Eckhaus-like instability of large scale coherent structures in a fully turbulent von Karman flow

E Herbert 1 P.-P Cortet 2 François Daviaud 1 Bérengère Dubrulle 1
1 SPHYNX - Systèmes Physiques Hors-équilibre, hYdrodynamique, éNergie et compleXes
SPEC - UMR3680 - Service de physique de l'état condensé, IRAMIS - Institut Rayonnement Matière de Saclay
Abstract : The notion of instability of a turbulent flow is introduced in the case of a von Kármán flow thanks to the monitoring of the spatio-temporal spectrum of the velocity fluctuations , combined with projection onto suitable Beltrami modes. It is shown that the large scale coherent fluctuations of the flow obey a sequence of Eckhaus instabilities when the Reynolds number Re is varied from 10 2 to 10 6. This sequence results in modulations of increasing azimuthal wavenumber. The basic state is the laminar or time-averaged flow at an arbitrary Re, which is axi-symmetric, i.e., with a 0 azimuthal wavenumber. Increasing Re leads to non-axisymmetric modulations with increasing azimuthal wavenumber from 1 to 3. These modulations are found to rotate in the azimuthal direction. However, no clear rotation frequency can be established until Re ≈ 4 × 10 3. Above, they become periodic with an increasing frequency. We finally show that these modulations are connected with the coherent structures of the mixing shear layer. The implication of these findings for the turbulence parametriza-tion is discussed. Especially, they may explain why simple eddy viscosity models are able to capture complex turbulent flow dynamics.
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E Herbert, P.-P Cortet, François Daviaud, Bérengère Dubrulle. Eckhaus-like instability of large scale coherent structures in a fully turbulent von Karman flow. Physics of Fluids, American Institute of Physics, 2014, 26, pp.015103. ⟨10.1063/1.4855018⟩. ⟨cea-01373320⟩

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