Vortex simulations of 2D turbulence in confined domains
Seminar Room 1, Newton Institute
AbstractThis talk considers the evolution of 2D turbulence in a confined domain with slip boundary conditions imposed. Several domain shapes are considered, both regular (e.g. a circle, a square) and irregular (e.g. random coastlines). The CASL (Contour-Advective Semi-Lagrangian) technique is employed, taking as the initial condition a random assembly of vortex patches. It is known that the initial angular momentum is important in determining whether the very long time state is dipolar or monopolar when no-slip boundary conditions are considered. Although this is not the case for slip boundary conditions, the initial total circulation plays a similar role. We explore the dependence of the final state on the initial circulation for a range of geometries. Some examples are shown where trapping of vortices in 'bays', caused by domain-scale interactions, can influence the long time evolution. Recent work on 2D turbulence in a periodic box has shown how the rate of dipole/monopole interactions can be related to the time rate of decay of enstrophy at intermediate to long times (once the initial very strong interactions are over). The presence of the domain boundary provides a mechanism for enhancing the rate of such interactions, as monopoles of opposite sign tend to hug the boundaries, travel in opposite directions and then meet to form dipoles which are then launched into the flow. Accordingly, we consider the effect of domain shape on the frequency of dipole formation and dipole/monopole interactions and the corresponding rate of decay of enstrophy. Finally, we discuss extensions of this work to the 3D quasi-geostrophic case.
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