Numerical simulation of vortex dipole formation and evolution in stably stratified fluid

Abstract

Direct numerical simulation has been used to study how axisymmetric vertical flow structures evolve whilst propagating horizontally in both homogeneous fluid and in fluid with a linear stable density stratification in the vertical direction. The structures studied were initially toroidal vortex rings and impulsive jets formed from a brief, horizontal injection of fluid into a quiescent domain. Previous experimental studies have demonstrated that when these initially axisymmetric structures are allowed to evolve under the influence of stable stratification, acceleration due to buoyancy acts to suppress vertical displacement of fluid particles, eventually reducing the flow to a pair of contra-rotating, planar vortices, commonly referred to as a vortex dipole. The numerical simulations documented in this thesis demonstrate the process by which the initially axisymmetric structures are transformed into late time dipoles in a stratified fluid, with the stages of this transformation categorised both through visual changes in the flow field as well as characteristic variations in kinetic energy and buoyancy variance histories that are inaccessible to the experimental work, thus allowing the energetics and vorticity fields of these flows to be directly correlated for the first time. Additionally, it has been demonstrated that while different means of imparting horizontal momentum to the fluid through an initial solution or different profiles of momentum injection may generate distinct vorticity fields at the early time, the energetics, scaling behaviours and agreement with theoretical models appear universal across the late time dipoles formed from these cases, which has not been addressed directly in previous literature.

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ORCID for Neil Sandham: orcid.org/0000-0002-5107-0944

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