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| Some physically significant consequences of recent advances in the theory of
self-preserved homogenous statistical solutions of the Navier-Stokes equations
are presented. Integral lengthscales based on the solutions are discussed, and
used to derive rigorously a new recursion equation, which would be help to
understand the dynamics of turbulence, especially for the cascade. The energy
spectrum and its behavior in the lowest wave number range are discussed.
Previous two different theory (the Batchelor spectra, the Saffman spectra) could
be unified by using present theory. According to the present theory, the
Loitsianskii’s integral invariant is not an invariant in general case.
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| Keywords:isotropic turbulence, scales |
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