Direct Numerical Simulation of Turbulent Katabatic Slope Flows with an Immersed-Boundary Method

Abstract

We investigate a Cartesian-mesh immersed-boundary formulation within an incompressible flow solver to simulate laminar and turbulent katabatic slope flows. As a proof-of-concept study, we consider four different immersedboundary reconstruction schemes for imposing a Neumann-type boundary condition on the buoyancy field. Prandtl's laminar solution is used to demonstrate the second-order accuracy of the numerical solutions globally. Direct numerical simulation of a turbulent katabatic flow is then performed to investigate the applicability of the proposed schemes in the turbulent regime by analyzing both first-and second-order statistics of turbulence. First-order statistics show that turbulent katabatic flow simulations are noticeably sensitive to the specifics of the immersed-boundary formulation. We find reconstruction schemes that work well in the laminar regime may not perform as well when applied to a turbulent regime. Our proposed immersed-boundary reconstruction scheme agrees closely with the terrain-fitted reference solutions in both flow regimes.

Stability of the anabatic Prandtl slope flow in a stably stratified medium

“…The pressure Poisson equation is solved with a geometric multigrid technique. Umphrey et al (2017) validated the current code using the Prandtl model and demonstrated globally second-order-accurate solutions. This same code was also used to study the katabatic flow instabilities in Xiao & Senocak 2019.…”

“…The weakly stable regime, defined here purely by the linear instability growth rates, encompasses large Π s values in which the growth rate of the three-dimensional transverse mode is weaker than that of the two-dimensional longitudinal mode, thus reverting to the more familiar stability behaviour predicted by Squire's theorem. This regime, which approximately begins for Π s ≈ 5000, includes the fully turbulent conditions for slope flows which have been studied by Fedorovich & Shapiro (2009), Umphrey, DeLeon & Senocak (2017) and Giometto et al (2017). Fedorovich & Shapiro adopted a Prandtl number of unity, which gives Π s of 3000 and 5000 for the turbulent cases considered in their study.…”

Immersed boundary method for multiphase transport phenomena

“…On one hand, the utilization of the Dirac delta function leads to an artificially finite-size boundary problem. This is critical to high Reynolds number flows, where the turbulent statistics are quite sensitive to the construction of the boundary conditions (Umphrey et al 2017). On the other hand, the Dirac delta function could smooth the spurious pressure oscillations when handling the moving/deformable boundaries (Seo and Mittal 2011b).…”

Boundary-Layer Flow Over Complex Topography

“…Of more general application is the finding of Burkholder et al (2011), who determined that, although their simulated mean fields were insensitive to the choice of sub-filter-scale model, the model choice did substantially impact the simulated second-order moments, especially the buoyancy fluxes and vertical velocity variances. Although generally limited to low Reynolds numbers, direct numerical simulations have also been performed (Shapiro and Fedorovich 2014;Umphrey et al 2017). These tend to overpredict jet strength and under-predict the height of the jet peak.…”