Scale Invariance, Symmetries, Fractals, and Stochastic Simulations of Atmospheric Phenomena

Advances in remote sensing and in situ measurement techniques have revealed the full continuum of atmospheric motions and have underlined the importance of mesoscale processes. This paper examines the implications of three observed characteristics of mesoscale circulations: 1) the energy spectrum of the horizontal wind in the horizontal is of the form k−βh with βh ~ 5/3, (k is a wave-number); 2) the corresponding spectrum in the vertical direction is of the same scaling form, but with a very different slope (βv ~ 11/5); and 3) the variability is extreme. Some recent work in turbulence, physics, and meteorology, that is relevant to systems with extreme variability over a wide range of scales is reviewed. The concepts of scaling, intermittency, and fractals, are briefly introduced to show how they can be used to understand the physics of both homogeneous and intermittent energy cascades in isotropic atmospheres. These concepts may be generalizable (with a formalism called generalized scale invariance), to a...