Research

[Under construction] Here I briefly describe current areas of research, as well as the projects I pursued in the past.

SWOT Science team

I am a member of the SWOT (Surface Water Ocean Topography) science team. This satellite is scheduled to be launched in 2020 and will measure the fluctuations of the sea surface height at an unprecedented resolution of 500 m horizontally. Unfortunately, the temporal resolution will be of 10 to 21 days, which is much too slow to distinguish the fast internal waves from geostrophic flows such as mesoscale (~100 km in mid-latitudes) or even sub-mesoscale (~10 km in mid-latitudes) vortices, which are much slower to evolve.

SWOT art

My self-appointed role in this endeavor is to come up with ways to (i) diagnose the effects of wind-generated internal waves on those geostrophic flows and (ii) to disentangle tide-generated internal waves from geostrophic flows.

Problem (i) is tricky because wind-generated internal waves flow horizontally and do not displace the sea surface. Even when extremely powerful, they will be invisible to SWOT, and yet, they might impact mean and geostrophic flows it will measure (see "Critical reflection of internal waves in submesoscale flows" and "Particle dispersion by stochastic waves" below for examples). Our understanding of these types of wave-mean flow interactions is still in its early stages, and I intend to pursue idealised studies of the fundamental physics at play. I work on this problem in collaboration with Leif Thomas (Stanford University).

In a way, Problem (ii) is the opposite from Problem (i): tide-generated internal waves do displace the sea surface vertically, and "pollute" (or are polluted by, depending on one's point of view) the measurement of geostrophic flows. The silver bullet to separate the two types of flows is using time analysis, but SWOT data will not have the temporal resolution to do so. In collaboration with Aurélien Ponte (Ifremer Brest), Brian Arbic (University of Michigan) and Francis Poulin (University of Waterloo), I plan on devising filtering methods using idealised studies and (synthetic) data.

 


Critical reflection of internal waves in submesoscale flows

[This is a modified version of this article published about me in our April 2015 departmental newletter]

Fronts criss-cross the surface of the ocean. They can trap internal waves, which are then squeezed towards the surface and reflect on it. When they do, and this is where the internal wave physics is unlike any other, they do not reflect against it in a specular manner, like light against a mirror or sound against a wall. Instead, the angle of propagation of their energy is modified after reflection, and if the conditions are right, this angle can even be parallel to the ocean surface, effectively trapping the waves in a thin and very energetic layer just below the surface:

[For caption, go directly to the YouTube page]

As it turns out, and this is one of the many small miracles happening in this problem, the “right conditions” are often met in the ocean: the waves simply have to oscillate at the same frequency as the rotation rate of the Earth, and nature finds many ways to create such waves.

When focused in this thin, energized layer, the waves become very non-linear, break and dissipate. They don’t do it with a whimper but a bang: some of the energy associated with the front also dissipates with it, one of the practical consequences this seemingly abstract problem. Why does it matter? Fronts occupy a special place in oceanography; for example, they host intense ecosystems. They are also cracks in which the large ocean vortices that store most of the ocean’s kinetic energy dissipate, although in ways that are still mysterious. Our study provides the oceanographic community with a new process, which could partially explain how internal waves make this dissipation happen.

[More videos about this project on YouTube]

References:
  1. Grisouard, N. and L. N. Thomas. Energy exchanges between density fronts and near-inertial waves reflecting off the ocean surface. Journal of Physical Oceanography, 46:501–516, 2016. (doi | | poster).
  2. Grisouard, N. and L. N. Thomas. Critical and near-critical reflections of near-inertial waves off the sea surface at ocean fronts. Journal of Fluid Mechanics, 765:273-302, 2015. (pdf* | doi | poster)

 


 

Particle dispersion by stochastic waves

When dropped in the ocean, a patch of dye will diffuse much faster that if released in an absolutely still body of water, even in the quietest parts of the ocean. This indicates that even there, fluid motions are at work to mix tracers, but which types of motions? We tested the hypothesis that the advection of particles by a background white noise of internal waves could be sufficient to explain the value for the horizontal diffusivity, measured in the ocean. We combined simple stochastic models and direct nonlinear numerical simulations of three-dimensional internal waves that weakly dissipate. In contrast with the results for perfectly non-dissipative internal waves, in which such dispersion arises only at fourth-order in wave amplitude, our dissipative model induces a diffusivity at second-order. This finding reinforces the possibility that internal waves are much more efficient horizontal mixers than previously thought.

NoisePhysical        What the internal wave field looks like,...

Trajectories

... the trajectories of a set of Lagrangian particles,
dropped in the wave field above,...

Trajectory
... and a close-up of one trajectory in particular. On top of the
oscillations due to the internal waves (the hundreds of circular
oscillations), the particle slowly drifts, describing a random walk.

 

Reference: O. Bühler, N. Grisouard and M. Holmes-Cerfon. Strong particle dispersion induced by weakly dissipative random internal waves. Journal of Fluid Mechanics, 719:R4, 2013. (pdf, copyright Cambridge University Press | doi)

Internal waves forcing mean flows

At the simplest level, two sets of independent eigenmodes are sufficient to describe oceanic fluid motion: fast inertia-gravity waves, and slow, balanced motions. In the ocean's interior, the former are the cousins of the surface waves, swells, and tides that most people are familiar with. The latter on the other hand are the cousins of the weather systems and jet streams of the atmosphere and look like vortices or ribbon-like jets.

When the dynamics are linear, and away from any forcing or dissipation, both sets of eigenmodes live happy independent lives. Waves keep oscillating, while balanced modes keep jetting and whirling, conserving their so-called potential vorticity (a quantity whose conservation law, one deduces from the conservation laws for angular momentum, mass, and entropy in a rotating, stratified flow). But when the dynamics are non-linear, exchanges between fast and slow modes arise. While the fundamental process is well-known in other areas of physics and fluid dynamics (look up "acoustic streaming"), how it might play out in the oceans, and its consequences there, are still barely understood.

While most of my studies on this topic have been curiosity-driven, oceanography as a community is getting to a point where such processes can be both measured, and believed to be important.

My first exposure to this phenomenon came serendipitously, as a parasite phenomenon in the lab. While studying nonlinear wave-wave interactions on the Coriolis turntable in Grenoble (FR), I came across a systematic bending of my otherwise-perfectly-crafted wave beams. The slow, balanced flow that would develop over time was the culprit. You can see a video of it below, with a camera sitting on the side of the setup, looking at a vertical slice of the flow (false contrast).

 

My first post-doctoral experience at the Courant Institute of Mathematical Sciences addressed this question from an analytical point of view. We were able to compute the non-linear forcing of the balanced modes, by a dissipating internal tide, using the Generalize Lagrangian Formalism. Our particular theoretical setup explains how to generate balanced flows on top of seamounts. It could potentially close the angular momentum budget of the vortices, ubiquitously hovering above seamounts. See animations below.

 References (see Publications page for pdfs or pre-prints):

  • Grisouard, Nicolas, Matthieu Leclair, Louis Gostiaux, and Chantal Staquet. 2013. “Large Scale Energy Transfer from an Internal Gravity Wave Reflecting on a Simple Slope.” Procedia IUTAM 8 (January). Moscow: Elsevier: 119–28. doi:10.1016/j.piutam.2013.04.016.

  • Grisouard, Nicolas, and Oliver Bühler. 2012. “Forcing of Oceanic Mean Flows by Dissipating Internal Tides.” Journal of Fluid Mechanics 708 (August): 250–78. doi:10.1017/jfm.2012.303.

Internal "solitons" generated by linear internal waves

Coming up... later. Just wait.

 


Internal wave attractors

I'll write a blurb about this when I get the time. In the meantime, here's a video of what it looks like:

Attractor gif

And the references are:

  1. J. Hazewinkel, N. Grisouard and S.B. Dalziel. Comparison of laboratory and numerically observed scalar fields of an internal wave attractor. European Journal of Mechanics B/Fluids, 30(1):51-56, 2011. (, damn you Elsevier! | doi)
  2. N. Grisouard, C. Staquet and I. Pairaud. Numerical simulation of a two-dimensional internal wave attractor. Journal of Fluid Mechanics, 614:1-14, 2008. (pdf* | doi | poster)