A Study of Barotropic Model Flows: Intermittency, Waves and Predictability

TLDR

Two‑dimensional turbulence is typically nonlocal, but this study examines barotropic flows that challenge that expectation. The study investigates the predictability of barotropic flows using Leith‑Kraichnan theory. Spectral models on the plane and sphere are employed to simulate barotropic nondivergent flows with forcing, drag, and subgrid‑scale dissipation. The simulations reveal an enstrophy‑cascading inertial range with steeper spectra, a reverse energy cascade inhibited by Rossby waves, persistent zonal anisotropy, and enhanced predictability due to wave‑induced suppression of nonlinear transfers and slowed error growth.

Abstract

The régime flows corresponding to the barotropic nondivergent equation with forcing, drag and subgrid-scale dissipation are studied using spectral model on the plane and on the sphere. The flow régimes obtained exhibit clear evidence of the existence of an enstrophy-cascading inertial range, together with a reverse energy cascade toward small wavenumbers. It is shown, however, that the enstrophy cascade is not associated with the k−3 spectral slope expected from the Kolmogorov-Kraichnan theory of two-dimensional turbulence; the slopes obtained are significantly steeper. This apparent paradox is tentatively resolved by a phenomenological theory of space-time intermittency in two dimensions; it is further shown that such intermittency associated with steeper spectra also restores locality of the nonlinear transfers in wavenumber space. In contrast to the well-known nonlocality typical of two-dimensional non-intermittent turbulent flows. The effect of differential rotation in connection with Rossby wave propagation is also studied: the reverse energy cascade is actually inhibited, and zonal anisotropy prevails in the large scales as expected from Rhines' theory. But it is shown that this anisotropy is in fact carried down by nonlinearity throughout the enstrophy inertial range. Finally, the predictability properties of our flows are investigated with reference to the Leith-Kraichnan theory. It is shown that the presence of Rossby waves actually increases predictability through several mechanisms: direct inhibition of the nonlinear transfers in the larger scales, concentration of energy in highly predictably large-scale zonal structures, and slowdown of error propagation in the enstrophy inertial range due to the presence of anisotropy at small and intermediate scales.