  Viscous heating can play an important role in the dynamics of fluids with
strongly temperature-dependent viscosities because of the coupling between the
energy and momentum equations. The heat generated by viscous friction produces
a local temperature increase near the tube walls with a consequent decrease of
the viscosity and a strong stratification in the viscosity profile. The problem
of viscous heating in fluids was investigated and reviewed by Costa & Macedonio
(2003) because of its important implications in the study of magma flows.
Because of the strong coupling between viscosity and temperature, the
temperature rise due to the viscous heating may trigger instabilities in the
velocity field, which cannot be predicted by a simple isothermal Newtonian
model. When viscous heating produces a pronounced peak in the temperature
profile near the walls, a triggering of instabilities and a transition to
secondary flows can occur because of the stratification in the viscosity
profile. In this paper we focus on the thermal and mechanical effects caused by
viscous heating. We will present the linear stability equations and we will
show, as in certain regimes, these effects can trigger and sustain a particular
class of secondary rotational flows which appear organised in coherent
structures similar to roller vortices. This phenomenon can play a very
important role in the dynamics of magma flows in conduits and lava flows in
channels and, to our knowledge, it is the first time that it has been
investigated by a direct numerical simulation.
