Ernesto Horne

My personal website

Researcher in fluid mechanics

Research interests:
Modelling in fluid mechanics; Experiments in Fluids; Computational fluid dynamics; Geophysical flows; Rotating turbulence; Stratified flows and mixing; Internal gravity waves.

- Postdoctoral researcher at Ecole Polytechnique, Paris. 2017 - present

- Postdoctoral researcher at Ecole Centrale de Lyon, Lyon. 2016 - 2017

- PhD at Ecole Normale Superieur de Lyon, Lyon. 2012 - 2015

- Sci. Physics at University of Buenos Aires. 2012.

Current Position

I am a postdoctoral researcher at the Laboratoire d'Hydrodynamique de l'Ecole Polytechnique (LadHyX), working on the transfer of energy through scales in rotating and stratified flows.

Current Research

My current research is related to rotating and stable stratified flows. I am working both, numerical and experimentally, in the question of how the energy is transfer through scales by turbulence in these environments. The break of the isotropy in the media produced by stratification and rotation will generate an energy spectrum with different power laws in the vertical and horizontal component of the wavenumber. The main motivation to study this process is given by the fact that both the ocean and the atmosphere are rotating and stratified environments. In particular, we can observe the difference between the power laws in the vertical and horizontal component of the wavenumber for the submesoscales in the oceans and the mesoscales in the atmosphere. This work is done with Paul Billant and Jean-Marc Chomaz , from LadHyX.

I also work in the study of turbulence mixing of stratified flows through high resolution DNS with Alex Delache and Louis Gostiaux , from the LMFA at Ecole Centrale de Lyon, and Antoie Venaille from the ENS de Lyon.

In addition, I keep collaborating with my former supervisors Sylvain Joubaud and Philippe Odier in experimental work related to my PhD thesis done at the ENS Lyon. We are working in collaboration with Nelly Pustelnik in developping a variational mode decomposition method for estimating critical reflected internal waves. With Felix Beckebanze we are describing a theoretical framework for experimental observations of particle transport induced by internal wave beam streaming in lateral boundary layers, done with Diane Micard .

Find my thesis manuscript "Transport properties of internal gravity waves" here.

Energy cascade in stratified and rotating flows

Turbulence in the ocean and atmosphere is dominated by stratification and rotation. Understanding how the energy is transported from large eddies to the small dissipative scales would improve the modeling of the unresolved scales in meteorological and oceanic models. We use a stratified tank set on a rotating table and direct numerical simulations to study stratified and rotating turbulence. The turbulence is produced by the interaction of multiple columnar vortices.


Figure: Evolution of the vertical vorticity field obtained from numerical simulations.

The combination of stratification and rotation produces a particular type of turbulence, with a dual cascade of energy towards the large scales and small scales where the energy is dissipated. The eddies are large (see horizontal plane) but with a small thickness that induces strong shear and the formation of small scales (see vertical plane).

Turbulence mixing in high resolution DNS


Figure: Snapshot of a 3D buoyancy field of a turbulent decaying flow with initial linear stratification.

Stratified fluids are common to many geophysical and industrial environments. The dynamics of these systems are driven by the complex balance between turbulent decay, buoyancy restoring force and irreversible mixing ; where the local mixing can produce an effect in the global energy budget of the system.

In particular, turbulent mixing in the ocean interior plays a crucial role in its global energy budget. This mixing partially drives large scale dynamics, as evidenced in the meridional overturning circulation (Wunsch and Ferrari (2004)). In addition, vertical transport in the ocean is substantial for sequestering large quantities of dissolved greenhouse gases from the atmosphere to the deep ocean. The proportion of energy transferred from turbulent structures to effective mixing is very difficult to estimate through observations (Ivey et al. (2008)), and the details of this energy transfer is yet not fully understood.

In order to resolve irreversible mixing produced by turbulence in a stable stratification, we introduce boundaries at the top and bottom of our domain which allows the mean stratification to evolve in time. This differs with the classical approach of homogeneous stratified turbulence where the background stratification is fixed. The main interest of our approach is that the irreversible mixing is directly computed from the full density field. A porous penalization region is introduced to take into account non-flux conditions at the bottom and at the top of the box (see Kadoch et al. (2012)).

Figure : (a) Vertical cut of the instantaneous reduced density field . (b)Vertical profile of the horizontal mean reduced density field (red line) and horizontal mean of the sorted reduced density field (green line). The initial reduced density profile is also indicated (dashed line). The penalization region is indicated by two arrows and the letter P between both figures.

Internal gravity waves

Watch a video of an internal plane wave propagating in experimental conditions here.

When difference of density exists within a fluid, it will tend to redistribute driven by the force of gravity so that the lighter fluid remains above the heavier forming a stable stratification profile. This particular configuration will be stable in time and if not perturbed, static. When the fluid is slightly vertically displaced, it will feel a buoyancy restoring force acting in a direction opposite to the displacement. The force will act as a spring, and therefore the fluid will oscillate around an equilibrium position. These oscillations are know as internal gravity waves, which differ from the well known surface waves, as they occur inside the fluid where the density of the fluid changes continuously.
The atmosphere is stratified in temperature, and the ocean is stratified in both salinity and temperature. The main motivation for understanding the dynamics of internal gravity waves is that they occur naturally in these systems. These waves have an effect over the dynamics of stratify systems, and may be taken into account to be able to better predict large scale effects such as transport of energy and matter.

Thanks to several experimental techniques internal waves can be generated and observed in laboratory conditions.

Internal waves near-critical reflection

Watch a video of an internal wave near-critical reflection in experimental conditions here.

Figure : Velocity field of an internal wave near-critical reflection. The incident wave is coming from left to right, and the generator is located 30 cm from the center of the image.

The peculiar dispersion relation and the nonintuitive relation between group velocity and the wavenumber of internal gravity waves lead to some very unusual physical consequences. In particular, when internal waves are reflected on a sloped boundary the frequency is conserved, and therefore, its angle of propagation. In consequence, nonintuitive effects including reflection, focalization and wave attractors will emerge when internal waves interact with boundaries.

The detailed study of this process is principally motivated by the peculiar characteristics of internal waves reflection that can enhance the shear stress developed near boundaries and therefore generate erosion of particles settle at a boundary.

Many observational studies have been done that indicate that internal gravity waves are a cause of sediment resuspension, as for example Bogucki et al 1997., Quaresma et al. 2007 and Hosegood & van Haren 2004. In every case the capacity of generating sediment transport through the interaction of internal waves over the seafloor is limited by the shear stress generated at the boundary and the physical characteristics of the particles

Transport of particles by internal gravity waves

Oscillating column

Find a video here

Figure : Internal waves passing through a column of particles in suspension. The boundaries of the column are perturbed by the pass of the wave.

Displaced column


Figure : Snapshots of the front view of a column of particles in suspension in a linear stratified fluid. Time evolves from up-left to down-right. The snapshots are taken every 5 periods of the internal waves (T=25 s). The wave generator is turned on for the first snapshot. With blue dashed lines is indicated the borders of the wave beam. The column is displaced towards the wave generator.

In progress

E. Horne, A. Delache, A. Venaille, L. Gostiaux. Mixing efficiency and partition of energy in decaying stratified turbulence.

E. Horne, J. Schmitt, N. Pulstelnyk, S. Joubaud, P. Odier. Internal wave critical reflection and sediment transport


E. Horne, F. Beckebanze, D. Micard, P. Odier, Leo Maas, S. Joubaud. Particle transport induced by internal wave beam streaming in lateral boundary layers. Journal of Fluid Mechanics, Vol 870, p 848–869. 2019 [DOI]. Arxiv: [PDF] .

E. Horne, A. Delache, L. Gostiaux, A. Venaille. Irreversible mixing and energetic aspects of turbulent stratified flow. 16th European Turbulence Conference, Stockholm, Sweden. Aug. 2017. [PDF]

F. Beckebanze, E. Horne, Leo Maas. Mass transport generated by stratified internal wave boundary layers. 4th International Symposium of Shallow Flows, Eindhoven University of Technology. June 2017. [PDF]

E. Horne, A. Delache, L. Gostiaux, A. Venaille. Mélange irréversible et aspect énergétique de la turbulence stratifié. 23 eme Congres Francais de Mécanique, Lille, France. Sept. 2017. [PDF]

E. Horne, A. Delache, L. Gostiaux. Energetics aspects in Direct Numerical Simulations of a turbulent stratified flow: irreversible mixing. VIIIth International Symposium on Stratified Flows. San Diego. Aug. 2016. [PDF]

E. Horne, D. Micard, P. Metz, M. Moulin, P. Odier, S. Joubaud. Transport de particules par ondes internes. Rencontre du non-linéaire. Paris. Mar. 2016. [PDF]

J. Schmitt, E. Horne, N. Pulstelnyk, S. Joubaud, P. Odier. An improved variational mode decomposition method for internal waves separation. Eusipco, Nice. 2015. [PDF]

E. Horne and P. Mininni. Sign cancellation and scaling in the vertical component of velocity and vorticity in rotating turbulence. Physical Review E. 2013, 88, 013011. [PDF] .

C. Bengoa, E. Horne, T. A. Caselli and J. M. Ibanez. Seismic activity of Copahue volcano zone, Copahue, Neuquen, Argentine: High and low frequency events. Conference: XI International Meeting of Volcan de Colima., At Colima, Mexico. 2009.

PhD and master thesis

E. Horne Transport properties of internal gravity waves. Laboratoire de Physique, Ecole Normale Superieur de Lyon, France. Oct. 2015. [PDF]. Supervisor: S. Joubaud, P. Odier.

E. Horne Exponente de cancelacion en fujos turbulentos rotantes. Physics Department, University of Buenos Aires, Argentina. Jul. 2012. [PDF]. Supervisor: P. Mininni.


Environmental hydrodynamics with J.-M. Chomaz (Master 1 course), École Polytechnique, France.

Exercises (in french)

porous media surface waves internal waves waves refraction tides turbulence

Internship supervision

2015: Master 2 internship of Diane Micard, Ecole Normale de Lyon, France.

2019: Master 2 internship of M. H. Hamede, Ecole Polytechnique, France.


You can find my curriculum vitae



"Transport properties of internal gravity waves"

PhD Thesis PDF

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