Department: Mechanical & Aerospace Engineering
Faculty Advisor(s): Keiko Nomura

Primary Student
Name: Patrick J Folz
Email: pfolz@ucsd.edu
Phone: 858-822-0129
Grad Year: 2014

Two-dimensional vortical motions are prominent features in a wide variety of fluid flows, including planetary atmospheres, electromagnetically-driven flows, and circumstellar accretion disks. Two-dimensional vortex interactions also play an important role in two-dimensional turbulence. In particular, the merging of co-rotating vortices is often considered to be the underlying physical mechanism of the inverse energy cascade; as vortices in the flow merge, there are fewer, larger vortices remaining, thereby concentrating energy in ever-larger scales. Fundamental studies of the interaction of co-rotating vortices provide considerable insight on the merger process but have mainly focused on the simplest, highly idealized case of symmetric vortex pairs in which there are two vortices of equal size and strength. These studies indicate a criterion for merger in terms of a critical aspect ratio. In our research, we consider the more general case of asymmetric vortex pairs in which the size and/or strength of the vortices may differ. Two-dimensional numerical simulations of viscous flow are performed and results provide further details on the physical processes. In the case of a symmetric vortex pair, the mutually induced strain deforms and tilts the vortices, which leads to a core detrainment process. The weakened vortices are mutually entrained and rapidly move towards each other as they intertwine and destruct. The flow thereby develops into a single compound vortex. In the case of asymmetric pairs, the disparity of the vortices alters the interaction. Merger may result from reciprocal but unequal entrainment which yields a compound vortex, however other outcomes are possible. The various interactions are classified based on the relative timing of core detrainment and core destruction of the vortices. Through scaling analysis and simulation results, a more generalized merger criterion is developed in terms of a critical strain rate parameter. In general, the study suggests that in a turbulent flow field, since complete merger requires somewhat rare circumstances, it may not be the primary mechanism of upscale energy transfer. Further work will examine the vortex interactions in a two-dimensional turbulent flow.

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