doi:10.5194/npg-22-133-2015 © Author(s) 2015. CC Attribution 3.0 License. Time-dependent Long’s equation

Abstract. Long’s equation describes steady-state two-dimensional stratified flow over terrain. Its numerical so-lutions under various approximations were investigated by many authors. Special attention was paid to the properties of the gravity waves that are predicted to be generated as a re-sult. In this paper we derive a time-dependent generalization of this equation and investigate analytically its solutions un-der some simplifications. These results might be useful in the experimental analysis of gravity waves over topography and their impact on atmospheric modeling