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Investigation into nonlocal turbulence-closure at higher statistical order Modzelewski, Henryk

Abstract

This dissertation investigates whether higher-statistical-order nonlocal turbulence-closure can be utilized to describe some of the complex features of atmospheric turbulent flows. Transilient turbulence theory, a nonlocal forcing and mixing model, was chosen as a framework. This theory describes turbulent transport as a two-dimensional 'transilient' matrix of exchange coefficients between different layers in the fluid. A new higher-statistical-order nonlocal parameterization of the transilient matrix is proposed. The studies of former parameterizations of transilient matrices have indicated the following main deficiencies: lack of asymmetry of upward and downward motions in convective boundary layers, improper vertical distribution of turbulent mixing, ad hoc definition of diagonal elements of transilient matrices, and unrealistically large ranges of turbulent transport. This dissertation proposes a parameterization that addresses these deficiencies. The following concepts are utilized in the new parameterization: a virtual turbulent-transport eddy, convective potential-energy and shear potential-energy of mean-flow instabilities, decomposition of forcing into symmetric and asymmetric components, prognostic equations for the nonlocal turbulence kinetic energy budget and for the 3rd statistical moment of the vertical velocity, a limited turbulent-transport range, and a transilient tendency-matrix as a precursor of the transilient matrix. The parameterization utilizes eight parameters. A testbed atmospheric boundary-layer model is created to investigate, evaluate, and compare the new closure with three other turbulence-closure models and with two large-eddy-simulation data sets. The evaluation of testbed model led to the following conclusions. The parameterization of asymmetry qualitatively predicts the overall asymmetry of turbulent transport. An improper vertical distribution of mixing in convective boundary layers is evident, caused by improper height and scale-wise structure of buoyancy forcing. The utilization of the new transilient tendencymatrix successfully removed the necessity to parameterize the diagonal elements of transilient matrices. The limited transport-range approximation causes sensitivity discretization. Finally, the parameterization is computationally expensive, mainly due to the cost of solving the prognostic equations. In summary, the new parameterization has demonstrated the potential to improve turbulence parameterization, but more work needs to be done.

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