignment and a horizontal axisymmetrical shape by wobbling about its centre and going through three basic stages of evolution: (a) the circular horizontal cross-sections of the upper and lower parts of the vortex distort and become elongated; (b) the upper and lower sections then become vertically aligned by reducing their horizontal intercentroid distances; and (c) the distorted horizontal cross-sections relax towards axisymmetry, often through the process of filamentation. For a given vortex height, if the horizontal scale of the flow is close to the internal radius of deformation, or equivalently, the density stratification is not too strong, the processes of filamentation and vertical alignment are enhanced. However, for stronger stratifications, both filamentation and vertical alignment are found to be greatly inhibited. For relatively small initial inclination angles, filamentation only occurs in the upper and lower sections of the vortex. Increasing the angle of tilt also increases the tendency of the surface to steepen and filament in the middle sections of the vortex. For a fixed value of the ratio of horizontal scale of the flow to the deformation radius, taller vortices have an increased tendency to align and axisymmetrize than shorter vortices of equal inclination angle.