Two highly singular intermittent structures: Rain and turbulence

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Abstract

[1] Rainfall charges soil moisture and river basins among its many roles with respect to the hydrologic cycle. Research aimed at improved understanding and modeling of surface water processes includes attention to rainfall at a variety of space-time scales. Given the atmospheric environment in which rain events are observed, some similarities between certain rainfall data structures and fluid turbulence can be expected. So the space-time intermittency and large fluctuations observed in both rain rates and energy dissipation rates have provided an interest among hydrologists in developing physical theories, experiments, and mathematical models. In response to a request for insights into multiplicative cascade models, the main goal of this article is to single out a special mathematical transformation, namely, “size biasing” (or “tilting”), which has proven to be very powerful in the mathematical analysis of multiplicative cascades and which has also been successfully exploited within the context of turbulence from a physical perspective.

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