Structure–Function Parameters in the Convective Boundary Layer from Large-Eddy Simulation

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  • 1 Department of Meteorology, The Pennsylvania State University, University Park Pennsylvania
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Abstract

The conventional theory of the scattering of transmitted acoustic, microwave, and optical radiation by turbulence uses the refractive index structure-function parameter CN2. The authors calculate the vertical profiles of the structure function parameters on which CN2 depends, those for temperature and humility, CT2 and CQ2, and their joint structure-function parameter, CTQ, from large-eddy simulation (LES) data for convective boundary layers. The results agree well with experimental measurements.

Modern views of wave propagation through turbulence with substantial intermittency, such as that found in the high Reynolds number flows in geophysics, suggest that the structure–function parameter be interpreted as a local flow variable rather than the traditional ensemble average. Through the refined Kolmogorov–Obukhov similarity hypotheses, a set of local structure–function parameters is defined that depends on locally averaged values of the molecular destruction rates of velocity and scalar variances. Through analysis of the locally averaged variance budgets, the coupling between the resolvable-scale fields in LFS and these local destruction rates are outlined, with the focus on scalars. Using data from direct numerical simulation, we test two models of the locally averaged destruction rate of scalar variance. Each emulates its approximately lognormal statistics and can be used with LES codes, enabling predictions of local structure–function parameter fields.

Abstract

The conventional theory of the scattering of transmitted acoustic, microwave, and optical radiation by turbulence uses the refractive index structure-function parameter CN2. The authors calculate the vertical profiles of the structure function parameters on which CN2 depends, those for temperature and humility, CT2 and CQ2, and their joint structure-function parameter, CTQ, from large-eddy simulation (LES) data for convective boundary layers. The results agree well with experimental measurements.

Modern views of wave propagation through turbulence with substantial intermittency, such as that found in the high Reynolds number flows in geophysics, suggest that the structure–function parameter be interpreted as a local flow variable rather than the traditional ensemble average. Through the refined Kolmogorov–Obukhov similarity hypotheses, a set of local structure–function parameters is defined that depends on locally averaged values of the molecular destruction rates of velocity and scalar variances. Through analysis of the locally averaged variance budgets, the coupling between the resolvable-scale fields in LFS and these local destruction rates are outlined, with the focus on scalars. Using data from direct numerical simulation, we test two models of the locally averaged destruction rate of scalar variance. Each emulates its approximately lognormal statistics and can be used with LES codes, enabling predictions of local structure–function parameter fields.

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