Invariant solutions in a channel flow using a minimal restricted nonlinear model

Frédéric Alizard

doi:10.1016/j.crme.2016.11.005

Invariant solutions in a channel flow using a minimal restricted nonlinear model

Frédéric Alizard ^1,²

¹ LMFA, CNRS, Ecole Centrale de Lyon, Université Lyon 1, INSA Lyon, France
² DynFluid–CNAM, 151, boulevard de l'Hôpital, 75013 Paris, France

Comptes Rendus. Mécanique, Volume 345 (2017) no. 2, pp. 117-124.

Abstract

Simulations using a Restricted Nonlinear (RNL) system, where mean flow distortion resulting from Reynolds stress feedback regenerates rolls, is applied in a channel flow under subcritical conditions. This quasi-linear restriction of the dynamics is used to study invariant solutions located in the bulk of the flow found recently by Rawat et al. (2016) [14]. It is shown that the RNL system truncated to a single streamwise mode for the perturbation supports invariant solutions that are found to bifurcate from a relative periodic orbit into a travelling wave solution when the spanwise size is increasing. In particular, the travelling wave solution exhibits a spanwise localized structure that remains unchanged for large values of the spanwise extent as the invariant solution lying on the lower branch found by Rawat et al. (2016) [14]. In addition, travelling wave solutions provided by this minimal RNL system are self-similar with respect to the Reynolds number based on the centreline velocity, and the half-channel height varying from 2000 to 5000.

Received: 2016-09-05
Accepted: 2016-11-28
Published online: 2016-12-12

DOI: 10.1016/j.crme.2016.11.005

Keywords: Channel flow, Invariant solutions, Subcritical transition

Author's affiliations:

Frédéric Alizard ^{1, 2}

¹ LMFA, CNRS, Ecole Centrale de Lyon, Université Lyon 1, INSA Lyon, France
² DynFluid–CNAM, 151, boulevard de l'Hôpital, 75013 Paris, France

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     title = {Invariant solutions in a channel flow using a minimal restricted nonlinear model},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {117--124},
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     language = {en},
}

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Frédéric Alizard. Invariant solutions in a channel flow using a minimal restricted nonlinear model. Comptes Rendus. Mécanique, Volume 345 (2017) no. 2, pp. 117-124. doi : 10.1016/j.crme.2016.11.005. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2016.11.005/

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