GNGTS 2014 - Atti del 33° Convegno Nazionale

of the inertial Coriolis effect triggered by the Earth’s rotation. Indeed, the Earth is rotating from West toward East and consequently each vertical motion directed from the depths towards the surface should be deviated away from the perfect verticality by a sufficiently strong Coriolis force, undergoing a bending toward west (Fig. 2b). Obviously, the extrusion of mantle materials would not occur along perfectly vertical tracks, but following already existing discontinuity lines. For example the emerging flows adjacent to the western continental margins must have born already with a bending to west, and a more pronounced bending will be the result of the long time of action of the inertial force. If, on the contrary, the flows are near the eastern continental margins, starting already with an eastward bending, the Coriolis force will make them more vertical. The Pacific ocean-floor volcanism is more developed on the western side of the median ridge, and also this can be argued as caused by the prolonged westward action of the Coriolis force that possibly is able to detach “macro-drops” of rising materials and to lead them along more west directed bending paths. Also the asymmetric topography across the rift zones, the compositional, thermal and density asymmetries (Doglioni et al. , 2011), could find an integrated explanation in which the first cause is the Earth’s rotation and the consequent inertial forces. In the same way that the gravity force operates as a sort of filter that drives the lighter compounds towards the surface and the heavier ones towards the geocenter, the Coriolis force could constitute an “E-W filter”. It could drive the heavier minerals towards west, where they appear as constituting a “ fertile mantle ”, while a “ depleted mantle ” is the result to east. In the present short note, before to deal with the Coriolis effect, a reflection has to be made about the possibility of motion of the mantle as a fluid, namely of convective motion in the mantle. The Reynold Number. In fluid mechanics, the Reynolds number N Rey is a dimensionless number that gives a measure of the ratio of inertial forces to viscous forces and consequently quantifies the relative importance of these two types of forces for given flow conditions: where V is the mean velocity of the fluid, L is the characteristic length of the geometry (motions of mantle materials on lenght of undreds of kilometers), and ν is the kinematic viscosity. The higher the Reynolds number is, the more turbulent the flow will be: If N Rey < 2000 the flow is laminar; If 2000 < N Rey < 4000 it is called transition flow; If N Rey > 4000 the flow is turbulent. Recalling that kinematic viscosity ν is the ratio of dynamic viscosity to density ν = µ/ρ , we take the following values: V = 1 cm/yr ≈ 6.34 · 10 -10 m/s ; L = 10 5 m ; µ UM ≈ 10 · 10 19 Pa s, = kg/(s·m) (Harig et al. , 2010); ρ = 3.3 g/cm 3 =3.3 · 10 3 kg/m 3 . Consequently the Reynolds number for the Earth’s upper mantle is N Rey = 2.1 · 10 -21 which is a very little value indicating a slow laminar flow. However, all the researches on the mantle convection assume as starting point a layered non-expanding Earth, which may be a model far from reality. The Rossby Number. It is also important to know if the role of Coriolis effect is important with respect to other inertial forces. It is sufficient to evaluate the Rossby number: with V = typical velocity of the involved material; L = typical length on which the phenomenon develops; f =2 ω · sin φ = Coriolis parameter ( φ = latitude). The value of N Rossby must be very littler than 1.0 to assure that Coriolis effect is important. In the case of motions of mantle materials on length of hundreds of kilometers we can assume ω = 10 -5 rad/s, L = 10 5 m, V = 1 cm/yr ≈ 6.34 · 10 -10 m/s. With the same values for L and V adopted in the preceding Reynold number and ω = 10 -5 rad/s it results: GNGTS 2014 S essione 1.2 177