On the Lamb vector divergence in Navier-Stokes flows. (English) Zbl 1147.76015

Hamman, Curtis W.; Klewicki, Joseph C.; Kirby, Robert M.

J. Fluid Mech. 610, 261-284 (2008).

Summary: We explore the mathematical and physical properties of Lamb vector divergence. Toward this aim, the instantaneous and mean dynamics of 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 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 Lamb vector divergence. New insight into coherent motion development and evolution is found through the analysis of Lamb vector divergence.

MSC:

76D05	Navier-Stokes equations for incompressible viscous fluids
76F10	Shear flows and turbulence

Keywords:

time rate of change of momentum; transport equation; coherent motions

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