Dynamic Transitions of Surface Tension Driven Convection

@article{Dijkstra2011DynamicTO,
  title={Dynamic Transitions of Surface Tension Driven Convection},
  author={Henk A. Dijkstra and Taylan Sengul and Shouhong Wang},
  journal={arXiv: Mathematical Physics},
  year={2011}
}

Figures from this paper

Transitions and bifurcations of darcy-brinkman-marangoni convection

This study examines dynamic transitions of Brinkman equation coupled with the thermal diffusion equation modeling the surface tension driven convection in porous media. First, we show that the

Stability and transitions of the second grade Poiseuille flow

Dynamical transition theory of hexagonal pattern formations

  • Taylan cSengul
  • Mathematics
    Communications in Nonlinear Science and Numerical Simulation
  • 2020

Complex bifurcations in Bénard–Marangoni convection

We study the dynamics of a system defined by the Navier–Stokes equations for a non-compressible fluid with Marangoni boundary conditions in the two-dimensional case. We show that more complicated

Navier-Stokes equations under Marangoni boundary conditions generate all hyperbolic dynamics

The dynamics defined by the Navier-Stokes equations under the Marangoni boundary conditions in a two dimensional domain is considered. This model of fluid dynamics involve fundamental physical

Dynamic transitions of generalized Kuramoto-Sivashinsky equation

In this article, we study the dynamic transition for the one dimensional generalized Kuramoto-Sivashinsky equation with periodic condition. It is shown that if the value of the dispersive parameter

Dynamic Transition Theory

This chapter introduces the dynamic transition theory for nonlinear dissipative systems developed recently by the authors. The main focus is the derivation of a general principle, Principle 1, on

Geophysical Fluid Dynamics and Climate Dynamics

Our Earth’s atmosphere and oceans are rotating geophysical fluids that are two important components of the planet’s climate system. The atmosphere and the oceans are extremely rich in their

References

SHOWING 1-10 OF 20 REFERENCES

Nonlinear dynamics of surface-tension-driven instabilities

A century after Henri Benard discovered cellular convective structures, thermal convection in fluid layers still remains a central subject in nonlinear physics. Within this framework,

Pattern Selection in Surface Tension Driven Flows

When a motionless liquid layer is heated from below, spontaneous convection appears when the vertical temperature gradient exceeds a critical value. Under slightly supercritical conditions, the

Dynamic transition theory for thermohaline circulation

HEXAGONAL MARANGONI CONVECTION IN A RECTANGULAR BOX WITH SLIPPERY WALLS

A linear and nonlinear study of surface-tension-driven instability in a rectangular box with slippery lateral walls is presented. Particular attention is devoted to steady convection with hexagonal

Rayleigh Bénard convection: dynamics and structure in the physical space

The main objective of this article is part of a research program to link the dynamics of fluid flows with the structure and its transitions in the physical spaces. As a prototype of problem and to

Nonlinear Marangoni convection in bounded layers. Part 1. Circular cylindrical containers

We consider liquid in a circular cylinder that undergoes nonlinear Marangoni insta- bility. The upper free surface of the liquid is taken to have large-enough surface tension that surface deflections

On convection cells induced by surface tension

A mechanism is proposed by which cellular convective motion of the type observed by H. Bénard, which hitherto has been attributed to the action of buoyancy forces, can also be induced by surface

Infinite Dimensional Dynamical Systems in Mechanics and Physics Springer Verlag

Contents: General results and concepts on invariant sets and attractors.- Elements of functional analysis.- Attractors of the dissipative evolution equation of the first order in time:

An introduction to semiflows

DYNAMICAL PROCESSES Introduction Ordinary Differential Equations Attracting Sets Iterated Sequences Lorenz' Equations Duffing's Equation Summary ATTRACTORS OF SEMIFLOWS Distance and Semidistance