a1 Laboratoire FAST, UPMC/Univ Paris-Sud/CNRS, Bât. 502, Campus Universitaire, 91405 Orsay, France
Buckling instabilities of thin sheets or plates of viscous fluid occur in situations ranging from food and polymer processing to geology. Slim, Teichman & Mahadevan (J. Fluid Mech., this issue, vol. 694, 2012, pp. 5–28) study numerically the buckling of a sheared viscous plate floating on a denser fluid using three approaches: a classical ‘thin viscous plate’ model; full numerical solution of the three-dimensional Stokes equations; and a novel ‘advection-augmented’ thin-plate model that accounts (in an asymptotically inconsistent way) for the advection of perturbations by the background shear flow. The advection-augmented thin-plate model is markedly superior to the classical one in its ability to reproduce the predictions of the Stokes solution, illustrating the utility of judicious violations of asymptotic consistency in fluid-mechanical models.
(Received December 01 2011)
(Reviewed December 01 2011)
(Accepted December 01 2011)