Initiation of rotation in a liquid near a free boundary

Using the Navier–Stokes system of equations, rotational regimes of thermocapillary fluid flows in a semi-infinite space bounded from above by a non-deformable free boundary, on which a local temperature distribution is specified, are calculated. It is shown that in the boundary layer near the free boundary, as a result of bifurcation, rotational regimes of fluid flows arise during non-uniform cooling of this boundary. Secondary rotational modes are calculated, which form two families of solutions that depend on several parameters, and two parameters are not determined by external conditions.