Journal of Fluid Mechanics


The structure of zonal jets in geostrophic turbulence

Richard K. Scotta1 c1 and David G. Dritschela1

a1 School of Mathematics and Statistics, University of St Andrews, St Andrews KY16 9SS, UK


The structure of zonal jets arising in forced-dissipative, two-dimensional turbulent flow on the $\ensuremath{\beta} $-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 non-dimensional parameter, which may be conveniently expressed as the ratio ${L}_{\mathit{Rh}} / {L}_{\varepsilon } $, where ${L}_{\mathit{Rh}} = \sqrt{U/ \ensuremath{\beta} } $ and ${L}_{\varepsilon } = \mathop{ (\varepsilon / {\ensuremath{\beta} }^{3} )}\nolimits ^{1/ 5} $ are two natural length scales arising in the problem; here $U$ may be taken as the r.m.s. velocity, $\ensuremath{\beta} $ is the background gradient of potential vorticity in the north–south direction, and $\varepsilon $ is the rate of energy input by the forcing. It is shown that jet strength increases with ${L}_{\mathit{Rh}} / {L}_{\varepsilon } $, with the limiting case of the potential vorticity staircase, comprising a monotonic, piecewise-constant profile in the north–south direction, being approached for ${L}_{\mathit{Rh}} / {L}_{\varepsilon } \ensuremath{\sim} O(10)$. 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}_{\mathit{Rh}} / {L}_{\varepsilon } $ is robust across a variety of different forcing types considered.

(Received October 26 2011)

(Reviewed July 17 2012)

(Accepted August 09 2012)

(Online publication September 20 2012)

Key Words:

  • geostrophic turbulence;
  • quasi-geostrophic flows;
  • turbulent mixing


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