Two-Dimensional Turbulence in Irregular Domains

James McWilliams
University of California, Los Angeles (UCLA)
Atmospheric Sciences

[Joint work with Guillaume Roullet (Brest)] The behavior of two-dimensional turbulence is greatly altered by the presence of side boundaries, a fortiori if the boundary shape is irregular. Adjacent flows cause boundary layers with strong vorticity generation, boundary layers separate and become unstable, and their fluctuations coalesce into a continually renewed population of small coherent vortices. In numerical solutions using Implicit Large Eddy Simulation (i.e., computational algorithms provide the necessary
regularization at small scale and vorticity generation at the boundary), flows in free decay from random initial conditions display perpetual turbulence with decreasing dissipation rate and intermittency and broadening vortex population distributions as the
grid number N increases (as a vision of increasing Reynolds number); this is in contrast to the non-turbulent (maximum entropy) end-states that arise in periodic domains. With random forcing flows achieve statistical equilibrium without artificial large scale dissipation. More generally, the classical picture of inverse energy and forward
enstrophy cascades in homogeneous turbulence is not particularly apt for bounded flows; rather there is an essential segregation between the deep-interior and near-boundary regions, with further segregation of the latter between bays and headlands. These partitions are also evident in the inhomogeneous scalar transport patterns. This idealized turbulence problem is germane to oceanic flows with strong
vorticity generation by flows adjacent to (continental) boundary slopes.

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