A new exact solution is obtained for the Oberbeck-Boussinesq equations describing the steady-state layered (shear) Marangoni convection of a binary viscous incompressible fluid with the Soret effect. When layered (shear) flows are considered, the Oberbeck-Boussinesq system is overdetermined. For it to be solvable, a class of exact solutions is constructed, which allows one to satisfy identically the “superfluous” equation (the incompressibility equation). The found exact solution allows the Oberbeck-Boussinesq system of equations to be reduced to a system of ordinary differential equations by the generalized method of separation of variables. The resulting system of ordinary differential equations has an analytical solution, which is polynomial. The polynomial velocity field describes counterflows in the case of a convective fluid flow. It is demonstrated that the components of the velocity vector can have one stagnant (zero) point inside the region under study. In this case, the corresponding component of the velocity vector can be stratified into two zones, in which the fluid flows in opposite directions. The exact solution describing the velocity field for the Marangoni convection of a binary fluid has non-zero helicity, the flow itself being almost everywhere vortex.

为Oberbeck-Boussinesq方程获得了一个新的精确解，该方程描述了具有Soret效应的二元粘性不可压缩流体的稳态分层（剪切）Marangoni对流。当考虑分层（剪切）流时，Oberbeck-Boussinesq系统是超定的。为了使其可求解，构造了一类精确解，该精确解可让人们完全满足“多余”方程（不可压缩方程）。所找到的精确解允许通过变量分离的广义方法将Oberbeck-Boussinesq方程组简化为常微分方程组。所得的常微分方程组具有多项式的解析解。多项式速度场描述了对流流体流动中的逆流。证明了速度矢量的分量在研究区域内可以有一个停滞（零）点。在这种情况下，速度矢量的相应分量可以分为两个区域，流体在两个区域中以相反的方向流动。描述二元流体的Marangoni对流速度场的精确解具有非零螺旋度，流动本身几乎遍布涡旋。