Dynamic mode decomposition of H-type transition to turbulence

Dynamic mode decomposition (DMD) [1] is applied to a direct numerical simulation database of H-type transition to turbulence of a compressible, nominally-zero-pressure-gradient, spatially developing flat-plate boundary layer. The objective of this work is to identify the structures of dynamical importance throughout the transition region. DMD, viewed as an optimal phase averaging process in the context of the triple decomposition [2], is employed to assess the contribution of each coherent structure to the total Reynolds shear stress. In this region, it is observed that the total Reynolds shear stress gradient can be estimated accurately from only a few low-frequency DMD modes. These low-frequency modes are observed to correspond to the legs of hairpin vortices. Furthermore, DMD is applied to a large-eddy simulation (LES) database of the same configuration, generated using the dynamic Smagorinsky subgrid-scale model. The low-frequency DMD modes extracted from the LES, are, however, of lower amplitude than in the DNS, resulting in an underprediction of the Reynolds shear stress gradient and corresponding skin-friction coefficients.\\[4pt] [1] Schmid, P. J. JFM, 1-24, 2010.\\[0pt] [2] Reynolds, W. C. and Hussain, A. K. M. F. JFM, \textbf{54}, 236-288, 1972.