We present new models to describe shallow water flows over non smooth topographies. The water waves problem is formulated as a system of two equations on surface quantities in which the topography is involved in a Dirichlet-Neumann operator. Starting from this formulation and using the joint analyticity of this operator with respect to the surface and the bottom parametrizations, we derive a no...

Capillary rise from shallow groundwater can decrease the need for irrigation water. However, simple techniques do not exist to quantify the contribution of capillary flux to crop water use. In this study we develop the Agricultural Water Productivity Model for Shallow Groundwater (AWPM-SG) for calculating capillary fluxes from shallow groundwater using readily available data. The model combines...

The development of large medium-speed catamarans aims increasing economic viability and reducing the possible negative influence on the environment of fast sea transportation. These vessels are likely to operate at hump speed where wave-making can be the dominating component of the total resistance. Shallow water may considerably amplify the wave-making and hence the overall drag force. Computa...

A reduced dynamical model is derived which describes the interaction of weak inertia-gravity waves with nonlinear vortical motion in the context of rotating shallow-water flow. The formal scaling assumptions are (i) that there is a separation in timescales between the vortical motion and the inertia-gravity waves, and (ii) that the divergence is weak compared to the vorticity. The model is Hami...

The shallow-water model is used as a testbench for understanding many fundamental dynamical problems (e.g. certain wave–mean interaction problems). One sometimes wants to allow large-amplitude gravity waves to propagate significant distances in such models without forming shocks. This paper presents a simple, and apparently unique, modification of the standard shallow-water model that prevents ...

Lie symmetry analysis is applied to study the nonlinear rotating shallow water equations. The 9-dimensional Lie algebra of point symmetries admitted by the model is found. It is shown that the rotating shallow water equations are related with the classical shallow water model with the change of variables. The derived symmetries are used to generate new exact solutions of the rotating shallow eq...

All shallow water hydro-sediment-morphodynamic (SHSM) models are prone to uncertainty arising from inadequate representation of the underlying physics and error in input parameters. At time writing, most SHSM solve deterministic problems, whilst studies quantification remain rare. Here a new stochastic model is proposed, extended well-balanced, operator-splitting-based, generalized polynomial c...

We consider the motion of an incompressible fluid confined to a shallow basin with varying bottom topography. A two-dimensional shallow water model has been derived from a three-dimensional anisotropic eddy viscosity model and has been shown to be globally well posed in [15]. The dynamical system associated with the shallow water model is studied. We show that this system possesses a global att...