Decay and growth laws in homogeneous shear turbulence

Abstract

International audienceHomogeneous anisotropic turbulence has been widely studied in the past decades, both numerically and experimentally. Shear flows have received a particular attention because of the numerous physical phenomena they exhibit. In the present paper, both the decay and growth of anisotropy in homogeneous shear flows at high Reynolds numbers are revisited thanks to a recent eddy-damped quasi-normal Markovian (EDQNM) closure adapted to homogeneous anisotropic turbulence. The emphasis is put on several aspects: an asymptotic model for the slow-part of the pressure-strain tensor is derived for the return to isotropy process when mean-velocity gradients are released. Then, a general decay law for purely anisotropic quantities in Batchelor turbulence is proposed. At last, a discussion is proposed to explain the scattering of global quantities obtained in DNS and experiments in sustained shear flows: the emphasis is put on the exponential growth rate of the kinetic energy and on the shear parameter

Spectral modelling for passive scalar dynamics in homogeneous anisotropic turbulence

“…This means that initial large scales velocity gradients do not alter the longtime decay of scalar integrated quantities. Such a result for the scalar field is similar to what was found for the velocity one (Briard et al 2016).…”

“…The important result here is that the value of the scalar exponential decay rate γ T seems not to depend on the shear rate S for moderate intensity, nor on the infrared exponents σ and σ T (and neither does γ for the exponential growth of K(t) (Briard et al 2016)). The scalar dissipation ǫ T , also displayed in figure 7, exponentially decreases with the same rate γ T = −0.52, which is consistent with the evolution equation (4.14).…”

“…As mentioned before, the kinetic energy eventually grows exponentially in shear flows at the rate γ = 0.34, defined in (4.13), within the present anisotropic EDQNM closure in a completely homogeneous framework Briard et al 2016). In this part, the emphasis is put on the growth of the scalar variance and its interactions with the Here is what happens simultaneously: the cross-correlation R 13 produces K S F through the mean scalar gradient Λ. R 13 brings energy to the transverse component R 33 thanks to non-linear redistribution, which causes K F to grow as well through Λ.…”

“…The estimation due to the present modelling gives γ ≃ 0.34. This seemingly high value of γ is discussed in Briard et al (2016). The relevant question is now: is there a similar growth for the scalar variance K T (t)?…”

Advanced spectral anisotropic modelling for shear flows

“…In the past years, the authors have analysed separately each of these configurations with the help of an adapted eddy-damped quasi-normal Markovian (EDQNM) closure able of handling strongly anisotropic flows, in order to better understand what are the intrinsic properties of each mechanism. A significant amount of results, both theoretical and numerical, were exposed in various publications [1][2][3][4][5][6][7][8][9], and still a lot of work needs to be done regarding shear flows specifically. Indeed, the anisotropic EDQNM model developed in Mons, Cambon, and Sagaut (MCS) [1] handles very satisfactorily various straining processes, for instance when the mean-velocity gradient matrix is symmetric, like in axisymmetric contractions or expansions, or in plane distortions.…”