Analytical and Computational Challenges of Incompressible Flows at High Reynolds Number

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Variability of Turbulence and its Outer Scales

Dr. Alex Mahalov

Department of Mathematics at Arizona State University

Abstract:   Variability of flow regimes and turbulence scalings in a model of an inhomogeneously stratified, tropopause jet is investigated through high-resolution, forced, three-dimensional numerical simulations (with 512 or 1024 vertical levels). Multi-valued scaling branches, with respect to the local gradient Richardson number, are shown to occur in several turbulent quantities (such as variances, fluxes, mixing efficiency, outer scales and their ratios etc.). We find two distinct scaling curves for the upper and lower flanks of the jet, each showing a clear branch switching at a critical height. Distinct scaling curves in the upper and lower flanks of the jet can be related to the doubling of buoyancy frequency in the background profile (across the model tropopause). The vertical levels corresponding to the inflection points (maximal shearing) in the quasi-equilibrium turbulent mean jet velocity profile is identified as the best criterion for branch switching along each of the scaling curves. A conceptual picture of regime transitions, for the jet-induced inhomogeneously stratified turbulence near the tropopause, is identified based on cross-overs in various turbulence outer scales. As one traverses away from the center of the jet, the following sequence of regime transitions may be identified: shear-dominated ----> buoyancy-affected ---> buoyancy-dominated. In the innermost core, turbulence, relatively unaffected by shear and stratification, is maintained through a balance between transport and dissipation terms. We also find that several of the turbulence scaling relations undergo a significant change at the transition from the buoyancy-affected to the buoyancy-dominated regime. Another significant feature is the extension of the outer scaling curve in the buoyancy-affected regime into the shear-dominated regime up to the inflection point level. This indicates that a portion of the latter regime is also influenced by stratification. Important scaling relations are deduced from the simulation results, and are compared with existing observational/numerical studies.