Energy spectra and passive tracer cascades in turbulent flows

Jolly, M.S.; Wirosoetisno, D.

Abstract

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.

Citation

Jolly, M., & Wirosoetisno, D. (2018). Energy spectra and passive tracer cascades in turbulent flows. Journal of Mathematical Physics, 59(7), Article 073104. https://doi.org/10.1063/1.5046773

• Journal Article Type: Article
• Acceptance Date: Jun 29, 2018
• Online Publication Date: Jul 19, 2018
• Publication Date: Jul 19, 2018
• Deposit Date: May 16, 2018
• Publicly Available Date: Jul 5, 2018
• Journal: Journal of Mathematical Physics
• Print ISSN: 0022-2488
• Electronic ISSN: 1089-7658
• Publisher: American Institute of Physics
• Peer Reviewed: Peer Reviewed
• Volume: 59
• Issue: 7
• Article Number: 073104
• DOI: https://doi.org/10.1063/1.5046773
• Public URL: https://durham-repository.worktribe.com/output/1326135