Couette and Poiseuille flows in a low viscosity asthenosphere: Effects of internal heating rate, Rayleigh number, and plate representation

• Mantle models with high viscosity plates and a low viscosity asthenosphere are investigated.
• Free-slip and force-balance surface boundary conditions are used.
• Long wavelength flows are found with changing heating rate and Rayleigh number.
• Mean heat flux decreases with aspect ratio in force-balance models.

Mantle convection models with a low viscosity asthenosphere and high viscosity surface plates have been shown to produce very large aspect ratio convection cells like those inferred to exist in Earth’s mantle and to exhibit two asthenospheric flow regimes. When the surface plate is highly mobile, the plate velocity exceeds the flow velocities in the asthenosphere and the plate drives a Couette-type flow in the asthenospheric channel. For sluggish plates, the flow velocities in the asthenosphere exceed the plate velocity and the asthenospheric flow is more Poiseuille-like. It has been shown that under certain circumstances, flows become increasingly Couette-like as the aspect ratio of the plate is increased in numerical simulations. These models also show an increase in the average surface heat flux with aspect ratio which is counterintuitive, as one would expect that large aspect ratio models would result in older and colder oceanic lithosphere. Previous investigations have used single internal heating rates and Rayleigh numbers and a plate formulation that did not preclude significant deformation within the plate. In this paper, we investigate the conditions necessary for Couette and Poiseuille asthenospheric flows and for surface heat flux to increase with plate aspect ratio by varying the internal heating rate, the Rayleigh number and the representation of surface plates in 2D mantle convection models Plates are represented as a high viscosity layer with (1) a free-slip top surface boundary condition and (2) a force-balance boundary condition that imposes a constant surface velocity within the plate. We find that for models with a free-slip surface boundary condition, the internal heating rate and Rayleigh number do not strongly affect the dominance of Couette or Poiseuille flows in the asthenosphere but the increase in surface heat flux with model aspect ratio in the Poiseuille asthenospheric flow regime increases with internal heating rate. For models using the force-balance representation of surface plates, the flow regime in the asthenosphere is found to be almost independent of the plate aspect ratio and spatially averaged surface heat flux decreases with increasing aspect ratio. The dependence of heat flux on plate aspect ratio is an important consideration in Earth’s thermal history while the preponderance of Poiseuille or Couette flows in the asthenosphere may be important for understanding the mobility of surface plates and asthenospheric seismic anisotropy.