Abstract:
Analytical solutions of stationary waves forced by sensible heating in a linear quasi-geostrophic model are obtained and effects of the basic flow, the Newton cooling and surface friction on the amplitude and phase of stationary waves are discussed. Results show that when the basic flow is easterly, the stationary waves exhibit a baroclinic structure in the vertical direction and the amplitude in the surface is stronger than in the middle and upper layer. When the basic flow is westerly, the waves propagate upward. In the lower layer, the cyclone (anticyclone) lies mainly to the west (east) of the heating center when the basic flow is easterly, and the cyclone (anticyclone) is located to the east (west) of the heating center when the basic flow is westerly. In the middle and upper layer, however, the opposite is true. It is found that the effects of the basic flow on the amplitude and phase of the waves are symmetric, which is different from the effects of condensation heating. The results also show that the Newton cooling has an important influence on the stationary waves especially when the basic flow is very weak. In a static atmosphere, the inviscid solution, i.e. the Sverdrup solution forced by sensible heating does not exist. When the Newton cooling is considered, the cyclone is forced in the lower layer and the anticyclone is forced in the middle and upper layers within the area influenced by the sensible heating, and the center of the cyclone is located slightly to the west of the heating center. In a non-static atmosphere, the Newton cooling makes the centers of the surface systems move upwind. As a dissipative term, it weakens the system in both the lower and upper layers, which is different from the effects of surface friction. The surface friction always weakens the system in the lower layer and intensifies the system in the upper layer.