Abstract
A dynamical mechanism is considered which connects the cascade with nongaussian statistics of velocity gradients. Turbulence is characterized by the continuous excitation of all scales, but in the Fourier space of the velocity field, the excited amplitude decreases rapidly with increasing wave numbers so that contribution to the total kinetic energy from the small scale components is negligibly small. Roughly speaking by the central limit theorem, the sum of a large number of Fourier modes is distributed normally when the Fourier amplitudes of different wave numbers are independent in the energy-containing eddies (Batchelor 1953).
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© 1993 Springer Basel AG
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Kambe, T. (1993). A Dynamical Theory of Cascade in Turbulence and Non-Gaussian Statistics. In: Dracos, T., Tsinober, A. (eds) New Approaches and Concepts in Turbulence. Monte Verità. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8585-0_6
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DOI: https://doi.org/10.1007/978-3-0348-8585-0_6
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