COHERENT FINE-SCALE EDDY CLUSTER IN A TURBULENT MIXING LAYER

Clustering of coherent fine-scale structures in a turbulent mixing layer has been analyzed by a direct numerical simulation (DNS) data at Reλ ' 250. The coherent fine-scale structures are extracted based on the second invariant of the velocity gradient tensor and the vorticity vector. Their characteristics are consistent with the lower Reynolds number data. The clustering is evaluated by the number density of coherent fine-scale eddies. The large-scale structures are extracted by low-pass filtering velocity data. The correlations between the number density and large-scale turbulence characteristics such as the enstrophy, the strain rate magnitude and the enstrophy amplification rate are investigated. The enstrophy is more correlated with the number density compared to the strain rate and the enstrophy amplification rate. Furthermore, the alignments of the vorticity vector and the eigenvectors of the large-scale strain rate tensor are evaluated. These alignment are computed by imposing a condition on the number density or the strain rate magnitude. The intense strain rate indicates the strong preferential alignment between the vorticity and the eigenvectors. On the other hand, the alignment becomes weaker in the high number density region of the fine-scale eddies. Finally, the inter-scale energy transfer is evaluated from the energy transfer between grid and subgrid scales. By definition, the significant positive correlation is observed in the magnitude of the strain rate and the inter-scale energy transfer while it is not much apparent with the number density. INTRODUCTION In the classical picture of turbulence, the kinetic energy is injected at a large-scale, and it is transferred through the inertial subrange down to small dissipative scales. This is hypothesized in physical space such that a large-scale eddy is broken into smaller ones until the energy is dissipated into heat. Such small-scale turbulence structures responsible for dissipation are represented by eddies with the most probable diameter of 8η (Tanahashi et al., 1997, 2001; Wang et al., 2007), and they are known as worms (Jiménez et al., 1993). These small-scale turbulence structures exhibit universal characteristics in different flow types (Tanahashi et al., 1997, 2001, 2004; Wang et al., 2007). On the other hand, it is not straightforward to define turbulence structures responsible for the energy cascade in physical space. Leung et al. (2012) identified structures of different scales by using band pass filtering, and found that ∗Present affiliation: Department of Aeronautics and Astronautics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan the energy cascade process is relevant to the vortex stretching by a slightly larger scale, which is consistent with the classical picture of energy cascade. They have also pointed out that small-scale structures tend to form clusters around a larger structure. The relation between the coherent fine-scale eddy cluster and the energy cascade in a homogeneous isotropic turbulence has been investigated by Tanahashi et al. (2008). Clustering of fine-scale eddies in the near wall region of the turbulent channel flow has also been revealed by Kang et al. (2007). Clustering of small-scale structures has been also found by Ishihara et al. (2013). The scale of the cluster is significantly larger than the Kolmogorov length scale and it has an order of the integral length scale. The strain rate and the vorticity are two fundamental quantities to describe the dynamics of turbulence. Buxton et al. (2011) analyzed their interaction based on the transport equations of the enstrophy and the magnitude of the strain rate tensor. The key quantity is that the production term in the enstrophy equation, ωiSi jω j , where ωi = εi jkWjk is the vorticity vector, Si j is the strain rate tensor and Wi j is the rotation rate tensor. Fiscaletti et al. (2016) investigated scale interactions by amplitude modulation analyses. The present study analyzes the large-scale clustering of coherent fine-scale structures using a numerical database of a temporally developing turbulent mixing layer. A DNS at the turbulent Reynolds number Reλ ' 250 has been performed. The degree of clustering fine-scale turbulence is measured by the number density of the coherent fine-scale eddies. The large-scale strain and vorticity fields are obtained by applying low-pass filtering. The relation between the large-scale structures of the strain and the vorticity field, and clustering of the fine-scale turbulence structures is quantified. DNS OF A TURBULENT MIXING LAYER A DNS of a temporally developing turbulent mixing layer has been performed. The solver was originally developed and reported in our previous study (Tanahashi et al., 2001). Variables in the streamwise and spanwise directions are expanded into Fourier series and into sine/cosine series in the transverse direction. The time integration is conducted by the low-storage third-order Runge-Kutta scheme. The boundary conditions are periodic in the streamwise and spanwise directions, and free-slip in the transverse direction. The initial mean velocity distribution is given by a hyperbolic tangent profile: ũ(y) = 0.5tanh (2y), and the small random perturbations are superposed. The dimensions of computational domain are set to be 4Λ× 6Λ× 8/3Λ, where Λ is the most unstable wave-