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A-priori quasilinear modeling and beyond

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TURW04 - Wall-bounded turbulence: beyond current boundaries

The quasilinear (QL) reduction, in which nonlinearities among fluctuation fields are retained only where they modify the evolution of the mean fields, has proven surprisingly effective in the description of both wall-bounded and free (geophysical) turbulent shear flows. Although generally invoked as a useful but ad hoc approximation, the QL reduction can be justified asymptotically in the limit of temporal scale separation between the mean and fluctuating flow. Notably, in the limit of large Reynolds number, certain classes of invariant solutions asymptotically satisfy a QL reduction of the Navier-Stokes equations known as the vortex-wave interaction (VWI) equations. We begin by introducing a new class of these asymptotically-QL invariant solutions that reproduce the uniform-momentum-zone/internal-shear-layer structure characterizing the inertial domain of turbulent wall flows. Next, we show how the formal asymptotic analysis motivates the generalized quasilinear (GQL) reduction, which effects a homotopy from QL to fully nonlinear models and frequently yields a significant increase in accuracy. Finally, we introduce a new method for time-integrating slow-fast (G)QL systems that obviates the need to resolve the fast dynamics while also allowing fully nonlinear interactions (associated with bursting behavior) to be reincorporated intermittently when prompted by the dynamics.

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