Related papers: On a Mathematical model for traveling sand dune
Consider the dynamics of turbulent flow in rivers, estuaries and floods. Based on the widely used k-epsilon model for turbulence, we use the techniques of centre manifold theory to derive dynamical models for the evolution of the water…
We consider steady gravity-driven flow of a thin layer of viscous fluid over a curved substrate. The substrate has topographical variations (`bumps') on a large scale compared to the layer thickness. Using lubrication theory, we find the…
Barchan dunes were found to transform into parabolic dunes and vice versa when the amount of vegetation on and around them changes. This work presents the first numerical simulation of this effect. We propose a continuum model for the…
Lubrication equations for a surfactant-driven flow of a thin layer of fluid are considered with a singular surfactant-dependent surface tension. It is shown that there exists a bounded traveling wave solution which connects a fully…
We extend the model of surface granular flow proposed in \cite{bcre} to account for the effect of an external `wind', which acts as to dislodge particles from the static bed, such that a stationary state of flowing grains is reached. We…
We apply nested-sampling (NS) Bayesian analysis [AshtonEA22] to a model for the transport of MHD-scale solar wind fluctuations. The dual objectives are to obtain improved constraints on parameters present in the turbulence transport model…
We describe traveling waves in a basic model for three-dimensional water-wave dynamics in the weakly nonlinear long-wave regime. Small solutions that are periodic in the direction of translation (or orthogonal to it) form an…
Action of solar wind on arbitrarily shaped interplanetary dust particle is investigated. The final relativistically covariant equation of motion of the particle contains both orbital evolution and change of particle's mass. Non-radial solar…
Aeolian transport in coastal areas can be significantly affected by the presence of an exposed water table. In some dune fields, such as in Len\c{c}\'ois Maranhenses, northeastern Brazil, the water table oscillates in response to seasonal…
Crescent shaped barchan dunes are highly mobile dunes that are usually presented as a prototypical model of sand dunes. Although they have been theoretically shown to be unstable when considered separately, it is well known that they form…
Models describing dust-driven winds are important for understanding the physical mechanism and properties of mass loss on the asymptotic giant branch. These models are becoming increasingly realistic with more detailed physics included, but…
We consider two scalar conservation laws with non-local flux functions, describing traffic flow on roads with rough conditions. In the first model, the velocity of the car depends on an averaged downstream density, while in the second model…
The evolution of protoplanetary discs and the related process of planet formation is regulated by angular momentum transport and mass-loss processes. Over the past decade, the paradigm of viscosity has been challenged and MHD disc winds…
We propose a nonlinear hydrodynamical model of granular materials. We show how this model describes the formation of a sand pile from a homogeneous distribution of material under gravity, and then discuss a simulation of a rotating sandpile…
This article explores the dynamics of savanna ecosystems with grazing, browsing, and migration effects. Covering over one-eighth of the Earth's land area and supporting about one-fifth of the global population, the savanna is an ecological…
Sand dunes are often covered by vegetation and biogenic crusts. Despite their significant role in dune stabilization, biogenic crusts have rarely been considered in studies of dune dynamics. Using a simple model, we study the existence and…
In this paper we analyze the gravity model in the world passenger air-transport network. We show that in the standard form the model is inadequate to correctly describe the relationship between passenger flows and typical geo-economic…
The predictive power of mean-field theory is emphasized by comparing theory with simulations under controlled conditions. The recently developed test-field method is used to extract turbulent transport coefficients both in kinematic as well…
We introduce a simple model for the size distribution of avalanches based on the idea that the front of an avalanche can be described by a directed random walk. The model captures some of the qualitative features of earthquakes, avalanches…
We formulate a continuum model for aeolian sand ripples consisting of two species of grains: a lower layer of relatively immobile clusters, with an upper layer of highly mobile grains moving on top. We predict analytically the ripple…