Christina Morency, Caroline Dumoulin, Maxim Ballmer, Neil Ribe, and you may N. Asaadi rapidly taken care of immediately questions. One or two private reviewers and the associate editor Thorsten Becker promote comprehensive of good use reviewers. This research was a student in area backed by NSF gives Ear canal-0406658 and Ear-0909319. The latter give try financed under the American Healing and you may Reinvestment Work out of 2009 (ARRA) (Social Laws 111–5).
Appendix Good:: Extension in order to Nonlinear Viscosity
The tension speed when you look at the, such as for example in (3), could possibly get rely on deviatoric worry on nth energy. My personal derivation deal using when (3) is really modified [ Sleep, 2011 ]. Nonlinear convection having shear was complicated as the associated be concerned was another invariant of the be concerned tensor , and this highly partners convection that have shear. I qualitatively discuss the around three topics of my paper.
The derivations apply using (7) to obtain the dependence on T?, providing that ?down is understood to be an effective nonlinear viscosity.
My derivation of scalloping involves forces and flow at the apex of upwellings. Qualitatively, the thicker rheological boundary layer at high n from (7) suppresses scalloping at given T?. Formally, the pressure term in (25) may be modified to ?P n and N replaced with N/n in (26) and (27). Numerical calculations are necessary to obtain a calibrated expression analogous to (28).
Alignment of convection into rolls by plate motions does not appear to be strongly dependent on nonlinear viscosity.
