CPT Q. 028: How does limiting the minimum viscosity affect the time scale in your TERRA calculations?

Q. 28. Can you explain the ‘viscosity floor’ parameter you mention in your papers on CPT and describe how it affects the time scale of the TERRA calculations?

Response: What I have referred to as a ‘viscosity floor’ in TERRA is a limiting minimum value on the viscosity. It is an input parameter, vscmin, that multiplies the reference viscosity to establish a lower bound on the viscosity everywhere in the computational domain. Hence, as the rheological law—which determines the local viscosity as a function of temperature, strain rate, and yield stress—causes the local value of viscosity to become small, it is restrained to become no smaller than this lower bound. When vscmin is set to a modest value of, for example, 0.01, the viscosity can fall only two orders of magnitude below the reference viscosity value and no runaway takes place. However, if other conditions are right and a vscmin value on the order of 10-10 is used, then runaway will indeed take place. When this runaway behavior arises, the flow velocities become dramatically larger and the time scale for material traversing the depth of the mantle becomes dramatically shorter. One might ask whether such small values for vscmin are justified. As I have pointed out in many of my publications, there is strong experimental evidence that silicates do display such large reductions in strength as shear stress levels increase, within the range of stress levels that can exist in the mantles of planets like the earth. Please note that this feature currently exists only in the 2D version of TERRA because at present only the 2D version has the ability to handle the extreme gradients in material properties that arise under runaway conditions.

Let me make one final comment is that a major research goal is to improve the numerical methods in the 3D version of TERRA such that it matches the ability of the 2D version to handle extreme gradients in material strength. I myself as well as some of my European collaborators are working earnestly to reach this goal.