Despite significant advancements in the understanding of fluid flows, combustion and material technologies, hypersonic flight still presents numerous technological challenges. In hypersonic vehicles turbulence is critical in controlling heat generation in the boundary layer, mixing inside the combustor, generation of acoustic noise, and mass flow in the intake. The study of turbulence in highly compressible flows is challenging compared to incompressible due to a drastic change in the behavior of pressure and a relaxation of the incompressibility constraint. In addition fluid flow inside a flight vehicle is complicated by wall-effects, heat generation and complex boundary conditions. Homogeneous shear flow contains most of the relevant physics of boundary and mixing layers without the aforementioned complicating effects. In this work we aim to understand and characterize the role of pressure, velocity-pressure interaction, velocity-thermodynamics interaction in the late-stage transition-to-turbulence regime in a high speed shear dominated flow by studying the evolution of perturbations in in a high Mach number homogeneous shear flow. We use a modal-analysis based approach towards understanding the statistical behavior of turbulence. Individual Fourier waves constituting the initial flow field are studied in isolation and in combination to understand collective statistical behavior. We demonstrate proof of concept of novel acoustic based strategies for controlling the onset of turbulence. Towards this goal we perform direct numerical simulations (DNS) in three studies: (a) development and evaluation of gas kinetic based numerical tool for DNS of compressible turbulence, and perform detailed evaluation of the efficacy of different interpolation schemes in capturing solenoidal and dilatational quantities, (b) modal investigation in the behavior of pressure and isolation of linear, non-linear, inertial and pressure actions, and (c) modal investigation in the possible acoustic based control strategies in homogeneously sheared compressible flows. The findings help to understand the manifestation of the effects of compressibility on transition and turbulence via the velocity-pressure interactions and the action of individual waves. The present study helps towards the design of control mechanisms for compressible turbulence and the development of physically consistent pressure strain correlation models.

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Two codes have been developed and implemented for use on massively parallelsuper computers to simulate two-dimensional and quasigeostrophic turbulence.The codes have been found to scale well with increasing resolution and width ofthe simulations. This has allowed for the highest resolution simulations of two-dimensional and quasigeostrophic turbulence so far reported in the literature.The direct numerical simulations have focused on the statistical characteristicsof turbulent cascades of energy and enstrophy, the role of coherent vorticesand departures from universal scaling laws, theoretized more than 40 yearsago. In particular, the investigations have concerned the enstrophy and energycascade in forced and decaying two-dimensional turbulence. Furthermore, theapplicability of Charney’s hypotheses on quasigeostrophic turbulence has beentested. The results have shed light on the flow evolution at very large Reynoldsnumbers. The most important results are the robustness of the enstrophycascade in forced and decaying two-dimensional turbulence, the unexpecteddependency on an infrared Reynolds number in the spectral scaling of theenergy spectrum in the inverse energy cascade, and the validation of Charney’spredictions on the dynamics of quasigeostrophic turbulence. It has also beenshown that the scaling of the energy spectrum in the enstrophy cascade isinsensitive to intermittency in higher order statistics, but that corrections mightapply to the ”universal” Batchelor-Kraichnan constant.

<p>Two codes have been developed and implemented for use on massively parallelsuper computers to simulate two-dimensional and quasigeostrophic turbulence.The codes have been found to scale well with increasing resolution and width ofthe simulations. This has allowed for the highest resolution simulations of two-dimensional and quasigeostrophic turbulence so far reported in the literature.The direct numerical simulations have focused on the statistical characteristicsof turbulent cascades of energy and enstrophy, the role of coherent vorticesand departures from universal scaling laws, theoretized more than 40 yearsago. In particular, the investigations have concerned the enstrophy and energycascade in forced and decaying two-dimensional turbulence. Furthermore, theapplicability of Charney’s hypotheses on quasigeostrophic turbulence has beentested. The results have shed light on the flow evolution at very large Reynoldsnumbers. The most important results are the robustness of the enstrophycascade in forced and decaying two-dimensional turbulence, the unexpecteddependency on an infrared Reynolds number in the spectral scaling of theenergy spectrum in the inverse energy cascade, and the validation of Charney’spredictions on the dynamics of quasigeostrophic turbulence. It has also beenshown that the scaling of the energy spectrum in the enstrophy cascade isinsensitive to intermittency in higher order statistics, but that corrections mightapply to the ”universal” Batchelor-Kraichnan constant.</p>

Two codes have been developed and implemented for use on massively parallelsuper computers to simulate two-dimensional and quasi-geostrophic turbulence.The codes have been found to scale well with increasing resolution and width ofthe simulations. This has allowed for the highest resolution simulations of twodimensionaland quasi-geostrophic turbulence so far reported in the literature.The direct numerical simulations have focused on the statistical characteristicsof turbulent cascades of energy and enstrophy, the role of coherent vorticesand departures from universal scaling laws, theoretized more than 40 yearsago. In particular, the investigations have concerned the enstrophy and energycascades in forced and decaying two-dimensional turbulence. Furthermore, theapplicability of Charney’s hypotheses on quasi-geostrophic turbulence has beentested. The results have shed light on the flow evolution at very large Reynoldsnumbers. The most important results are the robustness of the enstrophycascade in forced and decaying two-dimensional turbulence, the sensitivity toan infrared Reynolds number in the spectral scaling of the energy spectrumin the inverse energy cascade range, and the validation of Charney’s predictionson the dynamics of quasi-geostrophic turbulence. It has also been shownthat the scaling of the energy spectrum in the enstrophy cascade is insensitiveto intermittency in higher order statistics, but that corrections apply to the”universal” Batchelor-Kraichnan constant, as a consequence of large-scale dissipationanomalies following a classical remark by Landau (Landau &amp; Lifshitz1987). Another finding is that the inverse energy cascade is maintained bynonlocal triad interactions, which is in contradiction with the classical localityassumption. / QC 20101029