Dynamics of vortex interaction with a density interface

Abstract

We present results from an experimental and numerical investigation into the dynamics of the interaction between a planar vortex pair or axisymmetric vortex ring with lengthscale a and circulation Γ encountering a planar interface of thickness δ across which the fluid density increases from ρ1 to ρ2. Similarity considerations indicate that baroclinic generation of vorticity and its subsequent interaction with the original vortex is governed by two dimensionless parameters, namely (a/δ) A and R, where A ≡ (ρρ2 − ρ1)/(ρ2 + ρ1) and R ≡ (a3g/Γ2). For thin interfaces (δ [Lt ] a), the interaction is governed only by the parameters A and R. Furthermore, in the Boussinesq limit (A → 0), the dynamics are governed solely by the product AR and the interaction is entirely invertible with respect to the initial locations and direction of propagation of the vortices. We document details of the interaction dynamics in the Boussinesq limit over a range of the parameter AR. Results show that, for relatively small values of AR, rather than the vortex simply rebounding at the interface, its outermost layers are instead successively ‘peeled’ away by baroclinically generated vorticity and form a topologically complex backflow in which the ring fluid, the light fluid and the heavy fluid are intertwined. For larger values of AR the vortex barely penetrates the interface, and our results suggest that in the limit AR → ∞ the interaction with a density interface becomes similar to the interaction at a solid wall. We also present results for thick interfaces in the Boussinesq limit, as well as larger density jumps for which the density parameter A enters as a second similarity quantity. Comparison of the experimental and numerical results demonstrate that many of the features of such interactions can be understood within the context of inviscid fluids, and that inviscid vortex methods can be used to accurately simulate the dynamics of such interactions.

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