The structure of zonal jets in geostrophic turbulence

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_g, where L_Rh = √U/β and L_g = (ε/β³)^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_g, 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_g ∼ 0(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_g is robust across a variety of different forcing types considered.