On the Thermal Instability of Fluid Layers Heated from Below; Equations of Motion and Boundary Conditions

摘要

In the investigation of the interaction of a submerged disturbance with an unstably stratified fluid, it was necessary to formulate the governing equations and boundary conditions controlling the behavior of an unstable layer. This formulation was done in a manner so as to allow for expansion to multiple layers and for the introduction of a hydrodynamic disturbance. The memorandum presents an analysis of conditions required for instability, and develops the differential equations and boundary conditions using a normal mode treatment similar to that in Chandrasekhar's text. A more detailed examination of the interfacial deflection and the significance of surface tension was included in the section dealing with the boundary conditions. The differential equations and boundary conditions are summarized in a table. (Author)