Dresden 2014 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 37: Fluid Dynamics and Turbulence

DY 37.3: Talk

Thursday, April 3, 2014, 15:30–15:45, ZEU 146

Evolution equations for two dimensional elliptic shaped gaussian vortices — •Markus Blank-Burian — Institut für Physikalische Chemie, WWU Münster, Deutschland

The easiest model to describe two dimensional vortices in turbulent flows is the point vortex model. This model has an inherent problem, as it can not describe either attraction or repulsion of two vortices. By studying numerical and experimental data, one can see, that in first approximation two interacting vortices maintain a nearly elliptic gaussian shape for a rather long time. Vortices with the same sign attract each other and orientate themselves parallel with an angle of approximately 45^∘ to their connecting vector. Vortices with different sign orient themselves nearly perpendicular to each other while moving in the same direction.

Based on an idea in [1], one can derive equations of motion for two interacting elliptically shaped gaussian vortices, describing their evolution in time. This model then correctly predicts attraction and repulsion of two vortices, depending on the strenth and orientation of the vortices. The characteristic angles of 45^∘ are found stable as well. The famous Lamb-Oseen vortex is contained as a limiting case of symmetric shape.

[1] Friedrich, Friedrich: Generalized vortex-model for the inverse cascade of two-dimensional turbulence, http://arxiv.org/abs/1111.5808