5.step three. Scaling to have Shear Off Plate Motions

Getting assessment with my dating, 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? ? RTstomach 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 to have Date Dependency

I proceed with the expectation the brand new process in top http://www.datingranking.net/hot-or-not-review/ region of the rheological line covering govern the position away from downwellings and you will new inclination regarding downwellings in order to realign which have dish actions. I start off with the time scales to have convection regarding absence off shear. Then i examine these time bills having those getting shear so you’re able to distort the new rheological line layer. My method is a lot like that of van Hunen and Zhong , just who play with filter systems pricing unlike acceleration in the rheological boundary coating. It merge shear and you can convective filter systems cost to get the date on the rheological boundary level so you’re able to rearrange. I’ve found brand new proportion regarding shear in order to convective acceleration inside boundary covering. Out of Shape 2, filter systems price try a convenient factor, because cannot will vary much having breadth in the convecting area. Brand new speed during the line covering are its density moments the latest filters rate.

I implement (29) towards the model of Morency et al. when you look at the Profile nine. A tiny improvement will become necessary as their factor k?C try step 1.thirteen times better you to one to regarding dos-D habits; a respected coefficient when you look at the (29) are ninety Ma. Their steady-state temperatures disperse was 43.2/ moments mine. The line covering amount of time in (29) will then be 21 Ma. This time around is the dimensional date size to have material to go vertically from the laterally averaged speed from rheological line coating away from (4). This new panel moments when you look at the Figure nine disagree by the larger beliefs showing (while the evident) there is actually time for convection so you can rearrange.

We obtain scaling relationship with the tendency from shear in order to straighten convection from the evaluating shear and you can convection velocity in the higher region of the rheological boundary coating. My personal cures takes on limited amplitude convection instead of linear stability when you look at the the job from Korenaga and Jordan , and you may arrives at the same full end your Planet is on the physical factor set of Contour 9, where there clearly was a modest interest dependent on plate speed for convection to help you line up rolls.

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.

As expected on the similar opinions off shear acceleration and convective velocity from inside the rheological border layer, Profile 9 shows a failing desire to possess roll alignment. There was a propensity of one’s point from strenuous convection regarding the newest axis to cut back in time and for the the newest moves becoming increasing aligned. New dish went 1640 kilometer when you look at the 41 Ma from inside the Rates 9b and you can 9c. The edge of aligned moves gone towards more mature plate way less than 1640 km. As well, the fresh new alter-parallel phony boundaries from inside the was indeed free slip since are my personal front side borders. The three-D alter-synchronous front boundaries performed tend to trap downwellings, however, did not tend to balance out downwellings in the exact middle of the domain name. Overlaying Rates 9b and you will 9c indicated no apparent interest getting convection designs to help you advect over 41 Ma. There’s no noticable scalloping of the foot of the lithosphere (Figure ten) to keep convection habits.