Fractal measures of passively convected vector fields and scalar gradients in chaotic fluid flows
The passive convection of vector fields and scalar functions by a prescribed incompressible fluid flow v(x,t) is considered for the case where v(x,t) is chaotic. By chaotic v(x,t) it is meant that typical nearby fluid elements diverge from each other exponentially in time. It is shown that in such cases, as time increases, a convected vector field and the gradient of a convected scalar will generally concentrate on a set which is fractal. The present paper relates the stretching properties of the flow to the resulting fractal dimension spectrum. Motivation for these considerations is provided by the kinematic magnetic dynamo problem (in the vector case) and (in the scalar case) by recent experiments which demonstrate the possibility of measuring the fractal dimension of the gradient squared of convected passive scalars.
- Research Organization:
- Laboratory for Plasma Research, Department of Electrical Engineering Department of Physics and Astronomy, University of Maryland, College Park, Maryland 20742
- OSTI ID:
- 6449933
- Journal Information:
- Phys. Rev. A; (United States), Journal Name: Phys. Rev. A; (United States) Vol. 39:7; ISSN PLRAA
- Country of Publication:
- United States
- Language:
- English
Similar Records
The spectrum of fractal dimensions of passively convected scalar gradients
Chaotic flows and fast magnetic dynamos