NSF Award
2406767
Small-scale wave motions in the atmosphere and oceans are ubiquitous and well-known to contribute significantly to the long-term global-scale evolution of these system, yet their direct numerical simulation remains elusive with present-day computational capacities. This leads to the necessity of understanding their dynamics from a fundamental theoretical perspective, which ultimately allows their impact on the global-scale dynamics to be modeled in a systematic and rational fashion. Early theoretical efforts were based on monochromatic wave models, i.e., they were based on studying a single wave interacting with its environment. More recently the theoretical focus has expanded to the more complicated and more realistic model of allowing a broad spectrum of waves to be present simultaneously. This is much closer to real atmosphere/ocean waves, and it also encompasses the study of the mutual interactions of many different wave components, which produces a peculiar dynamical evolution scenario known as wave turbulence. The present project focuses on internal gravity waves in the ocean, which owe their restoring mechanism to a combination of gravitational density stratification and the background rotation of planet Earth. This project will also provide opportunities for the integration of students into the research.<br/><br/>The project seeks to break new ground with a multi-pronged approach that combines theory and numerical modeling in three problem areas. First, it builds on previous theoretical advances in the study of how broadband wave spectra can be created from monochromatic sources via interactions with mean currents. Novel questions to be addressed include a study of the convergence or divergence of Lagrangian and Eulerian wave spectra, which is crucial to compare to observations. Second, recent results indicate that dual cascades based on twin conservation laws behave quite differently in hydrodynamic turbulence and in wave turbulence. This will be explored based on a new stochastic model that is surprisingly successful in predicting the observed wave turbulence spectral dynamics. Third, abstract theory suggests that strongly directional wave turbulence could undergo a kind of phase transition whereby the nonlinear transfer of wave energy across the scales reverses direction, so wave energy might flow upscale rather than downscale. This will be investigated in simple models that also touch on other fundamental questions related to the importance of conservation laws that are not sign-definite.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
