06 Sep 5.step 3. Scaling to own Shear Off Plate Motions
To possess comparison with my relationships, Morency ainsi que al
The 3-D model of Morency et al. is intended to represent vigorous convection beneath oceanic lithosphere (Figure 9). and Dumoulin et al. used thermodynamics to represent temperature-dependent viscosity; my scale temperature T? ? RTabs 2 /E, where R is the gas constant, Tabs is absolute temperature of the mantle adiabat, and E is activation energy. Their scale temperatures defined in this way were 106 and 153 K, respectively. The temperature contrasts across their domains were 1400 and 1527 K, respectively. Their ratios of temperature contrast to scale temperature were 13 and 10, respectively, within the expected range for stagnant-lid behavior. Absolute movement of their plates was transform-parallel in the models that I discuss. The ridge-parallel width of Morency et al.’s models was 2400 km (Figure 9) and Dumoulin et al.’s was 1340 and 2680 km, compared with 1500 km in my 2-D models.
5.2. Scaling having Big date Dependence
I follow the assumption this new techniques in upper region of the rheological boundary level regulate the career from downwellings and brand new interest regarding downwellings to help you realign which have plate movements. I start out with the time scales to possess convection throughout the lack of shear. Then i compare these types of date bills which have people getting shear in order to distort the new rheological boundary layer. My personal strategy is a lot like that of van Hunen and Zhong , exactly who use filters pricing rather than velocity in rheological line covering. They mix shear and you may convective strain rates to find the time towards the rheological border coating so you can reorganize. I find this new ratio regarding shear so you’re able to convective acceleration from inside the line coating. Of Contour dos, filters price is a convenient factor, whilst doesn’t are different far with depth about convecting part. The new speed during the edge coating try its density minutes new filters rate.
I use (29) into model of Morency ainsi que al. inside the Shape nine. A little adjustment is needed as their parameter k?C is actually step 1.13 minutes deeper one to you to in the dos-D habits; the leading coefficient during the (29) are going to be 90 Ma. Its steady-state temperature circulate are 43.2/ minutes mine. Their boundary coating time in (29) is then 21 Ma. Now ‘s the dimensional big date level to possess issue to move vertically in the sideways averaged acceleration from the rheological border covering away from (4). The newest panel minutes for the Shape 9 disagree by the big thinking demonstrating (because apparent) that there are time for convection in order to rearrange.
We see scaling matchmaking with the inclination off shear to realign convection by the evaluating shear and convection velocity regarding higher part of the rheological boundary level. My personal treatment assumes limited amplitude convection in the place of linear stability inside the the work from Korenaga and you can Michael jordan , and gets to the same full conclusion the Earth is actually on real parameter listing of Contour 9, where there’s a small interest according to dish velocity having convection to line-up moves.
Kinematically, shear from plate movements will tend to align rolls when its horizontal velocity across the uppermost boundary layer becomes comparable to the convective velocity in (4), VZ = qss/?CT?, 3.1 mm a ?1 . Flow in this region is necessary to rearrange flow that modulates the positions of downwellings.
Sure enough throughout the equivalent philosophy away from shear speed and you will convective acceleration inside the rheological edge covering, Shape 9 suggests a deep failing tendency to have move positioning. There was a propensity of your own point regarding vigorous convection regarding new axis to cut back over time and for the the brand new rolls in order to become broadening aligned. The fresh new plate gone 1640 km inside the 41 Ma for the Figures 9b and you will 9c. The boundary of aligned goes went with the earlier dish way less than 1640 kilometer. At exactly the same time, the alter-parallel fake limits for the was in fact 100 % free sneak because the is my personal side boundaries. The three-D change-parallel side limitations did often pitfall downwellings, however, failed to usually balance out downwellings in the brand new website name. Overlaying Rates 9b and you will 9c indicated zero evident inclination to own convection designs so you can advect more than 41 Ma. There’s absolutely no obvious scalloping of your own foot of the http://datingranking.net/es/por-etnia lithosphere (Profile 10) in order to maintain convection models.