Mantle convection with continents in an annulus#
This section was contributed by Cedric Thieulot and Erik van der Wiel.
UNDER CONSTRUCTION: This cookbook does currently not produce the results shown in the figures. The reason for that is that the original model of van der Wiel et al. [2024] used a more complicated parameter file and a different version of ASPECT. Do not rely on the results of this cookbook at the moment.
The setup for this experiment originates in van der Wiel et al. [2024]. The domain is an annulus with an inner radius of 3480 km and an outer radius of 6370 km. The Isentropic Compression Approximation (ICA) is used [Gassmöller et al., 2020], which is the default approximation for compressible flow in ASPECT.
Flow in the model is governed by the visco-plastic flow equations that describe dislocation and diffusion creep and we use the Drucker-Prager yield criterion to limit viscous stresses [Glerum et al., 2018]. The grain size in the diffusion creep is assumed constant and therefore incorporated in the pre-factor A. Note that in the lower mantle flow is based on diffusion creep only.
Both the inner and outer boundaries are free-slip boundaries so there is no external kinematic forcing on the model. The resulting existing rotational null space is removed by imposing no-net-rotation of the mantle. The boundaries have fixed temperatures of 3700 K and 300 K. Within the domain two compositional fields are defined: mantle and continent. The mantle domain consists of three different regions separated by the two major phase changes occurring at ~410- and ~660 km depths. We use the geodynamic World Builder [Fraters et al., 2019] to set the initial temperature and compositional field distribution (see Fig. 154, Fig. 155 and Fig. 156).
Fig. 154 Initial viscosity field.#
Fig. 155 The initial position of the three continents.#
Fig. 156 Initial temperature field.#
Similar to Ulvrova et al. [2019], we use viscous rafts as “continents” to aid with modelling one-sided subduction systems. We use three continents of 5000, 5000 and 3000 km length, covering roughly 30% of the model surface. To avoid subduction of the continents, we assign the viscous rafts a reference density of 2916 kg/m3, which corresponds to a 400 kg/m3 density contrast with the reference mantle density. Furthermore, to avoid deformation of the continents, we assign them a viscosity that equals the maximum cut-off viscosity in the model, i.e. 6e24 Pa s. We also configure three subduction zones in the initial set-up to seed the model with initial negative buoyancy.
As the goal of the cookbook (and the corresponding publication in van der Wiel et al. [2024]) is to investigate how average slab sinking rates relate to the vigor of mantle convection and mixing, various rheologies are considered in the lower mantle, as shown in Fig. 157. We will focus on the ‘R’ (reference) profile in this cookbook (green line).
Fig. 157 Radial viscosity profiles for the three models discussed in the original publication (solid lines) compared to viscosity profiles as used in other studies. See original publication for the references corresponding to the dashed lines.#
After 500 Myr we see multiple subductions taking place as well as many plumes/upwellings, as shown in Fig. 158
Fig. 158 Results of the reference model (R) after 500 Ma of mantle convection simulation. Snapshots of the model at t = 500 Ma are shown for the viscosity (a) and temperature (b) within the modelled domain, showing five slabs actively subducting below the continents (pink). (c) Solid lines indicate average surface velocity (blue) and mobility M (red) of model R as well as their dashed time-averages Vsurf=2.1 cm/a and M = 2.218. Mobility is defined as the ratio of rms surface velocity to rms velocity averaged over the entire 3D domain [Tackley, 2000]. (d) Radial velocity of all tracers defined as slabs plotted at their position in the model where blue indicates sinking slabs and red slowly rising. Shown tracers are 300 K colder than the radial averaged temperature at similar depth and automatically obtained (see methods section of the publication). (e) 2D-histogram showing the tracer depth vs the radial velocity in 25 km by 2 mm/a bins. The colour indicates the number of particles within a certain bin.#