Intermittency in the turbulent Ekman layer

Abstract

The structure of the turbulent Ekman layer is explored by examining the three-dimensional velocity fields generated by means of direct numerical simulation (DNS). Emphasis is placed on determining the relation between the instantaneous structure of the velocity field and the turbulent dissipation. The results of our simulation show the following: (1) The pseudo-dissipation exhibits lognormal behavior, with a magnitude range spanning many orders of magnitude, (2) in horizontal planes within the Ekman layer, spatially localized regions of high and low pseudo-dissipation are found, with a magnitude ratio of about 10⁴ between low and high regions, (3) the Ekman layer is found to be composed of a series of quasi-periodic plume-like structures, and (4) the pseudo-dissipation is found to be large at the outer edge of a typical plume, with much lower levels in the plume interior. Conjectures are put forth regarding the relevance of this work to known observations of clear air radar scattering, and suggestions are made for possible future efforts.

Keywords:

• Ekman boundary layer
• turbulence
• intermittency
• dissipation
• pseudo-dissipation
• flatness
• Tatarskii–Bragg scattering
• radar

Acknowledgements

This work was supported by the Office of Naval Research (Contract N00014-08-1-0086) via the Research Foundation of the City University of New York. Additional funding was provided by the Office of Naval Research (ONR) through the basic research program at the Naval Research Laboratory, and through the Counter Directed Energy Weapons Program at ONR. The authors would also like to thank the DOD-HPC program for the computer time and technical support.