Abstract It has been proposed that hot spot tracks are caused by moving rigid plates above relatively stationary hot spots. However, the fixity of hot spots remains under debate. Here, we perform 3‐D very high resolution (<25 km laterally) global mantle convection models with realistic convection vigor to investigate the lateral motion of mantle plumes. We find that the lateral motion of plumes beneath the Pacific plate is statistically similar to that beneath the Indo‐Atlantic plates. In the past 80 Ma, the majority (>90%) of plumes move laterally with an average speed of 0–20 mm/year under the no‐net‐rotation reference frame, and there are a small portion (~10–20%) of plumes whose lateral motion is less than 5 mm/year. The geodynamic modeling results are statistically in a good agreement with the hot spot motions in the last 5 Ma estimated from observation‐based kinematic models. Our results suggest a small‐to‐moderate (0–20 mm/year) lateral motion of most plume‐induced hot spots.
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Large Amplitude Radially Symmetric Spots and Gaps in a Dryland Ecosystem Model
Abstract We construct far-from-onset radially symmetric spot and gap solutions in a two-component dryland ecosystem model of vegetation pattern formation on flat terrain, using spatial dynamics and geometric singular perturbation theory. We draw connections between the geometry of the spot and gap solutions with that of traveling and stationary front solutions in the same model. In particular, we demonstrate the instability of spots of large radius by deriving an asymptotic relationship between a critical eigenvalue associated with the spot and a coefficient which encodes the sideband instability of a nearby stationary front. Furthermore, we demonstrate that spots are unstable to a range of perturbations of intermediate wavelength in the angular direction, provided the spot radius is not too small. Our results are accompanied by numerical simulations and spectral computations.
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- Award ID(s):
- 2105816
- PAR ID:
- 10530148
- Publisher / Repository:
- Springer Nature
- Date Published:
- Journal Name:
- Journal of Nonlinear Science
- Volume:
- 33
- Issue:
- 6
- ISSN:
- 0938-8974
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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