# Berkeley Fluids Seminar

## University of California, Berkeley

### Bring your lunch and enjoy learning about fluids!

**Monday, September 25, 2017**

**3110, Etcheverry Hall**

Dr. Mostafa Momen (Stanford University)

Reduced Models of Environmental Flows

** Abstract: **
Environmental flows are dynamical systems that evolve nonlinearly with time. Atmospheric boundary layers (ABL) and gravity currents are two examples of geophysical flows that often vary in time. In ABLs, non-stationary shear and buoyancy forces are the main sources that drive the unsteadiness. However, due to their inherent complexity, most previous studies focused on steady-state conditions. In the ABL, the pressure gradient, buoyancy, Coriolis, and friction forces interact. The mean partial differential equations (PDEs) governing the unsteady version of the problem are solvable only for a limited set of forcing variability modes, and the resulting solutions are intricate and difficult to interpret. Here, we derive a simpler physical model that reduces the governing RANS equations into a second-order ordinary differential equation (ODE), which is analogous to a damped oscillator. The reduced model is straightforward and solvable for arbitrary turbulent viscosity variability, and it captures LES results. Then, we present theoretical, numerical, and experimental studies of the dynamical behavior of a gravity current problem. We consider the release of a finite volume of fluid instantaneously from the edge of a rectangular domain for high-Reynolds-number flows. The setup is relevant in environmental, geophysical, and engineering applications such as open channels, ventilation flows, and dam-break problems. Based on scaling arguments, we reduce the shallow-water PDEs into two nonlinear ODEs (representing the continuity and momentum equations), which are then solved analytically. The new self-similar solutions are in good agreement with the performed experiments and direct numerical simulations for various geometries and fluid densities, after a transition period. These findings provide new insights into the dynamical behavior of ABLs and edge drainage flows.

** Bio: ** Mostafa Momen is currently a postdoctoral scholar in the School of Earth, Energy and Environmental Sciences at Stanford University. In his postdoc, he studies land-surface interactions using remote sensing satellite data. He did his undergraduate work in Civil and Environmental Engineering at Sharif University of Technology. Inspired to explore the mysteries of fluid motion, he started his Ph.D. in the environmental fluid mechanics lab at Princeton University. In 2015, he was also an exchange scholar in the Department of Mechanical Engineering at MIT. In his Ph.D. research at Princeton, Mostafa investigated the underlying dynamics of the atmospheric boundary layer by integrating numerical simulations and mathematical modeling to overcome uncertainties associated with wind-energy forecasting. Additionally, he worked on the reduced models of the drainage mechanism of gravity currents.