On the geometry of mantle flow beneath drifting lithospheric plates

The convective flow pattern beneath the oceanic lithosphere is strongly influenced by the movement of the lithospheric plate on top. Assuming upper mantle convection, the wavelengths, geometric structure and time of onset for ridge-perpendicular rolls as functions of the Rayleigh number and the plate velocity have been investigated by numerical modelling. The related gravity anomalies have been estimated and compared to observations from the SE Pacific, which show ridge-perpendicular anomalies with wavelengths of 150-220km and amplitudes of about 10 mGal. For constant viscosity, the type of secondary circulation perpendicular to the diverging ridge depends on the relation between imposed plate velocity, v_s, and maximum velocity in the free-convection case, v_Hfree. If v_s is less than v_Hfree the flow is dominated by off-ridge up- and downwellings if v_s is about 10 times larger than v_Hfree the flow remains 2-D. If v_s is between these extrema, a chain of ridge plumes develops from the lower thermal boundary layer with adjacent ridge-perpendicular walls that lead to roll-like circulation (`Richter rolls') throughout the model box. The wavelength of these rolls is a function of the Rayleigh number and the plate velocity. For parameters realistic for the Earth, rolls with considerable amplitude first develop after more than 50Myr with wavelengths of at least 250km. For temperature- and pressure- (depth-) dependent viscosity, the wavelengths of the evolving rolls are determined by the Rayleigh number related to the maximum viscosity in the interior of the convecting system (and not to the average viscosity). For models with a strong decrease in viscosity to values of about 10¹⁹Pas in a 100-km-wide asthenospheric channel below the lithosphere, ridge-perpendicular rolls, which only fill the low-viscosity layer, appear after a few million years. After a transitional stage of some tens of millions of years rolls in the whole upper mantle also evolve. The asthenospheric rolls develop from instabilities of the upper thermal boundary layer and have wavelengths of about 220-280km. The time needed for alignment of these rolls to the direction of plate movement is a few million years and the distance from the ridge to the point of onset of the rolls is about 200-500km both are functions of the plate velocity. While the formation time for rolls in the whole upper mantle is quite large and their existence is related largely to two-layered convection, this type of flow might not be very relevant for the Earth, although it has been used to account for 3-D structures at oceanic ridges. To explain the observed gravity anomalies in the SE Pacific, roll-like circulation in a low-viscosity asthenospheric layer is the preferred candidate, where the modelled amplitudes and wavelengths of gravity anomalies fit the observations.