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Elastic-plated gravity currents with a temperature-dependent viscosity

We develop a set of equations to explore the behaviour of cooling elastic-plated gravity currents for constant influx conditions. In particular, we introduce a temperature-dependent viscosity to couple the flow thermal structure with the velocity field. We show that this coupling results in important deviations from the isoviscous case. In particular, the bending and gravity asymptotic regimes, characteristic of the isoviscous case, both split into three different thermal phases: a first ‘hot’ isoviscous phase, a second phase where the spreading rate drastically decreases and the flow thickens and a third ‘cold’ isoviscous phase. The viscosity that controls the spreading rate differs in both asymptotic regimes; it is the average viscosity of a small peeling region at the current tip in the bending regime and the average flow viscosity in the gravity regime. In both regimes, we characterize the evolution of the thermal anomaly and determine the time scale of the phase changes in terms of the Péclet number and of the viscosity contrast. Finally, we show that the evolution with bending and gravity can result in six different evolution scenarios depending on the combination of dimensionless numbers considered. We provide a phase diagram which summarizes them as a function of the flow Péclet number and viscosity contrast.