Skip to main content

Research Repository

Advanced Search

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

Jolly, MS; Wirosoetisno, D

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


MS Jolly


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.


Jolly, M., & Wirosoetisno, D. (2020). Tracer turbulence: the Batchelor--Howells--Townsend spectrum revisited. Journal of Mathematical Fluid Mechanics, 22(2), Article 18.

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
Related Public URLs


Accepted Journal Article (358 Kb)

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:

You might also like

Downloadable Citations