This paper is a review on the results inspired by the publication “Hyperbolic conservation laws with relaxation” by Tai-Ping Liu [1], with emphasis on the topic of nonlinear waves （specifically, rarefaction and sho...This paper is a review on the results inspired by the publication “Hyperbolic conservation laws with relaxation” by Tai-Ping Liu [1], with emphasis on the topic of nonlinear waves （specifically, rarefaction and shock waves）. The aim is twofold： firstly, to report in details the impact of the article on the subsequent research in the area; secondly, to detect research trends which merit attention in the （near） future.展开更多
Tidal forces are generally neglected in the discussion about the mechanisms driving plate tectonics despite a worldwide geodynamic asymmetry also observed at subduction and rift zones.The tidal drag could theoreticall...Tidal forces are generally neglected in the discussion about the mechanisms driving plate tectonics despite a worldwide geodynamic asymmetry also observed at subduction and rift zones.The tidal drag could theoretically explain the westerly shift of the lithosphere relative to the underlying mantle.Notwithstanding,viscosity in the asthenosphere is apparently too high to allow mechanical decoupling produced by tidal forces.Here,we propose a model for global scale geodynamics accompanied by numerical simulations of the tidal interaction of the Earth with the Moon and the Sun.We provide for the first time a theoretical proof that the tidal drag can produce a westerly motion of the lithosphere,also compatible with the slowing of the Earth’s rotational spin.Our results suggest a westerly rotation of the lithosphere with a lower bound ofω≈(0.1-0.2)°/Myr in the presence of a basal effective shear viscosityη≈10^(16)Pa-s,but it may rise toω>1°/Myr with a viscosity ofη≈≤3×10^(14)Pa-s within the Low-Velocity Zone(LVZ)atop the asthenosphere.This faster velocity would be more compatible with the mainstream of plate motion and the global asymmetry at plate boundaries.Based on these computations,we suggest that the super-adiabatic asthenosphere,being vigorously convecting,may further reduce the viscous coupling within the LVZ Therefore,the combination of solid Earth tides,ultra-low viscosity LVZ and asthenospheric polarized small-scale convection may mechanically satisfy the large-scale decoupling of the lithosphere relative to the underlying mantle.Relative plate motions are explained because of lateral viscosity heterogeneities at the base of the lithosphere,which determine variable lithosphere-asthenosphere decoupling and plate interactions,hence plate tectonics.展开更多
基金supported partially supported by the italian Project FIRB 2012 "Dispersive dynamics:Fourier Analysis and Variational Methods"
文摘This paper is a review on the results inspired by the publication “Hyperbolic conservation laws with relaxation” by Tai-Ping Liu [1], with emphasis on the topic of nonlinear waves （specifically, rarefaction and shock waves）. The aim is twofold： firstly, to report in details the impact of the article on the subsequent research in the area; secondly, to detect research trends which merit attention in the （near） future.
基金support from Progetto di Ricerca 2020,Progetto di Ricerca di Ateneo 2021,“Equazioni differenziali ellit-tiche e paraboliche non lineari”Sapienza n.RM120172B8F74615Oscar Bruno gratefully acknowledges support from NSF under con-tract DMS-2109831,from AFOSR under contract FA9550-21-1-0373+1 种基金from the NSSEFF Vannevar Bush Fellowship under ONR contract number N00014-16-1-2808The research was also sup-ported by ESA grant 4000133529/20/NL/GP(Doglioni).
文摘Tidal forces are generally neglected in the discussion about the mechanisms driving plate tectonics despite a worldwide geodynamic asymmetry also observed at subduction and rift zones.The tidal drag could theoretically explain the westerly shift of the lithosphere relative to the underlying mantle.Notwithstanding,viscosity in the asthenosphere is apparently too high to allow mechanical decoupling produced by tidal forces.Here,we propose a model for global scale geodynamics accompanied by numerical simulations of the tidal interaction of the Earth with the Moon and the Sun.We provide for the first time a theoretical proof that the tidal drag can produce a westerly motion of the lithosphere,also compatible with the slowing of the Earth’s rotational spin.Our results suggest a westerly rotation of the lithosphere with a lower bound ofω≈(0.1-0.2)°/Myr in the presence of a basal effective shear viscosityη≈10^(16)Pa-s,but it may rise toω>1°/Myr with a viscosity ofη≈≤3×10^(14)Pa-s within the Low-Velocity Zone(LVZ)atop the asthenosphere.This faster velocity would be more compatible with the mainstream of plate motion and the global asymmetry at plate boundaries.Based on these computations,we suggest that the super-adiabatic asthenosphere,being vigorously convecting,may further reduce the viscous coupling within the LVZ Therefore,the combination of solid Earth tides,ultra-low viscosity LVZ and asthenospheric polarized small-scale convection may mechanically satisfy the large-scale decoupling of the lithosphere relative to the underlying mantle.Relative plate motions are explained because of lateral viscosity heterogeneities at the base of the lithosphere,which determine variable lithosphere-asthenosphere decoupling and plate interactions,hence plate tectonics.
