Application of wavelet analysis to turbulence : Development of turbulent modeling and its validation

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A wavelet based non-empirical turbulent modeling for three-dimensional incompressible turbulence at high Reynolds number, called CVE, has been developed. Its validity was also assessed. It was shown that CVE reduces the number of degrees of freedom by a factor 10 with respect to direct numerical simulation, while preserving high-order statistics of the turbulent flow. CVE was generalized to modeling for magnetohydrodynamic turbulence and wall-bounded turbulence.