Stress-gradient Coupling in Glacier Flow: IV. Effects of the “T” Term

• Published in: Journal of Glaciology
• Main Authors: Kamb, Barclay, Echelmeyer, Keith A.
• Format: Article in Journal/Newspaper
• Language: English
• Published: Cambridge University Press (CUP) 1986
• Subjects: Journal of Glaciology
• Online Access: http://dx.doi.org/10.1017/s0022143000012016; https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022143000012016

Abstract The “ T term” in the longitudinal stress-equilibrium equation for glacier mechanics, a double y -integral of ∂ 2 τ xy /∂ x 2 where x is a longitudinal coordinate and y is roughly normal to the ice surface, can be evaluated within the framework of longitudinal flow-coupling theory by linking the local shear stress τ xy at any depth to the local shear stress τ B at the base, which is determined by the theory. This approach leads to a modified longitudinal flow-coupling equation, in which the modifications deriving from the T term are as follows: 1. The longitudinal coupling length is increased by about 5%. 2. The asymmetry parameter σ is altered by a variable but small amount depending on longitudinal gradients in ice thickness h and surface slope α . 3. There is a significant direct modification of the influence of local h and α on flow, which represents a distinct “driving force” in glacier mechanics, whose origin is in pressure gradients linked to stress gradients of the type ∂ τ xy / ∂ x. For longitudinal variations in h , the “ T force” varies as d 2 h/ d x 2 and results in an in-phase enhancement of the flow response to the variations in h , describable (for sinusoidal variations) by a wavelength-dependent enhancement factor. For longitudinal variations in α, the “force” varies as dα/d x and gives a phase-shifted flow response. Although the “ T force” is not negligible, its actual effect on τ B and on ice flow proves to be small, because it is attenuated by longitudinal stress coupling. The greatest effect is at shortest wavelengths (λ 2.5 h ), where the flow response to variations in h does not tend to zero as it would otherwise do because of longitudinal coupling, but instead, because of the effect of the “ T force”, tends to a response about 4% of what would occur in the absence of longitudinal coupling. If an effect of this small size can be considered negligible, then the influence of the T term can be disregarded. It is then unnecessary to distinguish in glacier mechanics between two length ...