Mechanisms for the Formation of Coherent Structures from Small-Scale Turbulence in Anisotropic Flows

University Of Wisconsin-Madison, Madison WI

Investigators

Abstract

Geophysical turbulence may be modeled by a hierarchy of partial differential equations including both waves and turbulence. In each model, the vortical, non-wave motions correspond to observed, long-lived structures such as the jet stream of the tropopause, the persistent horizontal layers of the stratosphere, and hurricanes. Despite decoupling of vortical modes and waves at first order in weak turbulence expansions, numerical simulations have demonstrated the generation of the anisotropic, vortical modes from fast waves. These simulations suggest major modifications to current models designed to capture only the large-scale dynamics. For example, they show the dominance of vertically sheared, horizontal flow modes in strongly stratified flows, presently not included in large-scale models. Our work focuses on (1) stability analyses to understand the mechanisms responsible for the formation of slow, large-scale coherent motions from fast, small-scale turbulence, and (2) the development of improved ordinary and partial differential equations describing the slowly varying, large-scale dynamics, reflecting the physics observed in the numerical simulations. Most current models of turbulence are based on isotropic theory, and assume that small-scale turbulence acts as a sink of energy for larger-scale flows. Such turbulence models are used in numerical prediction, for example, of weather and climate change. However, turbulence in nature and in engineering flows is anisotropic more often than not, for example, due to the presence of boundaries. In this study, we focus on anisotropy induced by strong rotation and stratification, both of which give rise to wave motions. In anisotropic wave-turbulence systems, turbulence may act as a source of energy for larger-scale flows. Furthermore, coherent structures often emerge spontaneously from small-scale, random fluctuations. One example in nature is the generation of hurricanes from smaller-scale motions in the atmosphere. This study aims to understand large-scale, coherent-structure generation from small-scale turbulence in the atmosphere and oceans. In addition, new models will be developed to capture these physical phenomena, absent in current models. The results should impact our ability to predict long-term variability in ocean-circulation, weather and climate.