Efforts to develop analytical models that predict the front velocity of gravity currents date back over several decades. The most significant of the prior models impose the conservation of mass and streamwise momentum in order to describe the current. However, in doing so they introduce an additional unknown in the form of the pressure jump across the gravity current front, so that an additional equation is required to obtain a closed system and an empirical energy argument needs to be invoked. Hence, all of them contain a certain degree of arbitrariness. Interestingly, high-resolution Navier-Stokes simulations by various authors show that the dynamics of gravity currents are determined by the conservation of mass and momentum alone, so that one should not be free to impose an additional energy constraint. Hence, a physically correct analytical gravity current model also should be based on the conservation of mass and momentum alone, and it should not invoke an energy argument. Rececently, the PI?s group showed that it is indeed possible to develop such a model, based on the vorticity formulation of the momentum conservation equation. In this approach, the pressure variable does not appear, so that it avoids the need for a closure assumption based on an empirical energy argument.
Predictions by the new model are shown to be in excellent agreement with numerical simulation results, much closer than the earlier models. These comparisons furthermore demonstrate that all of the earlier models violate the conservation of vertical momentum. The proposed research will use this novel concept of circulation-based modeling to investigate a wide range of gravity-driven flows with interfaces and free surfaces. Specifically, it will address such flows as internal bores, intrusions, stratified flows over obstacles, exchange flows over sills and particle-driven currents. Furthermore, high- resolution DNS simulations will be conducted in order to assess the range of validity of these models.
Intellectual Merit : The proposed research will develop a fundamentally new class of circulation-based models for a wide range of stratified flows. These models will be transformative in that they avoid the violation of vertical momentum inherent in existing models, along with their arbitrariness due to empirical, energy-based closure assumptions. This is accomplished by employing the vorticity form of the momentum conservation equation, thus eliminating the need for empirical closure assumptions.
Broader Impacts : The proposed research will develop conceptually new, more accurate models for a broad class of stratified flows driven by gravity. Such models serve as basis for describing a wide range of atmospheric and oceanic phenomena from sea breezes and thunderstorm outflows to powder snow avalanches and turbidity currents. In addition, they are employed in numerous technical applications involving two-phase flows. On the educational side, the proposed research project will educate and train graduate, undergraduate and high school students in the concepts of single-phase and two-phase flow modeling, large-scale numerical simulations, scientific computing, parallel computer architectures and flow visualization.