Application of the immersed boundary method to simulations of flow over steep, mountainous terrain

This study focuses on simulations of flow over complex, mountainous terrain at high resolutions where slopes become increasingly steep. This work is part of a multi-university research project, MATERHORN, which aims to improve weather prediction in mountainous terrain. An extensive field campaign will be conduced at the Granite Mountain Atmospheric Science Testbed (GMAST), located at the US Army Dugway Proving Grounds, Utah. This dataset will be used to support extensive numerical investigations with the Weather Research and Forecasting (WRF) model, including the use of large-eddy simulation (LES), and specific turbulence closure models, in a meso-to-fine scale numerical weather prediction (NWP) framework.

WRF uses a terrain-following vertical coordinate system, as do most mesoscale models used for NWP. While terrain-following coordinates are a convenient approach over smooth, large-scale spatial features, they have been shown to introduce significant numerical errors when used on a steep-sloping bottom boundary. When Granite Mountain is resolved on a grid that is appropriately scaled for LES studies, the errors and corresponding instability associated with the vertical coordinate system become problematic. One way to effectively resolve steep topography for use with LES is to immerse the bottom boundary in an orthogonal Cartesian grid, the so-called immersed boundary method (IBM). IBM has already been implemented in WRF (IBM-WRF) and has been shown to agree with WRF for gently-sloping terrain as well as eliminate the errors associated with terrain-following coordinates when steep terrain is present (Lundquist et al. 2010).

In this work we first demonstrate the differences between WRF and IBM-WRF for increasingly resolved simulations of Granite Mountain, and consider the range of grid resolutions that IBM-WRF is appropriate and/or necessary for. Granite Mountain has a maximum slope of 45 degrees when resolved on a 100-meter grid and a maximum slope of nearly 70 degrees when resolved on a 10-meter grid. In the future we will investigate the use of IBM-WRF nested within WRF as a single model that ranges from a mesoscale NWP model to a fine-scale LES model that is capable of capturing atmospheric motions from the synoptic-scale down to the micro-scale.