My research interest lies in applied mathematics that can be employed to get deeper insights into fluid dynamics. During the course of my PhD I have focused specifically on oceanic internal waves dynamics.
Below I explain the basic features of internal waves, and present three projects of my ongoing PhD.
Internal waves in the ocean, a fascinating topic
Internal waves are spectacular and fascinating waves occurring in stratified fluids, where low density water overlies high density water. An example of a stratified fluid are the oceans, which are stratified due to salt and temperature differences within the water column.
In some respect, internal (gravity) waves are similar to surface (gravity) waves, which we all know from the sea and lakes. Both types of waves are oscillations around an equilibrium due to the gravitational restoring force.
While surface waves can reach a few meters in height (up to about 25 meter in very extrem storms), internal waves can easily reach hundreds of meter in height in the deep ocean.
The reason for these enormes heights is the relative small density difference between low density and high density water - it costs much less energy to lift a dense water parcel in the deep sea into
lighter water, than any type of water into extremely light air (such as the case for surface waves). In the ocean, internal waves are generated at under water mountains through tides, and through wind at the surface (which also generates the well-known surface waves).
During my PhD-project, I investigate internal gravity waves in idealized settings with mathematical models. The goal is to better understand fundamental properties of these fascinating waves.
A better theoretical understanding of internal waves can help improving ocean-climate models, in which internal waves play a major role in mixing the ocean. Other applicaties are in
off-shore industry, marine biology and astrophysics.
Particle transport induced by internal wave beams
The generation mechanisms of internal waves in the ocean by tides and winds are fairly well understood.
By contrast, the dissipation of internal waves is still debated. One dissipation mechanism is the
generation of mean flow through wave-wave interaction (also known as streaming). The induced mean flow
can transport nutrition and plankton, which is relevant for many marine ecosystems.
Using small-amplitude expansions, we investigate the mass transport generated by monochromatic internal wave beams between two lateral boundaries
in the laminar regime. We find that the peculiar 3D structure of the lateral viscous boundary layers results in effective
Reynolds stresses near the lateral walls, which generates a horizontal circulation in the interior (Fig. 1). The theory is in good agreement with laboratory experiments by Ernesto Horne Iribane, see also our Conference Paper.
Streaming of three-dimensional non-linear internal wave beams
Internal gravity waves can induce mean flow through non-linear advection terms, a process known as streaming.
With a perturbational expansion, we construct exact solutions for 3D diffracting internal waves beams,
generated by an energy flux through a rigid wall, as sketched in Figure 3. Such energy input also generates localized curl-free
and divergence-free horizontal oscillations, which interact with the wave beam to generate a mean flow.
This is a noval streaming mechanism, which has not yet been discussed in literature.
Internal wave attractors
Internal wave attractors are highly energetic, focused periodic wave structures
that can occur in stratified fluids such as the deep ocean. In the vicinity of a
wave attractor (see Fig 3), the fluid undergoes large amplitude oscillations in the vertical
direction, making wave attractors a potential source of diapycnal
As part of my PhD project, I study the dissipation mechanism of 3D internal wave attractors,
by constructing asymptotic wave attractor solutions for three-dimensional laboratory set-ups.
The goal is to understand how internal wave attractors scale from laboratory to oceanographic settings,
such that predictions can be made on where stable wave attractors in the ocean may exist.
Partial results are published JFM and in this conference proceeding.