Related papers: The Dynamics of a Meandering River
We consider a linearized dynamical system modelling the flow rate of water along the rivers and hillslopes of an arbitrary watershed. The system is perturbed by a random rainfall in the form of a compound Poisson process. The model…
The effects of erosion, avalanching and random precipitation are captured in a simple stochastic partial differential equation for modelling the evolution of river networks. Our model leads to a self-organized structured landscape and to…
The hierarchy of channel networks in landscapes displays features that are characteristic of non-equilibrium complex systems. Here we show that a sequence of increasingly complex ridge and valley networks is produced by a system of partial…
This study is motivated by problems related to environmental transport on river networks. We establish statistical properties of a flow along a directed branching network and suggest its compact parameterization. The downstream network…
We study the dynamics of flow-networks in porous media using a pore-network model. First, we consider a class of erosion dynamics assuming a constitutive law depending on flow rate, local velocities, or shear stress at the walls. We show…
In meandering rivers, interactions between flow, sediment transport, and bed topography affect diverse processes, including bedform development and channel migration. Predicting how these interactions affect the spatial patterns and…
Natural rivers connect to each other to form networks. The geometric structure of a river network can significantly influence spatial dynamics of populations in the system. We consider a process-oriented model to describe population…
A new model to simulate the time evolution of river delta formation process is presented. It is based on the continuity equation for water and sediment flow and a phenomenological sedimentation/ erosion law. Different delta types are…
Earth and soils are indispensable elements of river environment. Dam-downstream environment and ecosystems have been severely affected by reduced or even stopped sediment supply from the upstream. Replenishing earth and soils from outside…
Meandering instability is familiar to everyone through river meandering or small rivulets of rain flowing down a windshield. However, its physical understanding is still premature, although it could inspire researchers in various fields,…
Although riparian vegetation is present in or along many water courses of the world, its active role resulting from the interaction with flow and sediment processes has only recently become an active field of research. Especially, the role…
We consider the deterministic and stochastic versions of a first order non-autonomous differential equation which allows us to discuss the persistence of rivers ("fleuves") under noise.
We investigate the dependence of river network scaling on the relative dominance of slope vs. noise in initial conditions, using an erosion model. Increasing slope causes network patterns to transition from dendritic to parallel and results…
The Lorenz '96 model is an adjustable dimension system of ODEs exhibiting chaotic behavior representative of dynamics observed in the Earth's atmosphere. In the present study, we characterize statistical properties of the chaotic dynamics…
Water distribution networks are hydraulic infrastructures that aim to meet water demands at their various nodes. Water flows through pipes in the network create nonlinear dynamics on networks. A desirable feature of water distribution…
The local statistical and geometric structure of three-dimensional turbulent flow can be described by properties of the velocity gradient tensor. A stochastic model is developed for the Lagrangian time evolution of this tensor, in which the…
We study nonlinear dynamics on complex networks. Each vertex $i$ has a state $x_i$ which evolves according to a networked dynamics to a steady-state $x_i^*$. We develop fundamental tools to learn the true steady-state of a small part of the…
The origin of hydrodynamical instability and turbulence in the Keplerian accretion disk is a long-standing puzzle. The flow therein is linearly stable. Here we explore the evolution of perturbation in this flow in the presence of an…
A proposal for a calculational program in fluid turbulence is presented. It is proposed that the fluid probability density functional has an attractor for its time-evolution, just as the dynamical system itself has. The evolution of the…
The universal fractality of river networks is very well known, however understanding of the underlying mechanisms for them is still lacking in terms of stochastic processes. By introducing probability changing dynamically, we have described…