Geostrophic Adjustment and Inverse Cascades in Rotating Stratified Turbulence

Abstract

Rotating stratified turbulence is examined both numerically and analytically, guided by energy and potential enstrophy conservation as well as resonant interaction theory, in order to investigate the cascade properties of rotational and wave modes at Froude numbers of order one or below, over a range of Rossby numbers. As Ro → 0, rotational modes are only weakly coupled to wave modes, and there are only weak rotational wave energy exchanges when initial conditions are random. A catalytic interaction involving two waves and a rotational mode, leaving the rotational mode unchanged, then provides the mechanism for geostrophic adjustment via a downscale cascade of wave energy. When simulations are initially balanced, gravity modes act to damp large-scale rotational modes through a transfer into intermediate-scale gravity modes and a subsequent downscale wave cascade involving the catalytic interaction. At larger Ro transfer from rotational to wave modes is important at any Froude number, and geostrophic adjustment may not take place. The consequences in terms of the proposed inverse cascade of rotational energy from convective scales are discussed.