Angular momentum in forced 2D flow on a bounded square domain

D. Molenaar, H.J.H. Clercx and G.J.F. van Heijst
Eindhoven University of Technology, The Netherlands

In decaying 2D turbulence on a bounded square domain there may occur a sudden increase in the absolute value of the angular momentum |L|, followed by a slow decay. This process is referred to as spontaneous spin-up of the flow [1]. Spin-up is caused entirely by the boundedness of the flow, whereas the angular momentum is not relevant for the flow evolution in the unbounded case [3]. New computational results show that the spin-up phenomenon may also be observed in forced 2D turbulence on a bounded domain. In forced 2D flow several consecutive events of increased |L| occur, in which the sign of the angular momentum is chosen spontaneously. These events coincide with the formation and break-down of a central vortex structure that dominates the flow in the interior of the domain. Shear and normal stresses exerted on the fluid, resulting from the interaction of this emerging central vortex with the domain boundaries, cause the spin-up phenomenon [1,2]. The formation of the central vortex structure is thought to be a direct physical manifestation of the inverse energy cascade, in which energy is passed onward from smaller to larger scales. The central structure is broken down by the development and the destabilizing effect of intense boundary layers. Finally, the apparently similar behavior of |L| and the energy E is discussed. A preliminary result quantifies the lower and upper bounds between which a correlation of |L| and E may occur.


  1. H.J.H. Clercx, S.R. Maassen, and G.J.F. van Heijst, "Spontaneous spin-up during the decay of 2d turbulence in a square container with rigid boundaries", Physical Review Letters 80, 5129-5132 (1998).
  2. H.J.H. Clercx, A.H. Nielsen, D.J. Torres, and E.A. Coutsias, "Two-dimensional turbulence in square and circular domains with no-slip walls", European Journal of Mechanics B/Fluids 20, 557-576 (2001).
  3. S. Li, D. Montgomery, and W.B. Jones, "Inverse cascades of angular momentum", Journal of Plasma Physics 56, 615-639 (1996).