Analysis of Idealized Numerical Simulations to Calibrate and Validate Boundary Layer Models

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Jabbari Sahebari, Aidin
Structure Function Method , Direct Numerical Simulations , Inertial Dissipation Method , Large Eddy Simulations , Boundary Layers
The accuracy of the inertial dissipation method (IDM), commonly applied to estimate the observed rate of turbulent dissipation in bottom boundary layers (BBL), is evaluated by performing direct numerical simulations (DNS) and large eddy simulations (LES) of unidirectional turbulent channel flows. Errors in the IDM occur as the mean velocity is commonly used for the convection velocity and when the canonical Kolmogorov -5/3 constants, which assume isotropy and homogeneity of the flow, are applied. The optimal convection velocity, as previously shown by many researchers, is found to be 2 times greater than the local mean velocity near the bed and the Kolmogorov constants are significantly affected by anisotropy. Usage of the canonical Kolmogorov constants leads to significant errors (>50%) in computation of dissipation. Using the same DNS and LES data, the accuracy of Kolmogorov 2/3 constants, used in the structure function method (SFM) to compute dissipation, is also investigated. As with the IDM, comparison of the dissipation, calculated directly from DNS/LES with that from the SFM, shows that usage of canonical constants results in considerable error (>50%) from the vertical or spanwise velocity components. Application of anisotropy-adjusted constants to data from the BBL of Lake Erie shows that these constants improve computed dissipation by a factor of two, with results within 20% of published dissipation obtained from the Batchelor fitting method. DNS and LES of oscillating turbulent flows were also carried out to calibrate and evaluate common analytical models used in oscillatory BBLs in lakes and costal oceans. These include the log-law, Stokes second problem, the IDM, and a one-equation Spalart-Allmaras model. Velocity profile predictions from the Spalart-Allmaras model were found to be more accurate than those from the log-law and Stokes’ second problem. Comparison of the LES data and the turbulence models, with published field measurements, shows that the rate of dissipation from the IDM is more accurate than that obtained from the log-law, particularly when the flow reverses. The differences between the IDM and LES suggest that the errors in prediction of dissipation can be due to the anisotropy conditions in the BBL.
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