A numerical study of impulsively generated vortices between non-deformable stress-free layers

Abstract

A wake behind an unsteady moving submerged vehicle is of interest and importance in a broad variety of engineering disciplines, ranging from underwater to aeronautical engineering. When the vehicle changes its speed or direction, under certain conditions, it can lead to the appearance of a coherent kilometre-scale quasi-planar counter-rotating vortical structure which persists for the order of days. The aims of this work are to determine the conditions under which such a large coherent vortex can appear and to obtain deeper understanding of its dynamics by investigating the evolution of a turbulent patch created by either an impulsively accelerating axisymmetric self propelled body or an impulsive jet in the small-scale upper ocean via direct numerical simulation. A non-conservative body force is applied to the governing equations to represent an impulsive jet, while an accelerating motion of a self-propelled body is emulated by the combination of an immersed boundary method and the body force. Criteria for the occurrence of a vortex dipole are found to depend on a dimensionless parameter, called the confinement number. Once the confinement number is higher than about unity, the vertical growth of an impulsively generated turbulent patch is restricted by the top and bottom layers of the upper ocean leading to the formation of a vortex dipole at the free surface. The contrast and strength of a surface signature increase linearly with increasing confinement number. The late-time dynamical structures, i.e. the propagation velocity, size and the decay rate of maximum vorticity, of the dipolar eddy induced by the presence of vertical confinement can be predicted by scaling laws relevant to a stratified fluid, even though the dipole possesses a Reynolds-number dependence.

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