Related papers: Fluid Flow on Vegetated Hillslope
We describe the physical hypothesis in which an approximate model of water waves is obtained. For an irrotational unidirectional shallow water flow, we derive the Camassa-Holm equation by a variational approach in the Lagrangian formalism.
We investigate effective equations governing the volume expansion of spatially averaged portions of inhomogeneous cosmologies in spacetimes filled with an arbitrary fluid. This work is a follow-up to previous studies focused on irrotational…
The magnetohydrodynamic equations system for heavy fluid over an arbitrary surface in shallow water approximation is studied in the present paper. It is shown that simple wave solutions exist only for underlying surfaces that are slopes of…
The inclusion of stochastic terms in equations of motion for fluid problems enables a statistical representation of processes which are left unresolved by numerical computation. Here, we derive stochastic equations for the behaviour of…
We consider a layer of an inviscid fluid with free surface which is subject to vertical high-frequency vibrations. We derive three asymptotic systems of equations that describe slowly evolving (in comparison with the vibration frequency)…
Irreversible processes play a major role in the description and prediction of atmospheric dynamics. In this paper, we present a variational derivation of the evolution equations for a moist atmosphere with rain process and subject to the…
A basic shallow water system with variable topography is analyzed from the point of view of a Lagrangian derivation of momentum, energy, and pseudomomentum balances. A two-dimensional action and associated momentum equation are derived. The…
In this paper, we present a new fractional mathematical model to describe the dynamics and the interaction between plants and water in arid and semi-arid environments with and without slope. By the Caputo fractional operator, the model…
This article analyses the assumptions regarding the influence of pressure forces during the calculation of the motion of a Newtonian fluid. The purpose of the analysis is to determine the reasonableness of the assumptions and their impact…
We analyze differences in dynamics and in properties of the sampled potential energy landscape between different equilibrium trajectories, for a system of rigid water molecules interacting with a two body potential. On entering in the…
Because of their capability to preserve steady-states, well-balanced schemes for Shallow Water equations are becoming popular. Among them, the hydrostatic reconstruction proposed in Audusse et al. (2004), coupled with a positive numerical…
Various methods for numerically solving Stokes Flow, where a small Reynolds number is assumed to be zero, are investigated. If pressure, horizontal velocity, and vertical velocity can be decoupled into three different equations, the…
Energy distributions of high frequency linear wave fields are often modelled in terms of flow or transport equations with ray dynamics given by a Hamiltonian vector field in phase space. Applications arise in underwater and room acoustics,…
In the papers (Shvidler, 1985 and 1993, and Shvidler and Karasaki, 1999, 2001, 2005, and 2008) we developed an approach for finding the exactly averaged equations of flow and transport in porous media. We studied for steady state flow with…
A physically-based method to derive well-posed instances of the two-fluid transport equations for two-phase flow, from the Hamilton principle, is presented. The state of the two-fluid flow is represented by the superficial velocity and the…
The shear shallow water model provides an approximation for shallow water flows by including the effect of vertical shear in the model. This model can be derived from the depth averaging process by including the second order velocity…
Stability of inviscid shear shallow water flows with free surface is studied in the framework of the Benney equations. This is done by investigating the generalized hyperbolicity of the integrodifferential Benney system of equations. It is…
Nonlinear plant-scale interactions controlling the soil-water balance are generally not valid at larger spatial scales due to spatial heterogeneity in rainfall and vegetation type. The relationships between spatially averaged variables are…
The forest plays an important role in a watershed hydrology, regulating the transfer of water within the system. The forest role in maintaining watersheds hydrological regime is still a controversial issue. Consequently, we use the Soil and…
We consider the governing equations for the motion of compressible fluid on an evolving surface from both energetic and thermodynamic points of view. We employ our energetic variational approaches to derive the momentum equation of our…