Hydrodynamics of an Atmosphere Excited by an Underlying Turbulent Convective Zone. II. Response of an Atmosphere to an Applied Random Body-Force
Abstract
The response of atmospheres to stationary random applied forces homogeneous over horizontal planes is formulated in a very general way (Part I and II). We discuss the occurrence of divergences at cut-off frequencies on the special case of an isothermal atmosphere. The analysis applies without modifications to a large class of models characterized by a propagation operator whose Green's function is singular when the group velocity vanishes. We ultimately relate these divergences to the lack of reflections in the medel and we show that the common energy argument is inadequate (Part II and III). Our view is supported by a detailed analysis of the response of two models: the semi-infinite isothermal atmosphere bounded by a rigid bottom (Part IV), and an infinite model with reflections at one level (Part V). The response is discussed in terms of the spatial extention and coherence of the momentum sources. It is shown that the response to a white-noise force can be enhanced at frequencies different from the local cut-off frequency of the region where the force acts. A prelinary discussion of the implications of this result to the situation prevailing in the solar upper layers strongly suggest the relevance of this study to the interpretation of the photospheric oscillation. (Part VI)
- Publication:
-
Astronomy and Astrophysics
- Pub Date:
- August 1970
- Bibcode:
- 1970A&A.....7..227S