Thermocapillary driven flows in differentially heated cavities and cyl
indrical liquid bridges are reviewed. The exploration of the Bow struc
tures and the transitions between two- and three-dimensional solutions
has made significant progress by the application of numerical methods
. Results of these calculations together with comments concerning the
applied numerical techniques are presented in order to give a comprehe
nsive picture of the possible Bow phenomena. Although linear and nonli
near steady two-dimensional flows are well understood, their stability
and the nonlinear dynamics of fully developed three-dimensional therm
ocapillary convection still provide challenges for future numerical in
vestigations.