Karman-Howarth equation

This Karman-Howarth equation involves a double correlation that corresponds to the Reynolds stress. [Pg.98]

Further, an interesting question is how the kinetic energy of turbulence will be distributed according to various eddies/frequencies. Such a distribution of the energy among the eddies/frequencies is usually termed the energy spectrum. Our focus is now on the double correlation in the Karman-Howarth equation, and finally, the dynamic equation for the energy spectrum that is obtained by the Fourier transform of the double correlation is derived as... [Pg.98]

For isotropic turbulence the following equation of the energy spectrum can be obtained by taking the Fourier transform of the Karman-Howarth equation (H9) ... [Pg.202]

Brackets denote spatial or ensemble averages. Starting from the Navier-Stokes equation and assuming a statistically isotropic and homogeneous velocity field one can derive the Karman-Howarth equation for the longitudinal structure functions as... [Pg.12]

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