Journal of Fluid Mechanics

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On the Lamb vector divergence in Navier–Stokes flows

CURTIS W. HAMMANa1 p1, JOSEPH C. KLEWICKIa2 and ROBERT M. KIRBYa1a3

a1 Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, UT 84112, USA

a2 Department of Mechanical Engineering, University of New Hampshire, Durham, NH 03824, USA

a3 School of Computing, University of Utah, Salt Lake City, UT 84112, USA

Abstract

The mathematical and physical properties of the Lamb vector divergence are explored. Toward this aim, the instantaneous and mean dynamics of the Lamb vector divergence are examined in several analytic and turbulent flow examples relative to its capacity to identify and characterize spatially localized motions having a distinct capacity to effect a time rate of change of momentum. In this context, the transport equation for the Lamb vector divergence is developed and shown to accurately describe the dynamical mechanisms by which adjacent high- and low-momentum fluid parcels interact to effect a time rate of change of momentum and generate forces such as drag. From this, a transport-equation-based framework is developed that captures the self-sustaining spatiotemporal interactions between coherent motions, e.g. ejections and sweeps in turbulent wall flows, as predicted by the binary source–sink distribution of the Lamb vector divergence. New insight into coherent motion development and evolution is found through the analysis of the Lamb vector divergence.

(Received May 10 2007)

(Revised May 27 2008)

Correspondence:

p1 Present address: Center for Turbulence Research, Stanford University, Stanford, CA, USA.

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