Scale interactions of turbulence subjected to a straining–relaxation–destraining cycle

Abstract

The response of turbulence subjected to planar straining and de-straining is studied experimentally, and the impact of the applied distortions on the energy transfer across different length scales is quantified. The data are obtained using planar particle image velocimetry (PIV) in a water tank, in which high-Reynolds-number turbulence with very low mean velocity is generated by an array of spinning grids. Planar straining and de-straining mean flows are produced by pushing and pulling a rectangular piston towards, and away from, the bottom wall of the tank. The data are processed to yield the time evolution of Reynolds stresses, anisotropy tensors, turbulence kinetic energy production, and mean subgrid-scale (SGS) dissipation rate at various scales. During straining, the production rises rapidly. After the relaxation period the small-scale SGS stresses recover isotropy, but the Reynolds stresses still display significant anisotropy. Thus when destraining is applied, a strong negative production (mean backscatter) occurs, i.e. the turbulence returns kinetic energy to the mean flow. The SGS dissipation displays similar behaviour at large filter scales, but the mean backscatter gradually disappears with decreasing filter scales. Energy spectra are compared to predictions of rapid distortion theory (RDT). Good agreement is found for the initial response but, as expected for the timescale ratios of the experiment, turbulence relaxation causes discrepancies between measurements and RDT at later times.

A spectral model for homogeneous shear-driven anisotropic turbulence in terms of spherically averaged descriptors

“…Different relaxation rates for directional anisotropy and polarization anisotropy allow us to correctly interpret the apparent delay in the RTI after axisymmetric expansion (Zusi & Perot 2014). In addition, our model fits well the recent experiment of Chen et al (2006) with a non-stationary straining cycle. For turbulence continuously subjected to a pure plane shear, the model ensures a correct asymptotic regime with constant values for the components of the dimensionless deviatoric tensor b ij (t) associated with the Reynolds stress tensor.…”

“…Figure 3(b) illustrates the temporal evolution of the anisotropy indicatorb 11 (t) defined by (4.7). Experimental and numerical values obtained with the present model are reported, along with the RDT prediction, provided by Chen et al (2006), corresponding to the mean flow defined by (4.12) and figure 3(a). The temporal evolution ofb 11 (t) shows good agreement between the experiment and the present model.…”

“…In these studies, two successive plane strains with different orientations are applied to grid-generated turbulence, and the RTI of the turbulence thus obtained is investigated in the latter experiment. We then consider the experiment of Chen, Meneveau & Katz (2006), where turbulence is subjected to a non-stationary straining-relaxation-destraining cycle. Both linear and nonlinear phenomena come into play in the response of turbulence to this particular straining.…”

“…The present model is further tested by comparing its predictions with the experiment of Chen et al (2006), where a piston is used to apply plane straining and destraining on turbulence generated by active grids. The mean-velocity gradient in the experiment is of the form (4.12) where the temporal evolution of S(t) is given by figure 3(a).…”

“…Initially, the mean flow corresponds to plane straining (S(t) > 0), until t/τ 0 0.5. After a relaxation (----) for the temporal evolution of the anisotropy indicatorb 11 (t) in the experiment of Chen et al (2006). phase (0.5 t/τ 0 0.7), destraining (S(t) < 0) is applied to the turbulence.…”