Interscale energy transport in quasi-two dimensional turbulent Ekman layer simulations

The nature of the interaction among turbulent motions, mesoscale circulations, and intermediate sub-mesoscale motions is poorly understood. Of particular interest is the impact that meso and sub mesoscales of have on the turbulent energy cascade and turbulent mixing at scales on the order of the boundary layer height. Understanding these interactions has the potential to improve our ability to model dispersion in atmospheric and ocean systems. Here, a series of large eddy simulations of the turbulent Ekman layer are presented for a range of Rossby numbers to study interscale energy transport in high aspect ratio domains. In the simulations, the ratio between the horizontal domain extent and the vertical domain height is approximately 85. In all of the simulations, persistent alternating high and low speed two-dimensional streaks are observed in the velocity field. These streaks have a spanwise width of approximately 1-3 Ekman layer heights and a streamwise length of approximately 20-30 Ekman layer heights. Analysis of the interscale energy transfer indicates that in the surface layer, energy dissipation has two scaling ranges. One at scales greater than or equal to the Ekman layer height and another at scales smaller than the Ekman layer height. Away from the surface, energy dissipation peaks at approximately the Ekman layer height at which point it decreases linearly at a constant rate. Streamwise velocity spectra in the surface layer also exhibit an additional scaling range at length scales significantly larger than the Ekman layer height that is not present away from the surface. It is hypothesized that these additional scaling ranges are a result of the interaction of meandering large scale two-dimensional motions with surface layer turbulence.