# Vortices and 2D turbulence

## Vorticity generation at a deforming wall (BSc/MSc)

How is vorticity generated at a deforming wall? Viscous vs. inviscid, sinusoidal deformation. Numerical simulations & analytical work. Application: fish and submarine robot propulsion

GertJan van Heijst, Leon Kamp

Contact: GertJan van Heijst

## Two-dimensional turbulence in bounded domain with sliding wall (MSc)

Numerical simulations on characteristics of two-dimensional turbulence in a compact domain with no-slip walls one of which is sliding. Spontaneous spin-up? Angular momentum reversals?

Leon Kamp, GertJan van Heijst

Contact: Leon Kamp

## Relaxation of a 2D vorticity distribution to a Lamb-Oseen vortex (BSc)

Numerical project: It has been shown that the late-time relaxation of a two-dimensional flow in an unbounded domain is governed by the classical Oseen vortex for situations involving a finite net circulation (or non-zero total integrated vorticity). The purpose of this research project is to study this relaxation process in more detail and to quantify the temporal evolution of arbitrary vorticity distributions towards the Oseen vortex using numerical simulation.

Leon Kamp, GertJan van Heijst

Contact: Leon Kamp

## Evolution of 2.5 dimensional turbulence (BSc/MSc)

Numerical / theoretical project: While forced and unforced (decaying) turbulence in two-dimensional geometries has been studied very extensively, this is not the case for axisymmetric fluid flows inside an axisymmetric geometry. Inside such geometry the fluid velocity has all three components but depends on time and only two spatial coordinates. Since the flow is axisymmetric, there is no dependence on the azimuthal coordinate. So one has a three-dimensional (3D) flow field that depends on just two spatial coordinates. Hence the name two-and-a-half dimensional (2.5D). The main research question is, what states an initially turbulent flow field relaxes into. To answer this question we propose to perform direct numerical simulations inside a cylinder with a circular cross-section. Starting from random initial conditions we are interested in the long time behaviour and the associated decay scenario towards final states.

Leon Kamp, GertJan van Heijst

Contact: Leon Kamp

## Transport in 2D turbulent channel flow with imposed shear (MSc)

Dit project betreft een numerieke studie van transport in een 2D turbulente kanaalstroming met een gemiddelde schuifstroming. Deze schuifstroming zal direct wisselwerken met de coherente structuren in de turbulente stroming en daarmee indirect het (lateraal) transport beïnvloeden. De simulaties zullen plaats vinden met de codes die in onze groep ontwikkeld/in gebruik zijn. Rekenwerk uit te voeren bij SARA, of eventueel op de fusion supercomputer in Jülich.

Herman Clercx, GertJan van Heijst, Niek Lopes Cardozo

Contact: Herman Clercx

## Interaction of line vortex rings (BSc/MSc)

Numerical simulations of a cloud of N line vortex rings, interacting on a doubly-periodic domain. Statistical behaviour? Other boundary conditions?

Leon Kamp, GertJan van Heijst

Contact: Leon Kamp

## Point-vortex dipoles in a shear flow (BSc/MSc)

Numerical simulations of point-vortex dipoles in a shear flow, e.g. Couette, Poiseuille or arbitrary. Ultimately: trajectory perpendicular to main flow (!). Clouds of pv dipoles? Compare modulated pv dipole on beta-plane with pv dipole in shear flow.

GertJan van Heijst, Leon Kamp

Contact: GertJan van Heijst

## Point vortices in a circular domain: trajectories and chaotic advection (BSc/MSc)

Numerical simulation of point vortices in a circular domain: point-vortex dipoles will split up when approaching the circular wall and the individual vortices may perform looped trajectories before re-uniting as a dipole. Periodicity or chaotic behaviour? Chaotic advection properties of these point-vortex structures.

GertJan van Heijst, Michel Speetjens (W)

Contact: GertJan van Heijst

## Elliptical vortex in azimuthal shear flow (BSc/MSc)

Numerical simulation of dipolar vortex approaching a rotating solid cylinder with a 1/r azimuthal velocity field: how does the dipole react? Torn apart, or establishment of an elliptical vortex steadily circling around the cylinder?

GertJan van Heijst, Leon Kamp

Contact: GertJan van Heijst

## Dipolar vortices colliding against obstacles: cylinders, porous walls, wall with gap (BSc/MSc)

Laboratory experiments on dipolar vortices in a shallow-layer fluid (EM forcing) or in a rotating fluid. Dye visualization, PIV flow measurements. Numerical simulations with COMSOL. Cases to be considered: dipole colliding against plate with sharp edge, against a corrugated wall (with a zigzag profile), against a row of cylinders, against a wall with an opening.

Leon Kamp, GertJan van Heijst

Contact: Leon Kamp

## Vortices generated by tidal exchange through a gap (BSc/MSc)

Experiments on oscillating flow through an opening in a wall. Different opening shapes. Parameters: frequency, tidal amplitude, opening shapes, bottom topography, geometry tidal basin. Experimental: flow visualization, PIV. Numerical: COMSOL.

GertJan van Heijst, Matias Duran-Matute, Leon Kamp

Contact: GertJan van Heijst

## Vortex instability: effect of bottom topography (MSc)

Experimental project, including comparison with theoretical/numerical results obtained by Prof. Ziv Kizner. By applying a vortex generator consisting of a few thin-walled coaxial cylinders we may generate vortices of some prescribed vorticity distribution. The vortices are created in a rotating fluid, and will be released over a conical bottom topography, in order to study the stabilising/destabilising (b-)effect on the vortex structure. Experiments: rotating fluid tank, flow visualisation, PIV measurements to determine vorticity distributions.

GertJan van Heijst, Ziv Kizner (Technion, Israel)

Contact: GertJan van Heijst

## Expulsion of magnetic fields from a vortex (BSc/MSc)

Flows of electrically conducting fluids interacting with magnetic fields are found throughout the universe and also play a major role in ongoing research on thermonuclear fusion. In order to understand the complex interactions of such flows and magnetic fields it is valuable to investigate simplified models such as a single, twodimensional, axisymmetric vortex in an electrically conducting fluid that is permeated by a magnetic field. In the so-called kinematic regime, the combined action of advection and diffusion of magnetic flux leads to the expulsion of the magnetic field from the core of the eddy resulting in magnetic fluxes that are concentrated near the edge of the vortex. From a mathematical point of view, this flux expulsion is equivalent to the Prandtl-Bachelor theorem of fluid dynamics.

The present project aims to numerically simulate this process in the dynamical regime, in which the magnetic field affects the flow via the Lorentz force. Commencing with a two-dimensional, monopolar, axisymmetric vortex and an initial uniform magnetic field the evolution of the flow and the magnetic field is studied as a function of the dimensionless numbers (the Reynolds number, the magnetic Reynolds number and the Alfvén number) that govern the dynamics. Extension to more complicated vorticity distributions including two-dimensional turbulence of a conducting fluid subjected to magnetic fields is possible.

Contact: Leon Kamp

## Contact

• prof.dr. Clercx, H.J.H.
• dr. Duran Matute, M.
• prof.dr.ir. Heijst, G.J.F. van
• dr.ir. Kamp, L.P.J.