(90i) Harmonic Regelation

beginning of a sustained scientific fascination with "regelation", the

pressure-induced thawing and refreezing of ice at solid boundaries. This

phenomenon has been invoked to explain various processes such as basal

melting of glaciers and a well-known classroom experiment involving the

passage without trace of a solid wire through a block of ice. Nye [1]

provides an elegant mathematical theory for the movement of a circular

wire, with speed controlled by a lubrication-type flow in an interfacial

liquid layer, together with conduction of heat through wire, layer and

surrounding ice. Nye derives an analytical solution to the problem,

based on the angular symmetry of the associated harmonic temperature and

pressure fields, Subsequent careful experiments, e.g. of [2], show close

agreement with Nye's theory in some cases but not in others. After a

brief review of the theory and experiment, it is shown here that Nye's

is a special case of a more general theory which admits solutions for the translation and rotation of symmetrical

bodies such as elliptic cylinders and general ellipsoids. This provides

a generalization of the "Stokes-law" drag proposed by Nye for the

motion of one rigid body through another. The current theory also

suggests a simpler regelation experiment with measurement of torque

required for the slow rotation of an elliptic cylinder in ice.

[1] J.F. Nye, "Theory of regelation". Phil. Mag.,16,1249-66,1967.

[2] L.D. Drake and R.L. Shreve,"Pressure melting and regelation of ice by round wires" Proc. Roy. Soc. A,, 332, 51-83, 1973.