ABSTRACT
Acknowledgments.................................................................................................................................. 477 References .............................................................................................................................................. 478
Kolmogorov (1941) proposed one of the most successful theories in the area of turbulence, namely, the existence of an inertial subrange. Successively, Kolmogorov (1962) revised the original theory to take the variability of the dissipation rate in space into account. The process of this reÞnement introduced a lognormal model to describe the distribution of dissipation rates. The inertial subrange theory requires an energy cascade process, whose length scale is much larger than that of the viscous dominating scale. Thus, the types of ßows to which the theory applies occur at high Reynolds numbers. Geophysical ßows provide an example in that they typically occur at high Reynolds numbers because the generation mechanism is usually much larger than the viscous dominating scale. In fact, the Þrst evidence of the existence of an inertial subrange came from observations of a high Reynolds number oceanic turbulent ßow (Grant et al. 1962). Gurvich and Yaglom (1967) further developed the lognormal theory that described the probability distribution of the locally averaged dissipation rates. In their work, the theory was also intended for high Reynolds number ßows to simplify the development (see also Monin and Ozmidov, 1985).
