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A Model of the Winter Runoff Depletion Curves in the Northeast of Russia. C. 5–14

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Section: Geosciences




Oleg N. Shablovskiy*, Dmitriy G. Krol’*
*Sukhoi State Technical University of Gomel (Gomel, Republic of Belarus)


The problem of dynamic external influence of a standing wave on the stationary periodic thermal structures – “stripes”, “rectangles”, “triangles”, “cells” is solved. The central point of the used model is based on the local nonequilibrium properties of heat transfer within the Maxwell relaxation model. For the heat transfer equations we have built a new exact analytical solution describing the effect of two energy sources on a substance. An alternating volume source simulates the competition between the temperature ranges with heat release and heat exchange. The external source acts on the rupture line of the thermal field and excites a standing wave. The stationary part of the solution refers to the stationary temperature and determines the post-relaxation space-periodic thermal rate. The non-stationary part of the solution describes oscillations and waves in the “medium – energy source” system. Explicit analytical expressions for the vector component of the heat flux are obtained; and the phase shift of longitudinal and traversal oscillations with respect to the rupture of thermal fluxes is calculated. The processes of the standing wave generation are studied both in the sub-sonic and super-sonic regimes with regard to the velocity of the thermal perturbations propagation. A non-linear nature of the interaction of the exciting oscillations and the non-equilibrium medium is established. The detailed analysis of the thermal behavior of the Mach numbers, defining the properties of waves in the longitudinal and transverse directions to rupture, is carried out. The dimensionless parameter of the non-equilibrium system is built; its significant impact on the sub-sonic and super-sonic modes of wave propagation is demonstrated. Morphological properties of isotherms are determined. The phase portrait of the thermophysical system is built in space of “longitudinal component of the heat flux vector – transverse component – temperature”. The values of the oscillation frequency obtained for a closed or non-closed phase trajectories are indicated. The examples of trajectories on a cylinder and a torus are presented. The applications of the problem are associated with the formation of periodic structures at explosive crystallization of amorphous films deposited on a substrate.


standing heatwave, energy source, local nonequilibrium heat transfer, periodic thermal structure, explosive crystallization
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