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

We study the dynamics of turbulence in a spatially developing turbulent boundary layer (SDTBL) separating over a curved ramp via direct numerical simulation (DNS). We have performed DNS using FastRK3 which is an explicit, third-order Runge-Kutta based projection method 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). We have derived, for the first time, the budget equations of the turbulence kinetic energy (TKE) and Reynolds stresses in orthogonal curvilinear coordinates, and compared them to those in Cartesian coordinates. The results of such comparison and physical mechanisms will be discussed.