Different-scale convective structures in a cooled liquid layer with a horizontal shear flow

Abstract

The paper is concerned with three-dimensional different-scale convective structures arising in a thin liquid layer cooled from above and subjected to a horizontal shear flow produced by tangent wind stresses on a free surface. In accord with the previous experiment the region of moderately large Grashof and Marangoni numbers and not too large Reynolds numbers is examined. The problem is solved numerically using a spectral method constructed on the basis of a spectral representation of the standard equations governing the gravity-capillary convection. Spectral decomposition with periodicity condition along the horizontal coordinates together with discretization in the vertical direction is used. The planeforms obtained in a horizontal subsurface section of vertical velocity field are analyzed. The mechanism of formation of coherent different-scale structures arising due to surface cooling and thermocapillarity effects is elucidated and the cell-to-roll transition occurring with the increase of horizontal flow velocity is studied. Roll patterns containing longitudinal (aligned in the mean flow direction) basic rolls and predominantly transversal small-scale rolls are revealed. The problem of upflow and downflow cells in question is discussed and the agreement of the computational results with the available experimental data is confirmed.