CMG: Non-Hydrostatic Effects and New Diagnostics for the Long-Time Dynamics of Rotating and Stratified Flows

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The dynamics of the oceans and the atmosphere are strongly influenced by the rotation of the earth and stratification. In the atmosphere, stratification results from solar heating coupled with earth's gravity, whereby colder, heavier air settles below warmer, lighter air. In the ocean, colder, saltier water lies below warmer, fresher water. The relative importance of both rotation and stratification depends on length and time scales. For example, the earth's rotation is critical to the dynamics of large-scale structures such as hurricanes, jet streams, and oceanic currents, but has a minor effect on smaller-scale motions such as cumulus clouds and waves generated by a ship.The wide range of spatial scales in geophysical flows, from thousands of kilometers to meters, is one reason why they are so rich in behavior, so costly to compute, and so difficult to understand. In certain scale regimes, intermediate-scale motions self-organize to generate larger-scale structures such as hurricanes, while in other regimes, energy is transferred from large-scale winds and tides to small-scale turbulent fluctuations. On large scales the flow becomes quasi-two-dimensional, with motions mainly parallel to the surface of the earth, whereas at small scales it is often fully turbulent in all three directions. Current mathematical models for studying the oceans and the atmosphere capture the large scales of the flow at the expense of removing small-scale dynamics. Even at the highest resolutions possible on today's computers, these models fail to accurately predict long-term variability. For example, in thousand-year ocean simulations, significant errors accumulate over time because of inadequate representation of small-scale processes such as deep-water mixing and dense-water overflows (e.g., from the Denmark Strait). Such errors indicate a significant obstacle for our ability to predict climate change, since breakdowns in the large-scale ocean circulation have previously occurred during relatively rapid changes in climate. Thus it is becoming increasingly clear that the intermediate-scale and small-scale motions play a significant role in long-time, large-scale dynamics.The goal of the proposed research is to probe the mechanisms for such multi-scale coupling in rotating and stratified flows. Mathematical models and a new statistical framework will be developed and tested with computer simulations on some of the largest available computers in the world at Los Alamos National Laboratory. Our combined theoretical and numerical approach provides a unique opportunity for the training of young scientists toward development of the next generation of ocean, atmosphere, and climate models.