Mostafa Momen and Prof. Elie Bou-Zeid
Princeton University, Princeton, N.J., US

Abstract Unsteady geostrophic forcing in the atmosphere or ocean not only influences the mean wind, but also affects the turbulent statistics. In these geophysical wall-bounded flows, it is important to understand when and if turbulence is in quasi-equilibrium with the mean flow. To that end, one needs to understand how the turbulence decays or develops, and how do the turbulent production, transport and dissipation respond to changes in the imposed forcing. The knowledge obtained from studying these questions help us understand the underlying physical dynamics of the unsteady boundary layers and develop better turbulence closures for weather/climate models and engineering applications. The present study focuses on the unsteady Ekman boundary layer where pressure gradient forces, Coriolis forces, and turbulent friction forces interact but are not in equilibrium. We perform a suite of large-eddy simulations with variable forcing and acquire the corresponding resolved turbulent kinetic energy budget terms for each simulation. Many cases with unsteady geostrophic forcing are simulated to examine how the turbulence is modulated by the variability of the mean pressure gradient. We also examined the influence of the forcing variability time scale on the turbulence equilibrium and TKE budget, and assessed the implications for mean-turbulence nonlinear interactions and turbulence modeling in such flows.

Abstract: In this talk, we present error analysis and numerical results showing optimal convergence and superconvergence properties of the hybridizable discontinuous Galerkin (HDG) methods. First, we study the convection-diffusion equations with variable-degree approximations on nonconforming meshes. Our results hold for any (bounded) irregularity index of the nonconformity of the mesh, and can be extended to hypercubes. Second, we design and analyze the first HDG methods for stationary, third-order linear equations in one-space dimension. 13 methods are analyzed in a unified setting. They all provide superconvergent approximations to the exact solution u and its two derivatives. Numerical results validate our theoretical findings.

Biography: Yanlai Chen is an Assistant Professor of Mathematics at UMass Dartmouth. Before joining UMassD, he was a postdoctoral research associate at Brown University. He received his Ph.D. in Mathematics and M.S. in computer science from University of Minnesota in 2007, and B.S. degree in Mathematics from University of Science and Technology of China (USTC) in 2002. Dr. Chen’s research area is numerical analysis and scientific computing, in particular discontinuous Galerkin finite element methods, hybridizable discontinuous Galerkin methods, reduced basis method and reduced basis element method. His research is currently supported by NSF.