Geostrophic turbulence near rapid changes in stratification

Geostrophic turbulence near horizontal surfaces on which the vertical velocity vanishes exhibits a forward cascade of buoyancy variance, characterized by a shallow energy spectrum, secondary roll-up of filaments, and a fat-tailed vorticity probability distribution. Such surfaces occur at rigid boundaries, but also at discontinuous jumps in stratification. Here we relax this mathematical idealization and investigate geostrophic turbulence near a rapid but smooth jump in stratification, modeled by N(z) = N0[1 + αtanh (z/h)]. The rapidity of change is controlled by the length scale h and the profile approaches a step function as h → 0. The approximated Green’s function for the quasigeostrophic potential vorticity (PV) is used to predict the spectral PV-streamfunction relationship, under various assumptions about the distribution of the initial PV. Numerical simulations of freely-evolving quasigeostrophic turbulence in the presence of the model stratification support the predictions and reveal that the jump has two effects: it alters the Green’s function in the region of the jump and it produces a peak in PV near the jump, approaching a Dirac delta-function as the jump scale h → 0. When the Green’s function is integrated against this sharp PV distribution, contributions far from the jump (|z| " h) are suppressed and the flow in a region |z| ! O(h) exhibits surface effects. This occurs for horizontal scales L " N0h/f, the deformation scale associated with the jump. These results have implications for geostrophic turbulence near the tropopause in the atmosphere and the base of the mixed layer in the ocean. C © 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4799470]