Equations of Motion of a Viscous Fluid; The Boundary Conditions
So far we considered the motions of an ideal fluid which reflect, so to speak, genetic features of a real fluid’s behavior and are not aggravated by the influence of irreversible thermodynamic processes. The latter, however, are always present due to internal friction (viscosity) and thermal conductivity of the medium. With regard to global geophysical flows, the situation is complicated by the fact that the role of irreversible non-adiabatic factors is assumed not only (or rather to a much lesser degree) by molecular viscosity and thermal conductivity, but rather by small-scale motions that are not taken into account by quasi-geostrophic approximation.
As we shall see below, the Earth’s surface has a very special and crucial influence on the formation of general atmospheric circulation. Without friction on this surface the weather and climate on the Earth would have been totally unsuitable for human civilization. Irreversible diabatic processes start to noticeably affect the behavior of global atmospheric motions already on the third day after observations begin. Therefore, one cannot avoid including these irreversible processes in weather predictions for longer terms and for climate descriptions. We are going to start our consideration with a derivation of the equations of motion of a viscous fluid.