HR: 0800h
AN: T11E-1324    [Abstracts]
TI: Periodic Folding of Viscous Sheets: A Model for Subducted Slabs at the CMB
AU: * Ribe, N M
EM: ribe@ipgp.jussieu.fr
AF: IPGP, 4 Place Jussieu, Paris, 75005 France
AB: A sheet of viscous fluid falling from a sufficient height onto a surface undergoes regular periodic folding. This instability is easily observed in the home kitchen with cake batter or honey, and may occur in the earth when subducted lithosphere impinges on the core-mantle boundary. Using a numerical model for a 2-D thin sheet that deforms by combined bending and stretching with negligible inertia, I determine how the folding frequency depends on the height of fall $L$, the sheet's initial thickness $H_0$, the volume flux per unit length $q$, and the fluid's viscosity $\mu$ and anomalous density $\delta\rho$. Two distinct folding modes are possible. When buoyancy is weak, ``viscous'' folding occurs with a frequency proportional to $f_V = q/L H_1$, where $H_1$ ($\leq H_0$) is the thickness of the portion of the sheet that folds. When buoyancy is strong, ``gravitational'' folding occurs with a frequency proportional to $f_G = (\delta\rho g q^3/\mu H_1^5)^{1/4}$. The bifurcation from viscous to gravitational folding occurs sharply at a critical value ($= 3.9$) of the parameter $f_G/f_V$ that measures the importance of buoyancy. In both modes, the instability generates a multilayered ``sandwich'' of strongly folded sheet material and intercalated ambient fluid. In the earth, such a structure is likely to be associated with complex seismic anisotropy. I will also present results of a numerical study of the closely related phenomenon of 3-D coiling of a viscous filament. While not directly relevant to subduction, this phenomenon is important in many engineering contexts and has been observed to occur in falling lava streams. Coiling can occur in viscous and gravitational modes analogous to those of 2-D folding, and also in an ``inertial'' mode in which viscous forces are balanced by rotational inertia. Coiling is multivalued in the gravitational-inertial transition regime, where three distinct frequencies are possible for the same values of the flow rate and fall height.
DE: 8005 Folds and folding
DE: 8120 Dynamics of lithosphere and mantle--general
DE: 3220 Nonlinear dynamics
SC: Tectonophysics [T]
MN: 2004 AGU Fall Meeting