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The Scalings of Scalar Structure Functions in a Velocity Field with Coherent Vortical Structures | | Md. A. I. Khan
; J. C. Vassilicos
; | | Date: |
10 Mar 2000 | | Journal: | Phys. Rev. E, vol 65, 2002. | | Subject: | Chaotic Dynamics | nlin.CD | | Abstract: | In planar turbulence modelled as an isotropic and homogeneous collection of 2-D non-interacting compact vortices, the structure functions S_p(r) of a statistically stationary passive scalar field have the following scaling behaviour in the limit where the Péclet number Pe -> infty S_p(r) ~ constant+ln({frac{r}{LPe^{-1/3}}}) for LPe^{-1/3} << L, S_p(r) ~ ({frac{r}{LPe^{-1/3}}})^{6(1-D)} for LPe^{-1/2} << LPe^{-1/3}, where L is a large scale and D is the fractal co-dimension of the spiral scalar structures generated by the vortices (1/2 <= D < 2/3). Note that LPe^{-1/2} is the scalar Taylor microscale which stems naturally from our analytical treatment of the advection-diffusion equation. The essential ingredients of our theory are the locality of inter-scale transfer and Lundgren’s time average assumption. A phenomenological theory explicitly based only on these two ingredients reproduces our results and a generalisation of this phenomenology to spatially smooth chaotic flows yields (kln k)^{-1} generalised power spectra for the advected scalar fields. | | Source: | arXiv, nlin.CD/0003027 | | Services: | Forum | Review | PDF | Favorites | |
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