Tracer turbulence: the Batchelor--Howells--Townsend spectrum revisited

Jolly, MS; Wirosoetisno, D

doi:10.1007/s00021-019-0478-6

Tracer turbulence: the Batchelor--Howells--Townsend spectrum revisited

Jolly, MS; Wirosoetisno, D

Authors

MS Jolly

Dr Djoko Wirosoetisno djoko.wirosoetisno@durham.ac.uk
Associate Professor

Abstract

Given a velocity field u(x, t), we consider the evolution of a passive tracer θ governed by ∂tθ + u · ∇θ = Δθ + g with time-independent source g(x). When u is small in some sense, Batchelor, Howells and Townsend (J Fluid Mech 5:134, 1959) predicted that the tracer spectrum scales as |θk| 2 ∝ |k| −4|uk| 2. In this paper we prove that, for random synthetic two-dimensional incompressible velocity fields u(x, t) with given energy spectra, this scaling does indeed hold probabilistically, asymptotically almost surely for large |k| and small u. We also propose an asymptotic correction factor to the BHT scaling arising from the time-dependence of u.

Citation

Jolly, M., & Wirosoetisno, D. (2020). Tracer turbulence: the Batchelor--Howells--Townsend spectrum revisited. Journal of Mathematical Fluid Mechanics, 22(2), Article 18. https://doi.org/10.1007/s00021-019-0478-6

Journal Article Type	Article
Acceptance Date	Dec 6, 2019
Online Publication Date	Feb 24, 2020
Publication Date	Jun 30, 2020
Deposit Date	Dec 6, 2019
Publicly Available Date	Feb 24, 2021
Journal	Journal of Mathematical Fluid Mechanics
Print ISSN	1422-6928
Electronic ISSN	1422-6952
Publisher	Springer
Peer Reviewed	Peer Reviewed
Volume	22
Issue	2
Article Number	18
DOI	https://doi.org/10.1007/s00021-019-0478-6
Related Public URLs	https://arxiv.org/abs/1907.12633

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Copyright Statement
This is a post-peer-review, pre-copyedit version of an article published in Journal of mathematical fluid mechanics. The final authenticated version is available online at: https://doi.org/10.1007/s00021-019-0478-6