Decaying two-dimensional turbulence with rigid walls

Abstract

Decaying two-dimensional Navier-Stokes turbulence (or turbulence for the corresponding electrostatic “guiding center” plasma) has usually been studied in spatially periodic boundary conditions. It is known to exhibit a variety of features which are different from the three-dimensional case. By means of spectral-method direct numerical computation, we show that circular no-slip boundaries can significantly alter the decay scenario in two dimensions. In particular, the wall functions as an important source of vorticity and vorticity gradient, and the decay of energy is enhanced by this effect, relative to the decay in periodic boundary conditions. In addition, the very slow decay of angular momentum in high Reynolds number cases constrains the evolution in a way that has no analogue for rectangular periodic boundary conditions.