AbstractIt is argued that ‘sifting’ phenomena, in which fragments of fluid subjected to larger body forces move through those subjected to smaller body forces, are prevalent in turbulent flows, and that they can be simulated by means of mathematical methods which have been developed for two‐phase flows.A connection with Prandtl's mixing‐length theory is established; and it is deduced from the success of that theory for shear flows that there must exist a source term in the normal‐to‐wall‐velocity equations which is proportional to the gradient of along‐the‐wall velocity. This term is then included in the two‐fluid‐model equations.Solutions of the equations are presented for a turbulent Couette flow in which the heating of one of the walls and the presence of a gravitational field can cause ‘sifting’ phenomena to become dominant. The friction and heat‐transfer coefficients, and the profiles of velocity and temperature, are computed and discussed, for flows both with and