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TWOSCALE FILTERING APPROACH THEORY
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advective boundary conditions Chapter closure constant closure model components computed consider context convolution theorem corresponding cross terms Dakhoul defined differential equations dimensionless direct simulations discrete dx'dy'dz'dt energy ensemble average ergodic hypothesis evolution exact expression filter width filtering effect filtering operation filtering terms flow variables fluctuating forced Burgers equation Fourier space Fourier transform free Burgers frequency function Gaussian filter governing equations grid GSGS inertial subrange instantaneous velocity Leonard approximation LES-mesoscale LOGIWRVE NUMBER low wave LS velocity macroscale mesoscale Navier-Stokes Navier-Stokes equations nonlinear numerical simulation obtained periodic Burgers planetary boundary layer presented problem represents Reynolds number Reynolds stresses Richardson extrapolation shown in Figure space filtering space-filtered space-time filtered spatial spectral statistics spectrum stability stepping scheme STF approach STF velocity stresses Taylor series theory three-scale approach tion turbulence modeling turbulent flows two-scale un+1 values velocity field wave number