Formulations of mathematical models and statements of problems for investigating the behavior of multiphase systems under natural conditions are discussed. In particular, here we consider the hydrodynamics of the liquid-solid system in the context of possible surges of gas hydrates from the bottom of Lake Baikal. The results of numerical experiments on the simulation of hydrodynamic processes in a system where the source of disturbances is the income of solid particles from the bottom of the lake are presented. Parametrizations of the interphase dynamic exchange are studied.
The results of numerical experiments on the modeling of hydrothermodynamics and the processes of transport and transformation of gas emerging from the sources at the bottom of the lake are presented. The problem of large-scale convection that arises due to the buoyancy of bubbles coming from deep and shallow sources into the stratified water environment in the Selenga shallows is considered. The behavior of the heterogeneous system during the development of the spring thermal bar is studied.
Ice is highly transparent to solar energy; therefore, the spring heating of the water begins under the ice before melting. As the water temperature near the lower edge of the ice is less than the temperature of maximum density at this depth, the heat flux launches the natural convection in the upper water layer. At the same time, the forced convection may occur in the lake. We associate the origin of forced convection with random events of ascent and dissociation of methane hydrates. Using mathematical models, we study the processes of natural and forced convection beneath the ice in a deep lake under the specific conditions of Lake Baikal. The results of numerical experiments have shown that the natural convection under the ice intensifies the process of forced convection.
To study the behavior of heterogeneous methane-water system, a mathematical model describing the joint processes of hydrodynamics, transport, and transformation of methane in a deep freshwater body is used. There are three phases of methane in the system: solid (hydrate), gaseous (bubbles) and dissolved in water. We discuss the physical origin of phase transitions in the specific conditions of Lake Baikal and possible mathematical formulations of problems. Some preliminary results of calculations are presented.