Theoretical calculations of interactions between urban breezes and mountain slope winds in the presence of basic-state wind

Many big cities around the world are located near mountains. In city-mountain regions, thermally and topographically forced local winds are produced and they affect the transport of pollutants emitted into the urban atmosphere. A better understanding of the dynamics of thermally and topographically forced local winds is necessary to improve the prediction of local winds and to cope with environmental problems. In this study, we theoretically examine the interactions of urban breezes with mountain slope winds in the presence of basic-state wind within the context of the response of a stably stratified atmosphere to prescribed thermal and mechanical forcing. The interactions between urban breezes and mountain slope winds are viewed through the linear superposition of individual analytical solutions for urban thermal forcing, mountain thermal forcing, and mountain mechanical forcing. A setting is considered in which a city is located downwind of a mountain. In the nighttime, in the mountain-side urban area, surface/near-surface horizontal flows induced by mountain cooling and mountain mechanical forcing cooperatively interact with urban breezes, resulting in strengthened winds. In the daytime, in the urban area, surface/near-surface horizontal flows induced by mountain heating are opposed to urban breezes, giving rise to weakened winds. It is shown that the degree of interactions between urban breezes and mountain slope winds is sensitive to mountain height and basic-state wind speed. Particularly, a change in basic-state wind speed affects not only the strength of thermally and mechanically induced flows (internal gravity waves) but also their vertical wavelength and decaying rate. The examination of a case in a setting in which a city is located upwind of a mountain reveals that basic-state wind direction is an important factor that significantly affects the interactions of urban breezes with mountain slope winds.