Dissipative Structures of Marangoni Convection in a Thin Layer of liquid with Lattice of Localized and Continuously Distributed Heat Sources and Sinks

The three-dimensional solutions of nonlinear long-wavelength approximations for the problem of Marangoni convection in a thin horizontal layer of a viscous incompressible fluid with a free surface is being considered. The temperature distribution in the liquid corresponds to a uniform vertical gradient distorted by the imposition of a weakly inhomogeneous heat flux localized in the horizontal plane, caused by a lattice of either localized or continuously distributed heat sources and sinks. The lower boundary of the layer is solid and thermally insulated, while the upper one is free and deformable. The statement of the problem is motivated by the search for ways to control convection structures. The problem in long-wave approximation is described by a system of nonlinear transport equations for the amplitudes of temperature distribution and surface deformation. The numerical solution of the problem is based on the pseudospectral method. The dynamics of non-stationary dissipative structures is considered.