The University of Southampton
University of Southampton Institutional Repository

On the simultaneous cascades of energy, helicity, and enstrophy in incompressible homogeneous turbulence

On the simultaneous cascades of energy, helicity, and enstrophy in incompressible homogeneous turbulence
On the simultaneous cascades of energy, helicity, and enstrophy in incompressible homogeneous turbulence
We characterise the incompressible turbulence cascade in terms of the concurrent inter-scale and inter-space exchanges of the scale-by-scale energy, helicity and enstrophy. The governing equations for the scale-by-scale helicity and enstrophy are derived in a similar fashion to that of the second order structure function obtained by Hill (2002). We apply these equations to both forced periodic turbulence and a von Kármán flow, focusing on scales in the dissipative range r = 2.5η, the near-dissipative range r = 0.5λ and the onset inertial range r = λ (where η and λ are the Kolmogorov and Taylor length scales, respectively). The well-known random sweeping effect in the energy cascade between unsteady and non-linear transport is found to extend across all quantities considered. Additional mechanisms within the individual cascades are identified. Across cascades, the helicity cascade was found to be decorrelated from the others at all scales, however a connection between the energy cascade and helicity itself is identified kinematically. Further, the large-scale sweeping motions captured by the two-point velocity sum Σu i = u i + u i are shown to be a key element in the cascade of energy.
0022-1120
Baj, Pawel
49fc4e45-ccba-4239-aca1-dd2ae896f0ca
Alves Portela, Felipe
111319ab-31b1-4fbe-9afd-49958c6d9c4c
Carter, Douglas
75fd127b-b918-4bd3-9ada-6e1c7e1ad69d
Baj, Pawel
49fc4e45-ccba-4239-aca1-dd2ae896f0ca
Alves Portela, Felipe
111319ab-31b1-4fbe-9afd-49958c6d9c4c
Carter, Douglas
75fd127b-b918-4bd3-9ada-6e1c7e1ad69d

Baj, Pawel, Alves Portela, Felipe and Carter, Douglas (2022) On the simultaneous cascades of energy, helicity, and enstrophy in incompressible homogeneous turbulence. Journal of Fluid Mechanics. (doi:10.13140/RG.2.2.33457.04965). (In Press)

Record type: Article

Abstract

We characterise the incompressible turbulence cascade in terms of the concurrent inter-scale and inter-space exchanges of the scale-by-scale energy, helicity and enstrophy. The governing equations for the scale-by-scale helicity and enstrophy are derived in a similar fashion to that of the second order structure function obtained by Hill (2002). We apply these equations to both forced periodic turbulence and a von Kármán flow, focusing on scales in the dissipative range r = 2.5η, the near-dissipative range r = 0.5λ and the onset inertial range r = λ (where η and λ are the Kolmogorov and Taylor length scales, respectively). The well-known random sweeping effect in the energy cascade between unsteady and non-linear transport is found to extend across all quantities considered. Additional mechanisms within the individual cascades are identified. Across cascades, the helicity cascade was found to be decorrelated from the others at all scales, however a connection between the energy cascade and helicity itself is identified kinematically. Further, the large-scale sweeping motions captured by the two-point velocity sum Σu i = u i + u i are shown to be a key element in the cascade of energy.

Text
Simultaneous_turbulence_cascades_accepted - Accepted Manuscript
Available under License Creative Commons Attribution.
Download (2MB)

More information

Accepted/In Press date: 24 October 2022

Identifiers

Local EPrints ID: 471992
URI: http://eprints.soton.ac.uk/id/eprint/471992
ISSN: 0022-1120
PURE UUID: 82c3a864-0099-4df8-a0bd-868fcc5332a4

Catalogue record

Date deposited: 23 Nov 2022 17:45
Last modified: 06 Dec 2022 17:44

Export record

Altmetrics

Contributors

Author: Pawel Baj
Author: Felipe Alves Portela
Author: Douglas Carter

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×