The dynamics of confined extensional flows

Abstract

I present a theoretical and experimental study of floating viscous fluid films introduced into a channel of finite length, motivated by the flow of glacial ice shelves. The dynamics are characterized by a mixture of viscous extensional stresses, transverse shear stresses and a driving buoyancy force. A theory based on a width-integrated model is developed and investigated using analytical, asymptotic and numerical methods. With fluid introduced at a constant rate, the flow is found to approach a steady state with two possible asymptotic forms depending on the length of the channel. For channel lengths less than half the width, the flow is similar to a purely extensional one-dimensional flow, characterized by concave surface profiles and being insensitive to the position of the channel exit (or calving front). Greater lengths result in a more complex asymptotic structure in which the flow adjusts over a short distance towards a prevailing flow of universal dimensionless form. In complete contrast to the extensional regime, the prevailing flow is controlled by the position of the channel exit. Data from a new laboratory experiment involving particle velocimetry of a floating fluid film compares well with the predicted along-channel velocity. Motivated by glaciological application, the analysis is generalized to power-law rheologies and the results used to classify the flow regimes of a selection of ice shelves. The prediction for the frontal speed is in good agreement with geophysical data, indicating that the universal profile predicted by the theory is common in nature.