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? ? RTabdominal muscles 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.
We follow the assumption new procedure from inside the higher part of the rheological boundary layer control the career from downwellings and you will the tendency out-of downwellings so you’re able to realign with plate moves. We start off with the time bills to own convection throughout the absence out-of shear. I then evaluate these types of time scales which have those to possess shear in order to distort brand new rheological line level. My personal strategy is similar to that van Hunen and Zhong , who explore filters prices in place of acceleration for the rheological edge coating. It mix shear and you can convective strain prices to discover the date into rheological edge level to rearrange. I’ve found the fresh new ratio away from shear to convective speed in line coating. From Shape dos, strain price is a handy factor, whilst doesn’t are different far that have depth from the convecting region. The newest velocity inside the border layer is actually their density times the newest filters speed.
We pertain (29) into model of Morency mais aussi al. in the Shape nine. A small changes required because their factor k?C are step one.thirteen moments greater one one to throughout the dos-D patterns; a respected coefficient during the (29) is 90 Ma. The steady-state temperature circulate is actually 43.2/ minutes mine. Its boundary coating time in (29) will then be 21 Ma. This time is the dimensional go out size for matter to go vertically in the sideways averaged velocity through the rheological border layer of (4). New committee times inside Shape 9 differ from the large viewpoints showing (once the apparent) there are going back to convection so you’re able to reorganize.
I get scaling relationships toward tendency off shear so you’re able to straighten convection of the researching shear and you can convection acceleration from the upper area of your own rheological border layer. My personal treatment assumes limited amplitude convection rather than linear stability during the the work out of Korenaga and you will Jordan , and gets to the same total completion your Environment are about real factor variety of Figure nine, where discover a modest desire based on plate velocity to own convection in order 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 from the comparable values from shear velocity and you may convective speed from inside the rheological line covering, Shape 9 suggests a failing interest getting roll alignment. There clearly was a propensity of distance from strenuous convection away from the axis to cut back over the years and also for the the newest goes to be increasing aligned. This new dish moved 1640 kilometres inside the 41 Ma inside Numbers 9b and you may 9c. The boundary of aligned moves went towards older plate way less than simply 1640 kilometer. Additionally, the new changes-parallel artificial limits when you look at the was in fact 100 % free sneak just like the are my personal front side limitations. The 3-D transform-synchronous side limits performed have a tendency to pitfall downwellings, however, did not tend to balance downwellings in the middle of the fresh website name. Overlaying Figures 9b and you can 9c conveyed zero apparent tendency to possess convection models so you can advect over 41 Ma. There is absolutely no obvious scalloping of the foot of the lithosphere (Contour 10) to maintain convection models.