Temperature-dependent viscous gravity currents with shear heating

We have studied the effects of viscous dissipation on gravity current in the Stokes flow regime for both constant volume and constant flux boundary conditions. We have also examined the influence of temperature-dependent viscosity, as well as the relative importance of thermal and chemical buoyant forces. For the constant volume case a three-stage evolution was found. This aspect concerning the existence of the multiple stages is new and was not found previously. This three-stage behavior comes as a result of the interaction between the two quasi-isothermal regimes. The first regime corresponds to an early stage with a uniformly high temperature, whereas the third stage represents the final period, when most part of the current has cooled down to uniformly low temperature. This evolutionary process with three-stages is characteristic of a temperature-dependent viscous fluid and does not depend too much on viscous dissipation, which induces a longer transient period. In contrast to constant volume case, there is only one stage of development for the constant flux current. Although temperature-dependent viscosity influences the current dynamics, the rate of expansion follows a t^1/2 asymptote which is close to the prediction for a constant viscosity model with a constant flux condition. Viscous dissipation exerts definitely a stronger influence in the constant flux gravity currents as compared to the constant volume case, because of the faster velocities produced by the constant flux condition.