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====== randomfield ====== Create a velocity field with * random spectral coefficients that decay exponentially * zero divergence * Dirichlet boundary conditions at the walls ===== options ===== <code> -Nx --Nx <int> # x gridpoints -Ny --Ny <int> # y gridpoints -Nz --Nz <int> # z gridpoints -a --alpha <real> default == 0 Lx = 2 pi/alpha -g --gamma <real> default == 0 Lz = 2 pi/gamma -lx --lx <real> Lx = 2 pi lx -lz --lz <real> Lz = 2 pi lz -sd --seed <int> default == 1 seed for random number generator -s --smoothnes <real> default == 0.4 smoothness of field, 0 < s < 1 -m --magnitude <real> default == 0.2 magnitude of field, 0 < m < 1 -mf --meanflow perturb the mean -s1 --s1-symmetry satisfy s1 symmetry -s2 --s2-symmetry satisfy s2 symmetry -s3 --s3-symmetry satisfy s3 symmetry <fieldname> (trailing arg 1) output file </code> ===== mathematics ===== The field takes the form <latex> {\bf u}(x,y,z) = \sum_{jklm} u_{jklm} T_l(y) exp(2 pi i (jx/Lx + kz/Lz)) {\bf e}_m </latex> where the spectral coefficients are assigned according to <latex> u_{jklm} = (\text{random # in }[-1, 1]) * \text{smoothness}^{|l| + |j| + |k|} </latex> with corrections to meet boundary and divergence conditions and rescaling so that L2Norm(u) = magnitude.
