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Danny E. Scipión, Phillip B. Chilson, Evgeni Fedorovich, and Robert D. Palmer

that are not resolvable are assumed to carry only a small fraction of the total energy of the flow and are parameterized with a subgrid (or subfilter) closure scheme. In the LES of the atmospheric CBL, the environmental parameters such as surface heating, stratification, and shear can be precisely controlled. Retrieval of spatial turbulence statistics in LES does not necessarily rely on additional assumptions like the Taylor (1938) frozen turbulence hypothesis: thermodynamic and kinematic

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Rod Frehlich, Yannick Meillier, and Michael L. Jensen

; Wyngaard and Clifford 1977 ; Hill 1996 ) and assuming that the small-scale turbulence is locally homogeneous and isotropic ( Frehlich et al. 2003 ). Then, the spatial spectrum of longitudinal velocity E 1 ( k ) at high wavenumber k can be written as ( Monin and Yaglom 1975 , p. 354) where ν is the kinematic viscosity, ε is the energy dissipation rate, is the Kolmogorov microscale, C 2 is the Kolmogorov constant, and the universal function is ϕ 1 ( x ) = C 2 x −5/2 g ( βx 2 ) (see

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Steven E. Koch, Cyrille Flamant, James W. Wilson, Bruce M. Gentry, and Brian D. Jamison

reference frame, from which the bore-relative winds ( U *– C b ) were calculated. This procedure resulted in the generation of a uniform, two-dimensional space–height grid of values from z 0 = 75 m AGL up to z t ∼ 2325 m AGL, where the QC criteria were most often violated ( Fig. 10c ). Vertical velocities were computed by upwardly integrating the Boussinesq mass continuity equation from z 0 to z t under the assumption that w = 0 at z 0 , as shown here: This simple kinematic procedure

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Reginald J. Hill, W. Alan Brewer, and Sara C. Tucker

to rigid-body kinematics, The vector’s Ω and r are most conveniently given in the coordinate system of either the lidar or ship. Hence, the notation Ω × r implies performing the cross product in the lidar’s or POS MV’s coordinate system, and then transforming to the earth-fixed GPS coordinate system to obtain ( Ω × r ) E ; the Euler rotation matrix is used for that transformation. The Euler angles are obtained by temporal integration of Ω . The velocity of the elevation mirror

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