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

Jolly, M.S. and Wirosoetisno, D. (2020) 'Tracer turbulence : the Batchelor--Howells--Townsend spectrum revisited.', Journal of mathematical fluid mechanics., 22 (2). p. 18.


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.

Item Type:Article
Full text:(AM) Accepted Manuscript
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Publisher 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:
Date accepted:06 December 2019
Date deposited:12 December 2019
Date of first online publication:24 February 2020
Date first made open access:24 February 2021

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