Reynolds stress budgets in orthogonal curvilinear coordinates for a turbulent flow over a curved ramp via DNS

The physical mechanisms of turbulence in separated flows over curved walls are not yet well understood. In order to provide the necessary turbulence statistics to explain the physical mechanisms of such flows, we have derived analytically the equations for the mean flow, and for the budgets of turbulence kinetic energy (TKE) and Reynolds stress in orthogonal curvilinear coordinates. Also, we have recently developed an explicit, third-order Runge-Kutta based projection method, FastRK3, which requires solving the Poisson equation for pressure only once per time step to solve the incompressible Navier-Stokes equations in orthogonal curvilinear coordinates (Aithal & Ferrante, J. Comput. Phys, 2020). In the current work, using FastRK3, we have performed direct numerical simulations (DNS) of a spatially developing turbulent boundary layer over a curved ramp with adverse pressure-gradient and discuss the budgets of TKE and Reynolds stress in orthogonal curvilinear coordinates.