The structure of zonal jets in geostrophic turbulence

Abstract

The structure of zonal jets arising in forced-dissipative, two-dimensional turbulent flow on the β-plane is investigated using high-resolution, long-time numerical integrations, with particular emphasis on the late-time distribution of potential vorticity. The structure of the jets is found to depend in a simple way on a single nondimensional parameter, which may be conveniently expressed as the ratio L Rh /L ε , where L Rh = √ U/β and L ε = (ε/β 3 ) 1/5 are two natural length scales arising in the problem; here U may be taken as the r.m.s. velocity, β is the background gradient of potential vorticity in the north-south direction, and ε is the rate of energy input by the forcing. It is shown that jet strength increases with L Rh /L ε , with the limiting case of the potential vorticity staircase, comprising a monotonic, piecewise-constant profile in the north-south direction, being approached for L Rh /L ε ∼ O(10). At lower values, eddies created by the forcing become sufficiently intense to continually disrupt the steepening of potential vorticity gradients in the jet cores, preventing strong jets from developing. Although detailed features such as the regularity of jet spacing and intensity are found to depend on the spectral distribution of the forcing, the approach of the staircase limit with increasing L Rh /L ε is robust across a variety of different forcing types considered.

On the energetics of a two-layer baroclinic flow

“…This competition between thermal forcing and baroclinic instability gives rise to the formation of baroclinic jets and, in extreme cases, to stepped PV profiles or 'staircases'. Such staircase formation has already been demonstrated in the single-layer barotropic context (see Dritschel & McIntyre (2008) and Scott & Dritschel (2012)). Additionally, in the present model small-scale stochastic forcing is imposed, crudely mimicking convective processes.…”

“…The jets form through inhomogeneous potential vorticity mixing (Dritschel & McIntyre 2008;Scott & Dritschel 2012), in which potential vorticity is nearly homogenised in bands, but between which the potential vorticity abruptly jumps, forming a 'staircase' profile. Each jump is associated with a jet, eastward in the upper layer and westward in the lower layer, a direct effect of potential vorticity inversion (Dritschel & McIntyre 2008).…”

“…In the lower layer, by contrast, there are three bands of nearly homogeneous PV separated by two westward jets. As discussed in Dritschel & McIntyre (2008) and Scott & Dritschel (2012) in the context of a single-layer model, the 'equivalent latitude' PV profile y e (q) is particularly useful for identifying jets, here seen by the nearly flat portions of the curves shown in the right panels of these figures. The formation of a staircase profile in y e (q) indicates the presence of homogeneous regions (dy e /dq → ∞) and jets (dy e /dq → 0).…”

“…Instead, part of this decay must be due to inhomogeneous turbulent mixing, constrained by the mean PV gradient in each layer. The mixing acts to homogenise PV and sharpen jets, processes which are only enhanced by non-zonal variations (Dritschel & McIntyre 2008;Scott & Dritschel 2012). The mixing continues until most of the eddy energy (principally at higher wavenumbers where thermal damping is weak) is exhausted and converted into jets (qualitatively this is the argument behind the Rhines scale L Rh = U/β, where U characterises the eddy velocities and β is the background PV gradient, see Rhines (1975)).…”

“…Restoration of a linear slope would not have this effect, as a linear slope only generates a baroclinic flow, by construction. Instead, it must be that the eddying motions present even during quiescent phases continue to provide inhomogeneous PV mixing, maintaining sharp jets (Dritschel & McIntyre 2008;Scott & Dritschel 2012). These jets project on both barotropic and baroclinic modes, unlike the initial vertical shear flow.…”