Palinstrophy is the
curl
cURL (pronounced like "curl", ) is a free and open source computer program for transferring data to and from Internet servers. It can download a URL from a web server over HTTP, and supports a variety of other network protocols, URI scheme ...
of the
vorticity
In continuum mechanics, vorticity is a pseudovector (or axial vector) field that describes the local spinning motion of a continuum near some point (the tendency of something to rotate), as would be seen by an observer located at that point an ...
. It is defined as
where
is the vorticity.
Palinstrophy is mainly used in
turbulence
In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to laminar flow, which occurs when a fluid flows in parallel layers with no disruption between ...
study, where there is a need to quantify how vorticity is transferred from one direction to the others. It is closely related to
enstrophy In fluid dynamics, the enstrophy \mathcal can be interpreted as another type of potential density; or, more concretely, the quantity directly related to the kinetic energy in the flow model that corresponds to dissipation effects in the fluid. It i ...
, the latter being more equivalent to the "power" of vorticity.
References
*Lesieur, Marcel. "Turbulence in fluids: stochastic and numerical modeling." NASA STI/Recon Technical Report A 91 (1990): 24106.
*Pouquet, A., et al. "Evolution of high Reynolds number two-dimensional turbulence." Journal of Fluid Mechanics 72 (1975): 305-319.
*{{cite book, title=Turbulence: An Introduction for Scientists and Engineers, author=Davidson, P.A., date=2004, publisher=OUP Oxford, isbn=9780191589850, url=https://books.google.com/books?id=rkOmKzujZB4C&pg=PA571, page=571, accessdate=2015-11-15
Fluid dynamics