Invariant states in inclined layer convection. Part 2. Bifurcations and connections between branches of invariant states

@article{Reetz2019InvariantSI,
  title={Invariant states in inclined layer convection. Part 2. Bifurcations and connections between branches of invariant states},
  author={Florian Reetz and P. Subramanian and Tobias M. Schneider},
  journal={Journal of Fluid Mechanics},
  year={2019},
  volume={898}
}
Convection in a layer inclined against gravity is a thermally driven non-equilibrium system, in which both buoyancy and shear forces drive spatio-temporally complex flows. As a function of the strength of thermal driving and the angle of inclination, a multitude of convection patterns is observed in experiments and numerical simulations. Several observed patterns have been linked to exact invariant states of the fully nonlinear three-dimensional Oberbeck–Boussinesq equations. These exact… 

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References

SHOWING 1-10 OF 69 REFERENCES

Invariant states in inclined layer convection. Part 1. Temporal transitions along dynamical connections between invariant states

Thermal convection in an inclined layer between two parallel walls kept at different fixed temperatures is studied for fixed Prandtl number $\mathit{Pr}=1.07$. Depending on the angle of inclination

Spatio-temporal patterns in inclined layer convection

This paper reports on a theoretical analysis of the rich variety of spatio-temporal patterns observed recently in inclined layer convection at medium Prandtl number when varying the inclination angle

Transition to a wavy vortex régime in convective flow between inclined plates

  • J. Hart
  • Physics
    Journal of Fluid Mechanics
  • 1971
Experimental results concerning the supercritical behaviour of instabilities occurring in the thermal convective flow between inclined plates are presented. For inclination δ between 90° and 10° (δ =

Three-dimensional convection in an inclined layer heated from below

Longitudinal rolls aligned with the component of gravity parallel to the layer represent the preferred mode of convection at onset for a wide range of parameters of the inclined layer problem. As the

Visualizing the geometry of state space in plane Couette flow

Motivated by recent experimental and numerical studies of coherent structures in wall-bounded shear flows, we initiate a systematic exploration of the hierarchy of unstable invariant solutions of the

Transition Routes of Natural Convection in a Vertical Fluid Layer

Transition routes of natural convection in a vertical fluid layer contained in a tall cavity with differentially heated side walls are investigated theoretically on the assumption of two-dimensional

Stability of free-convection flows of variable-viscosity fluids in vertical and inclined slots

The stability of the buoyancy-driven parallel shear flow of a variable-viscosity Newtonian fluid between vertical or inclined plates maintained at different temperatures is studied theoretically. The

Pattern formation in inclined layer convection

A number of new nonlinear, mostly spatiotemporally chaotic, states are observed in thermally driven convection in an inclined layer of large aspect ratio in a fluid of Prandtl number sigma approximately 1.

Transitions of natural convection in a vertical fluid layer

Transitions of natural convection in a vertical fluid layer contained in a tall cavity with differentially heated side walls are investigated numerically and theoretically. Steady-state solutions are
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