Scalings of scalar structure functions in a velocity field with coherent vortical structures.
In planar turbulence modeled as an isotropic and homogeneous collection of two-dimensional noninteracting compact vortices, the structure functions S(p)(r) of a statistically stationary passive scalar field have the following scaling behavior in the limit where the Péclet number Pe-->infinity: S(p)(r) approximately const+ln(r/L Pe(-1/3)) for L Pe(-1/3)<<r<<L, S(p)(r) approximately (r/L Pe(-1/3))(6(1-D)) for L Pe(-1/2)<<r<<L Pe(-1/3), where L is a large scale and D is the fractal codimension of the spiral scalar structures generated by the vortices (1/2 < or =D < 2/3). Note that L Pe(-1/2) is the scalar Taylor microscale that stems naturally from our analytical treatment of the advection-diffusion equation. The essential ingredients of our theory are the locality of interscale transfer and Lundgren's time average assumption. A phenomenological theory explicitly based only on these two ingredients reproduces our results and a generalization of this phenomenology to spatially smooth chaotic flows yields (k ln k)(-1) generalized power spectra for the advected scalar fields.
Khan
M A I
MA
Department of Applied Mathematics and Theoretical Physics, Silver Street, University of Cambridge, Cambridge CB3 9EW, United Kingdom.
Vassilicos
J C
JC