Linear stability of shallow morphodynamic flows

Nonclassical Shallow Water Flows

This paper deals with violent discontinuities in shallow water flows with large Froude number F . On a horizontal base, the paradigm problem is that of the impact of two fluid layers in situations where the flow can be modelled as two smooth regions joined by a singularity in the flow field. Within the framework of shallow water theory we show that, over a certain timescale, this discontinuity ...

Shallow granular flows

Generalized linear stability of noninertial coating flows over topographical features

The transient evolution of perturbations to steady lubrication flow over a topographically patterned surface is investigated via a nonmodal linear stability analysis of the non-normal disturbance operator. In contrast to the capillary ridges that form near moving contact lines, the stationary capillary ridges near trenches or elevations have only stable eigenvalues. Minimal transient amplificat...

Global linear stability analysis of weakly non-parallel shear flows

The global linear stability of incompressible, two-dimensional shear flows is investigated under the assumptions that far-field pressure feedback between distant points in the flow field is negligible and that the basic flow is only weakly nonparallel, i.e. that its streamwise development is slow on the scale of a typical instability wavelength. This implies the general study of the temporal ev...

Efficient iterative algorithms for linear stability analysis of incompressible flows

Linear stability analysis of a dynamical system entails finding the rightmost eigenvalue for a series of eigenvalue problems. For large-scale systems, it is known that conventional iterative eigenvalue solvers are not reliable for computing this eigenvalue. A more robust method recently developed in Elman & Wu (2012) and Meerbergen & Spence (2010), Lyapunov inverse iteraiton, involves solving l...