# Environmental and Geophysical Fluid Mechanics

## Modelling stratification in estuaries (MSc)

Sketch of the computational domain with, in color, the density distribution. The initial condition is on the left and the steady state on the right.

Estuaries are very important for economical (ports and waterways), ecological (bio-diversity) and agricultural (irrigation) reasons, and predicting their evolution is crucial for effective coastal management. Therefore, it is necessary to understand the hydrodynamics of estuaries. These hydrodynamics are governed by a complex density field in which the fresh, light water from the rivers and the salt, heavy water from the sea generate density gradients in both horizontal and vertical directions (the latter also being called stratification). In this master project, we would like to gain a better comprehension about the interaction between the horizontal density gradient and the stratification. The final is be to develop a model describing the evolution of the density distribution in an estuary. To achieve this, we will use an idealised numerical set-up of an estuary in COMSOL (see the figure). The river will be modelled by a tank containing fresh water (on the left) and the sea by a tank containing salt water (on the right). The channel models the estuary where the transition between fresh water and salt water leads to a gradual increase in density. An analysis of the evolution of the density and flow velocity between the initial condition and the steady state is the main objective of the project.

Steven Kaptein, Matias Duran Matute

Contact: Matias Duran Matute

## De nachtelijke atmosferische grenslaag (BSc)

Wat is het mechanisme achter grondvorst? Waarom valt de wind vaak weg rond zonsondergang? En hoe snel gaan die processen eigenlijk? In dit project ga je aan de slag met een dataset van de KNMI weertoren bij Cabauw (NL). Van deze uitstekende meetfaciliteit wordt al vele jaren gedetailleerde informatie (windsnelheden, temperatuur, turbulentie karakteristieken etc.) opgeslagen. Door slimme middeling van vele unieke nachten kunnen algemene karakteristieken gevonden worden; de atmosfeer wordt als een laboratorium. Omdat je aan de ene kant aan de slag gaat met praktische data en aan de andere kant fundamenteel begrip wilt krijgen is belangrijk dat je hier goed tussen kunt schakelen.

Ivo van Hooijdonk, Herman Clercx

Contact: Herman Clercx

## The influence of rotation on the flow through a rectangular cavity (MSc)

This is an experimental project (but some numerical work can also be performed) in collaboration with prof. Leo Maas (NIOZ, UU) and is motivated by our interest in understanding basic aspects of rotating turbulence. When background rotation affects turbulence through the Coriolis force but does not dominate the flow dynamics, there is a complex (and still poorly understood) interplay between inertial waves, the turbulent eddies, and the mean flow.

To gain further insight into this interplay a flow is driven through a box by a pressure difference between two holes on opposite sides of the tank. Without background rotation, the flow rate depends only on the pressure difference. However, when the setup is placed on top of a rotating table, the flow rate also depends on the rotation rate of the system. In addition, background rotation generates a pressure gradient in the span-wise direction (this is reminiscent of the Hall effect in electromagnetism).

Research questions: How does background rotation influence the flow and the flow rate? What is the role played by inertial waves? How do they interact with the mean flow?

Matias Duran Matute, GertJan van Heijst, Leo Maas (NIOZ, UU)

Contact: Matias Duran Matute

## Coastal flows driven by vertical pressure gradients (BSc)

Many well-known flows are driven by a pressure gradient. Two classical examples are the Poiseuille flow (in the laminar regime) and the turbulent plane channel flow (in the turbulent regime). For both of these flows, the pressure gradient is constant over the whole depth. However, in the atmosphere and in the ocean, the pressure gradient varies with altitude (resp. depth) due to changes in the density. The dynamics of these flows are different from the classical plane channel flows mentioned above. In this bachelor project, it is proposed to investigate a turbulent flow forced by a pressure gradient varying linearly with the depth. Particularly, turbulent quantities between the latter flow and a classical turbulent plane channel flow will be compared. This will be done by performing numerical simulations, in particular, Large Eddy Simulations.

Steven Kaptein, Matias Duran Matute, Herman Clercx

Contact: Matias Duran Matute

## The interaction of a Kelvin wave with a deformable coast (MSc)

Experimental project with potential for an analytical part in collaboration with dr. Henk Schuttelaars (TU Delft).

The Kelvin wave is a special type of gravity wave that is affected by the Earth’s rotation and trapped at the Equator or a vertical boundary like the coast. Actually, the tide along the Dutch coast is a Kelvin wave. Usually, the studies involving coastal Kelvin waves consider a fixed solid coastline. The idea behind this project is to relax this condition and allow for the coast to change due to the Kelvin wave traveling along. The main goal of this project is to observe and understand, in a laboratory experiment, the modifications that a Kelvin wave can produce on a coastline.

In a rectangular tank filled with water, a coast will be created along one of its sides using light polymer particles. The coast itself can be straight or have some small perturbations. The tank is placed on top of a rotating table to simulate the Earth's rotation. A Kelvin wave is produced by a plate oscillating up and down in one of the corners of the tank. Several parameters can be varied: the amplitude and frequency of the wave, the depth of the fluid, and the slope at the coast, for example.

Research questions: How does the wave modify the coast? Can perturbations at the coast be unstable? Can they travel along the coast?

Matias Duran Matute, GertJan van Heijst, Leon Kamp, Henk Schuttelaards (TUD)

Contact: Matias Duran Matute

## Morphodynamics of a tidal inlet (MSc)

Experimental project in collaboration with dr. Henk Schuttelaars (TU Delft).

Tidal inlets are the connections between the open sea and a coastal basin - the gaps between the Wadden Islands in the Northern Dutch coast are good examples. There is in general a great interest on the inlets since they greatly define the transport inward and outward of, for example, pollutants, nutrients, and larvae. A crucial aspect for these inlets is their temporal evolution since they change continuously due to the action of the tidal currents transporting the sediment composing the inlet itself.

We are interested in studying experimentally the evolution of a tidal inlet under the action of the tide. The experiments will be carried out in a rectangular tank divided into two basins: one being the sea and one being a coastal basin. The inlet will be composed of a hard structure surrounded by light polymer particles simulating the sediment. A tidal-like motion will be created by either an oscillating cylinder going up and down into the water or by a wave-maker that will generate gravity waves running along the shore. Similar experiments have been carried out recently at UU, but several important physical characteristics have been ignored.

Research questions: How does the inlet evolve in time? How does it branch out into the basin? What are the parameters defining the evolution? Does the way of forcing the tide have an effect on the evolution?

Matias Duran Matute, GertJan van Heijst, Henk Schuttelaars (TUD)

Contact: Matias Duran Matute

## The settling of particles in a rotating fluid (MSc)

Numerical/Experimental project in collaboration with Dr. Wim-Paul Breugem (TU Delft).

This project has a dual purpose: 1) gain further understanding on the motion of multiple spherical particles settling in a fluid subjected to background rotation, and 2) test the inclusion of background rotation into a numerical code for Direct Numerical Simulations (DNS) with an Immersed Boundary Method (IBM).

The motion of a sphere inside rapidly rotating fluid revealed in classic experiments the formation of a Taylor column extending above and below the sphere. The extension of the column depends on the relative importance of the background rotation. What happens when more than one sphere is falling? How does the Taylor column affect the spheres falling behind?

In a non-rotating fluid, the case of two spherical particles falling one after the other, is a typical case to test numerical codes where solid spheres are simulated. Can a similar test be used for a fluid subjected to background rotation?

Matias Duran Matute, GertJan van Heijst, Wim-Paul Breugem (TUD)

Contact: Matias Duran Matute

## Non-linear spin-up: the role of topography and granular matter at the bottom (MSc)

Spin-up of a fluid refers to the process where a fluid-filled container at rest is set to rotate at a constant rate. Hence, eventually setting the fluid itself to rotate as a solid body at the same rate of the container. In the linear case with a flat bottom, the speed at which the fluid reaches solid-body rotation is explained by the Ekman linear theory. This theory predicts that the speed of the fluid changes exponentially.

Recently, we have studied how a sediment layer at the bottom of a cylinder is transported when a fluid above is spun down or up. In this project, we are interested on how the sediment at the bottom modifies the spin-up process itself. Two lines of research are: 1) the influence of topography due to the piling up of sediment in certain regions and 2) the influence of suspending sediment into the water column (transfer of kinetic energy into potential energy). The laboratory experiment will be carried out on top of a rotating table with a cylindrical tank placed on top. Plastic particles slightly heavier than water will be used at the bottom. The velocity of the fluid in a horizontal slice will be measured using PIV.

Matias Duran Matute, Samuel Gonzalez Vera, GertJan van Heijst

Contact: Matias Duran Matute

## Kelvin waves around a tidal inlet (BSc)

The Kelvin wave is a special type of gravity wave that is affected by the Earth’s rotation and trapped at the Equator or a vertical boundary like the coast. Actually, the tide along the Dutch coast is a Kelvin wave. This wave is modified as it passes in front of tidal inlets like the ones between the Wadden Islands.

The goal of this project is to reproduce experimentally the interaction of a Kelvin wave and a tidal inlet. The experiments will be performed on a rotating table with a rectangular tank on top of it. A barrier with a tidal inlet will be placed through the midsection of the tank dividing the tank into a deep sea region and a shallow coastal basin. In a corner of the sea region, an oscillating wave maker will force the Kelvin wave. The water surface deformation will be measured using a synthetic Schlieren and the velocity using Particle Image Velocimetry.

Research questions: Under which conditions can the Kelvin wave propagate across the inlet? And how much of the wave is deformed as a function of the parameters of the problem (difference in depth, width of the inlet, wavelength)? This is an experimental project (a numerical component can be included if time permits).

Matias Duran Matute, GertJan van Heijst, Leon Kamp

Contact: Matias Duran Matute

## 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.

Experimental: flow visualization, PIV

Numerical: COMSOL

GertJan van Heijst, Matias Duran-Matute, Leon Kamp

Contact: GertJan van Heijst

## Heat islands (MSc)

Due to the presence of buildings and roads, urban areas take up more heat from the Sun than the surrounding rural areas. Temperatures within cities are remarkably higher than in the surroundings. A large metropolis may even influence the local weather. This effect of localized heating of the atmosphere is known as the ‘heat island’. There are also natural heat islands: a well-known example is the Tibetan Plateau. On such large length scales the rotation of the Earth becomes important in assessing the effect of the heat island on the dominant atmospheric flow. The buoyant air spins up to form a thermal vortex that can act as a barrier for passing winds, thus hindering transport of heat awayfrom the heat island.

We want to investigate the strength and stability of the thermal vortex as a function of the heating input. Numerical simulations (3D) of the turbulent flow will be carried out to determine when a thermal vortex can form and how strong it is.

Rudie Kunnen, Leon Kamp, GertJan van Heijst

Contact: Rudie Kunnen

## Transport of suspended sediment by vortices shed from a headland (BSc/MSc)

Vortices in the ocean are said to be very efficient in trapping and transporting material. When the tidal currents, going back and forth along the coast, encounter a headland or a man-made structure perpendicular to the coast, vortices are shed. How efficient are these vortices in transporting suspended sediment (e.g. mud, silt)? And where does the sediment go?

To quantify the transport efficiency and understand the mechanisms, we propose a numerical study using the General Estuarine Transport Model (GETM) couple to a suspended sediment module. GETM is a three-dimensional state-of-the-art code for the study of coastal processes. Several parameters can be varied: the size of the headland, the amplitude of the tide, the sediment properties. The results of the simulations can then be compared with analytical estimates.

Matias Duran Matute, GertJan van Heijst

Contact: Matias Duran Matute

## Dynamics of the Rhone outflow into Lake Geneva (BSc/MSc)

Airborne photography and in situ measurements (from vessels) have a revealed a number of surprising and striking features of the Rhone river entering Lake Geneva: the river plume may exhibit remarkable vortex structures, depending on the outflux and wind forcing. The local bottom topography has some quite pronounced features (such as a steep shallow-deep transition). Insight in the vortex dynamics is crucial for a better understanding of the river water dispersion in the lake. Observations (photographic and measurements), numerical simulations, and laboratory modelling by source flows in a rotating fluid tank with bottom topography.

GertJan van Heijst, Damien Bouffard (EPFL, Lausanne, CH)

Contact: GertJan van Heijst

## 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.
• dr.ir. Kunnen, R.P.J.