Jolly, M.S. and Wirosoetisno, D. (2018) 'Energy spectra and passive tracer cascades in turbulent flows.', Journal of mathematical physics., 59 (7). 073104.
We study the influence of the energy spectrum on the extent of the cascade range of a passive tracer in turbulent flows. The interesting cases are when there are two different spectra over the potential range of the tracer cascade (in 2D when the tracer source is in the inverse energy cascade range and in 3D when the Schmidt number Sc is large). The extent of the tracer cascade range is then limited by the width of the range for the shallower of the two energy spectra. Nevertheless, we show that in dimension d = 2, 3, the tracer cascade range extends (up to a logarithm) to κ p dD , where κdD is the wavenumber beyond which diffusion should dominate and p is arbitrarily close to 1, provided Sc is larger than a certain power (depending on p) of the Grashof number. We also derive estimates which suggest that in 2D, for Sc ∼ 1, a wide tracer cascade can coexist with a significant inverse energy cascade at Grashof numbers large enough to produce a turbulent flow.
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|Publisher Web site:||https://doi.org/10.1063/1.5046773|
|Publisher statement:||© 2018 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Jolly, M.S. & Wirosoetisno, D. (2018). Energy spectra and passive tracer cascades in turbulent flows. Journal of Mathematical Physics 59(7): 073104 and may be found at https://doi.org/10.1063/1.5046773|
|Date accepted:||29 June 2018|
|Date deposited:||05 July 2018|
|Date of first online publication:||19 July 2018|
|Date first made open access:||19 July 2019|
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