# A brief history of simple invariant solutions in turbulence

@article{Veen2018ABH, title={A brief history of simple invariant solutions in turbulence}, author={Lennaert van Veen}, journal={arXiv: Fluid Dynamics}, year={2018}, pages={217-231} }

When studying fluid mechanics in terms of instability, bifurcation and invariant solutions one quickly finds out how little can be done by pen and paper. For flows on sufficiently simple domains and under sufficiently simple boundary conditions, one may be able to predict the parameter values at which the base flow becomes unstable and the basic properties of the secondary flow. On more complicated domains and under more realistic boundary conditions, such questions can usually only be…

## 4 Citations

### Can preferential concentration of finite-size particles in plane Couette turbulence be reproduced with the aid of equilibrium solutions?

- PhysicsPhysical Review Fluids
- 2020

This work employs for the first time invariant solutions of the Navier-Stokes equations to study the interaction between finite-size particles and near-wall coherent structures. We consider…

### Spontaneous Periodic Orbits in the Navier–Stokes Flow

- MathematicsJournal of Nonlinear Science
- 2021

A general method to obtain constructive proofs of existence of periodic orbits in the forced autonomous Navier-Stokes equations on the three-torus using a Newton-Kantorovich theorem is proposed.

### On the classification of the laminar-turbulent transition process using the methods of nonlinear dynamics: general analysis and the future

- EngineeringJournal of Physics: Conference Series
- 2020

The definition of a turbulent flow is still not mathematically defined. Different methods exists that provide different definitions resulting in different approaches and classifications of the…

### About mathematics and reality, Albert Einstein (1921 Nobel Prize in Physics), in his Geometry and Experience talk at the Prussian Academy of Sciences in Berlin

- Physics
- 2019

— Turbulence is a long-standing mystery. We survey some of the existing (and sometimes contradictory) results and suggest eight natural questions whose answers would increase the mathematical…

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