University of Minnesota
Aerospace Engineering and Mechanics
Spring 1998 Seminar Series



The Inverse Turbulent Cascade and its Consequences in Laboratory and Astrophysical Flows


Professor Philip S. Marcus

Department of Mechanical Engineering
University of California, Berkeley


Abstract


One way of determining if one truly understands a physical process is to consider how that process acts under atypical conditions. Here we are interested in ³two-dimensional² turbulence in a three-dimensional world. In particular we interested in finding if the familiar concepts of a inverse energy cascade can be used to explain the large-scale structures of the atmospheres of Jupiter and Saturn which are dominated by long-lived east-west (zonal) flows.

Little is known about what sets their velocity scales or their length scales (i.e., the number of zones on each planet). Typically, the energy-containing modes in a turbulent flow span a range of scales, and in the rare cases that there are coherent features and that they all have the same size, their lengths are usually determined directly by the boundaries or the forcing length scales, e.g. the diameters of turbulent Taylor vortices in a Couette apparatus are determined by the width of the apparatus. Even turbulence in geophysical flows show this trait: the scale of granulation on the Sun (due to turbulent convection cells) is set by the depth of the convective zone; Jupiter's long-lived vortices, such as the Red Spot, are set by the widths of the local zonal flows in which they are situated.

By examining a simple forced/dissipated flow we show that the widths of zonal flows on a b-plane are determined by a subtle combination of the forcing and dissipation and not set by boundary conditions or by the length scale of the forcing.

We show that under a wide variety of conditions a turbulent flow without east-west winds forms via a inverse energy cascade and that zonal flows (with a single dominant length scale) form only for a small set of parameters.

We present a simple theory which determines these parameter values and which also provides scaling laws for the zones' velocities and widths. Thus we are able to adjust the widths and strengths of the zonal flows by changing the forcing and dissipation rates. We show that the coherent and the incoherent parts of the energy spectrum obey different scaling laws and we explain why. We show how two different effects block the energy cascade and lead to departures from Kolmogorov scaling. We discuss the implications for Jupiter, compare the numerical experiments with similar ones carried out previously by others, and show how one could build a laboratory experiment that would form jovian--like winds with two easily adjustable control parameters that determine their widths and strengths.

Friday, April 17, 1998
209 Akerman Hall
2:30-3:30 p.m.


Refreshments served after the seminar in 227 Akerman Hall.
Disability accomodations provided upon request.
Contact Audrey Stark-Evers, Senior Secretary, 625-8000.