Linear Theories and Nonlinear Numerical Simulations Across the Orographic Gravity Wave Spectrum (Code and sample data)

Dataset description

The full set of numerical simulations produced for this study is too large to be shared in a practical way, as the complete ensemble spans many sensitivity experiments with substantial storage requirements (approximately 2.5 TB). Therefore, we provide three representative reference simulations (L = 1, 10, and 100 km) examined in the manuscript, together with the code used for post-processing, figure generation, and analysis (see linked repository). Together, these materials document the workflow used in the manuscript and provide a practical basis for reproducing the main results and for generating analogous diagnostics.

Abstract of associated manuscript

Most parameterizations of orographic gravity wave drag (GWD) in global weather and climate models rest on linear theories that relate the drag to background wind,  stratification and mountain geometry. Despite their foundational role, these linear solutions have not been comprehensively tested against nonlinear numerical simulations across the full spectrum of mountain wave (MW) regimes within a single, controlled framework. This study provides such a thorough comparison by contrasting linear predictions with nonlinear numerical simulations ranging from the non-hydrostatic to the hydrostatic and hydrostatic–rotating MW regimes. A systematic sensitivity analysis demonstrates that reproducing linear solutions requires a carefully designed simulation setup, including adequate resolution, sufficiently large domains, open meridional boundaries, and small-amplitude topography. Deviations from this configuration introduce systematic biases, particularly in the low-frequency regime where rotational effects are significant. Periodic meridional boundaries overestimate the GWD in the hydrostatic-rotating regime, as increasing the mountain amplitude does, thereby introducing inconsistencies between the pressure drag and the vertical flux of angular momentum. For the validated reference configuration, the nonlinear simulations closely reproduce the linear predictions for the surface GWD across all MW regimes. A small negative bias remains in the transitional hydrostatic regime, where non-hydrostatic and rotational effects overlap. Extending the analysis vertically demonstrates that zonal-mean momentum and energy fluxes satisfy the Eliassen--Palm relation for rotating flows and follow established theoretical expectations for wave-energy partitioning. The results are robust across different numerical models and equation formulations, indicating that agreement with linear theory depends primarily on an appropriate simulation setup.