Related papers: Fluid Flow on Vegetated Hillslope
The hillslope hydrological processes are very important in watershed hydrology research. In this paper we focus on the water flow over the soil surface with vegetation in a hydrographic basin. We introduce a PDE model based on general…
The hillslope hydrological processes are very important in watershed hydrology research. In this paper we focus on the water flow over the soil surface with vegetation in a hydrographic basin. We introduce a PDE model based on general…
We derive general depth-integrated model equations for overland flows featuring the evolution of suspended sediment that may be eroded from or deposited onto the underlying topography ('morphodynamics'). The resulting equations include…
These are notes that I compiled while studying the equations of long-range groundwater flow for my first paper. By "long-range," I mean horizontal distances that are significantly greater than the vertical thickness of the aquifer, in…
A formulation of the shallow water equations adapted to general complex terrains is proposed. Its derivation starts from the observation that the typical approach of depth integrating the Navier-Stokes equations along the direction of…
The water circulation in the Soil-Plant-Atmosphere continuum and particularly the soil erosion induced by water are problems of main concern in the new era of climate change. The present paper aims to provide a mathematical tool to…
It is shown how a complete set of hydrodynamic equations describing an unsteady three-dimensional viscous flow nearby a solid body, can be reduced to a closed system of surface equations using the method of dimension reduction of…
In this work, we show how the rheology of granular suspensions can be related to the properties of the fluctuations of the velocity field inside the medium. In particular, effective Navier-Stokes equations in the different flow regimes are…
China has undertaken unprecedented, state-driven vegetation restoration on a continental scale. This large-scale land-surface intervention offers a rare opportunity to assess how deliberate biospheric change influences climate-relevant…
Long waves in shallow water propagating over a background shear flow towards a sloping beach are being investigated. The classical shallow-water equations are extended to incorporate both a background shear flow and a linear beach profile,…
The floating structure problem describes the interaction between surface water waves and a floating body, generally a boat or a wave energy converter. As shown by Lannes in [18] the equations for the fluid motion can be reduced to a set of…
We investigate the consequences of fluid flowing on a continuous surface upon the geometric and statistical distribution of the flow. We find that the ability of a surface to collect water by its mere geometrical shape is proportional to…
Understanding how submerged vegetation modifies the water surface is crucial for modeling momentum exchange between shallow waters and the atmosphere. In particular, quantifying its impact on the equivalent aerodynamic roughness of the…
In this work, the problem of constructing geometric flow equations that preserve Einstein field equations for the spacetime metric is addressed. After having briefly discussed the main features of Ricci flow, the on-shell flow equations for…
In this paper, we consider a system of partial differential equations modeling the evolution of a landscape. A ground surface is eroded by the flow of water over it, either by sedimentation or dilution. The system is composed by three…
We investigate the effect of a forest of pillars on a granular layer steadily flowing over a rough inclined plane. We quantify experimentally how the steady flow rate of grains is affected by the inter-pillars distance for different layer…
We introduce a physically relevant stochastic representation of the rotating shallow water equations. The derivation relies mainly on a stochastic transport principle and on a decomposition of the fluid flow into a large-scale component and…
The variational free-Lagrange (VFL) method for shallow water is a free-Lagrange method with the additional property that it preserves the variational structure of shallow water. The VFL method was first derived in this context by…
Through a discussion of some typical unsteady hydrodynamic flows, we argue that the time averaged hydrodynamic functions at each point give a rather sparse filling of the local jet space. This situation then suggests a set of time dependent…
General equations are derived for slow viscous thin fluid film flows on curved surfaces through an extension of Leal's pedagogical approach, which leaves the characteristic velocity scale unspecified and employs a direct through-thickness…