Geophysical Fluid Dynamics: Stratified Flows

Unlike in neutral flows, stable background stratification modifies the flow dynamics such that energy gets exchanged among the three components of turbulent kinetic energy (TKE) and turbulent potential energy (TPE). This exchange occurs through three mechanisms: (1) the vertical buoyancy flux; (2) the buoyancy pressure redistribution; and (3) the nonlinear pressure redistribution. The first mechanism connects the vertical component of TKE with TPE (k_w, k_p), and it arises from the correlation between the vertical velocity and density fluctuations. The second mechanism connects the three components of TKE (k_u, k_v, k_w), and it arises from the correlation between the pressure fluctuations associated with the buoyancy force and the diagonal components of the rate-of-strain tensor. Because the buoyancy redistribution depends on the density field, it modifies the behavior of the buoyancy flux and vice versa. The third mechanism also connects the three components of TKE (k_u, k_v, k_w), and it arises from the correlation between the pressure fluctuations associated with the nonlinear advection term and the diagonal components of the rate-of-strain tensor. In direct numerical simulations (DNS), all three coupled processes are present, making it difficult to deeply understand the role of each process separately. To address this, we study these three processes systematically through a hierarchy of analytical and numerical models that introduces them sequentially, helping us to quantify their impact on one another and the overall energy exchange. First, we consider just the coupling between k_w and k_p without any pressure effects. Second, we introduce an additional coupling between (k_u + k_v) and k_w by retaining the buoyancy pressure effects. Third, we introduce the last coupling between (k_u + k_v) and k_w by considering the full system of equations. This model hierarchy facilitates the study of energy exchange in stratified flows as a function of Reynolds and Prandtl numbers through forcing and damping mechanisms and also helps quantify the interplay between the intercomponent energy exchange processes and the energy cascade.

Funding acknowledgement

Y. R. Y. is supported by the Postdoctoral Environmental Teaching Fellowship from the High Meadows Environmental Institute at Princeton University.