Conference Organizer: Jalal Shatah
Wave Turbulence Theory is central to the understanding of physical phenomena featuring interactions of weakly nonlinear dispersive waves. This includes, but is not limited to, atmospheric and oceanic dynamics, wave weather forecasting, and climate prediction. In the past couple of years, scientists working under the umbrella of the Simons Collaboration on Wave Turbulence, using a collaborative and interdisciplinary approach, have made significant progress validating certain aspects of Wave Turbulence theory, increasing its reliability and effectiveness as a tool in these applications. The Annual Simons Collaboration on Wave Turbulence Conference aims at providing an update on some of the research conducted under the umbrella of the collaboration, as well as highlighting external research from related fields, with the scope of further developing the collaborative research approach started by the PIs of the grant.
Pierre Philipe Cortet
Laure Saint Raymond
8:30 AM CHECK-IN & BREAKFAST 9:30 AM Laure Zanna | Discovering equations for ocean turbulence 10:30 AM BREAK 11:00 AM Nicolas Mordant | Experimental investigation of stratified turbulence: weak turbulence and beyond 12:00 PM LUNCH 1:00 PM Pierre-Philippe Cortet | (Wave) Turbulence in rotating fluids 2:00 PM BREAK 2:30 PM Giorgio Krstulovic | Turbulent steady states in the nonlinear Schrodinger equation. 3:30 PM BREAK 4:00 PM Gregory Eyink | The Josephson-Anderson Relation and the Origin of Turbulent Drag 5:00 PM DAY ONE CONCLUDES
8:30 AM CHECK-IN & BREAKFAST 9:30 AM Laure Saint Raymond | Solutions of kinetic wave equations with constant fluxes (ZOOM) 10:30 AM BREAK 11:00 AM Oliver Buhler | Modified inertial range power laws due to finite spectral bandwidth: idealized modeling results and implications for waves in the ocean 12:00 PM LUNCH 1:00 PM Nigel Goldenfeld | Stochasticity in Transitional and Fully- Developed Turbulence 2:00 PM MEETING CONCLUDES
Courant Institute of Mathematical Sciences – New York University
Discovering equations for ocean turbulence
Ocean mesoscale eddies (horizontal scale of 10-100 km) are critical in setting the global ocean stratification and for mixing of momentum and tracers in the ocean. Mesoscale eddies are a key player in the ocean energy cycle: they extract available potential energy from the mean state and are central in the inverse kinetic energy cascade, energizing the large scale flow. Yet, most climate models only partially resolve them, and we must therefore find approximations to represent their effects on the large scale flow. Here, we will present results using data from numerical simulations and machine-learning techniques to learn equations that represents the effects of mesoscale eddies on the large scale. We will discuss the physical and mathematical properties of the equations learned and examine their role in improving coarse resolution simulations of the ocean.
Université de Grenoble
Experimental investigation of stratified turbulence: Weak turbulence and beyond
Wave turbulence of internal waves is a major part of the global ocean dynamics as it contributes to large extent to dissipation of kinetic energy and mixing of temperature and salt by establishing a direct cascade in length scales. Although measurements of turbulence in the ocean interior, the famous Garrett–Munk spectrum, are attributed to internal inertial-gravity wave turbulence, clear evidence of such turbulence in the laboratory was missing. The large-scale Coriolis facility in Grenoble, France, is dedicated to geophysical fluid dynamics investigations of stratified and/or rotating flows. It consists of a 13-meter diameter pool that can be filled with water with a vertical density gradient (using varying salt concentration) and that can rotate to mimic the action of the rotation of the Earth. We use this facility to obtain a state of stratified turbulence forced by large-scale waves. We report a state of weak wave turbulence of internal waves at intermediate scales. The global flow is more complex, as very large scale vortical structures can be observed as well, together with small scale strongly nonlinear turbulence resulting from wave overturning. This complex flow is consistent with the expected phenomenology of such gravity dominated turbulence as observed in the ocean.
Laboratoire FAST, CNRS – Université Paris-Saclay
(Wave) Turbulence in rotating fluids
The influence of a global rotation on hydrodynamic turbulence is a key ingredient of geo and astrophysical flows. A consequence of rotation is the emergence of a specific class of waves, called inertial waves, which propagate in the volume of the fluid. Within rotating turbulence, these waves and the classical eddy structures of fluid dynamics can be entangled in different ways, leading to several possible regimes: among these, the wave turbulence regime. The theory of wave turbulence applied to the case of inertial waves led to analytical predictions in the early 2000s . Since then, various attempts to discover experimentally this regime have been carried out, with limited success.
In this context, we recently built an original experimental setup that led to the first observation of the inertial wave turbulence regime in a rotating fluid . I will show that the features of our experimental wave turbulence are in quantitative agreement with the theory. This achievement was made possible by the prior discovery of an instability affecting inertial waves, which we named the “quartetic instability.” I will show that the understanding of how to inhibit this instability has been crucial for the observation of the wave turbulence regime .
 S. Galtier, Weak inertial-wave turbulence theory, Physical Review E, 68, 015301(R) (2003).
 E. Monsalve, M. Brunet, B. Gallet & P.-P. Cortet, Quantitative Experimental Observation of Weak Inertial-Wave Turbulence, Physical Review Letters, 125, 254502 (2020).
 M. Brunet, B. Gallet & P.-P. Cortet, Shortcut to Geostrophy in Wave-Driven Rotating Turbulence: The Quartetic Instability, Physical Review Letters, 124, 124501 (2020).
Université Côte d’Azur
Turbulent steady states in the nonlinear Schrodinger equation
The nonlinear Schrödinger (NLS) equation, also known as the Gross–Pitaevskii equation, is one of the most common equations in physics. Its applications go from the propagation of light in nonlinear media to the description of gravity waves and Bose–Einstein condensates. In general, the NLS equation describes the evolution of nonlinear waves. Such waves interact and transfer energy and other invariants along scales in a cascade process. This phenomenon is known as wave turbulence and is described by the (weak) wave turbulence theory (WWT). One of the most significant achievements of WWT is the complete analytical characterization of turbulent steady states obtained in the long time limit when the system contains forcing and dissipative terms acting on well-separated scales.
In the first part of my talk, I will present recent theoretical developments on the steady-state solutions of the 3D NLS equation in the four-wave regime. Those new predictions are validated using high-resolution numerical simulations of the NLS equation and its associated wave kinetic equation. In the second part, I will address the three-wave interaction regime of the NLS equation in which waves become non-dispersive. I will start by reviewing some of the mathematical issues of the WWT for acoustic waves in 2D and 3D. Then, I will present a new theory for 2D NLS in the acoustic regime, which is in excellent agreement with numerical simulations without adjustable parameters.
Johns Hopkins University
The Josephson–Anderson relation and the origin of turbulent drag
The Josephson–Anderson relation provides the modern understanding for energy dissipation in quantum superfluids and superconductors, relating drag to motion of quantized vortex lines across the background potential superflow. The same relation has been recently shown to apply widely to classical fluid flows described by the incompressible Navier–Stokes equation. Here it connects dissipation with flux of continuously distributed vorticity across the streamlines of the smooth potential Euler solution. We shall concisely review these concepts and explain how they give a new resolution of the classical d’Alembert paradox, connecting it with Onsager’s theory of high Reynolds number turbulence. The theory explains experimental puzzles about the wall conditions of solid bodies necessary for anomalous dissipation. The Josephson–Anderson relation is valid, however, at any Reynolds number and explains the origin of drag in flows ranging from low-Reynolds-number Stokes flow to transitional and fully developed turbulence. As such, it provides a sharp, precise tool with which to address the theoretical and practical issue of drag reduction. We shall review our initial efforts to apply the Josephson-Anderson relation to turbulent channel flow and to resolve the 75-year-old open problem of drag reduction by polymer additives.
Institut des Hautes Études Scientifiques – Université Paris-Saclay
Solutions of kinetic wave equations with constant fluxes
In this talk, I will present a new approach to Kolmogorov–Zakharov solutions of wave kinetic equations based on a work with F. Golse and M. Escobedo. This opens interesting perspectives regarding the anisotropic case.
Courant Institute of Mathematical Sciences – New York University
Modified inertial range power laws due to finite spectral bandwidth: Idealized modeling results and implications for waves in the ocean
Predictions for power laws from wave-kinetic theory are based on infinite spectral bandwidth, with arbitrarily large-scale separations assumed to hold between forcing and dissipation scales, for example. We show by way of very high resolution numerical simulations of an idealized model that large but finite spectral bandwidth has a strong and predictable impact on the observed power laws. This has practical implications for the interpretation of experimental results and field observations, and the relevance of this for the study of realistic ocean waves is discussed.
University of California, San Diego
Stochasticity in transitional and fully developed turbulence
There is growing evidence that turbulence in simple fluids is governed by two fixed points arising in the statistical mechanical description of flows. The first controls the behavior near the laminar-turbulence transition, while the second controls the behavior at asymptotically large Reynolds numbers. In the first part of the talk, I review the phenomena associated with the sub-critical transition to turbulence, primarily in quasi-one-dimensional flows such as pipe or high aspect-ratio Taylor–Couette, and show how theory and experiment are converging on a description based on a non-equilibrium phase transition. In particular, I present a stochastic model that captures decay and splitting of localized regions of turbulence (puffs), and the way in which regions of turbulence grow at higher Reynolds number, through two modes of growth (weak and strong slugs). I also show how recent experimental measurements on puff dynamics, when combined with renormalization group and simulation methods, unequivocally supports the identification of laminar-turbulence transition of pipes in the directed percolation universality class. In the second part of the talk, I discuss more briefly the widely unappreciated role of thermal fluctuations in the far dissipation range of turbulence and, using shell models, show how these are amplified and propagated to large scales by spontaneous stochasticity, reaching the integral scale eddies in just a few eddy turnover times.
Work performed in collaboration with: Hong-Yan Shih (UIUC/Academia Sinica, Taiwan), Xueying Wang (University of Illinois at Urbana-Champaign), Tsung-Lin Hsieh (UIUC/Princeton), Björn Hof (Institute of Science and Technology, Austria), Joachim Mathieson (Niels Bohr Institute, Denmark), Grégoire Lemoult (University of Le- Havre, France), Vasudevan Mukund (Institute of Science and Technology, Austria), Gaute Linga (Niels Bohr Institute), Dmytro Bandak (University of Illinois at Urbana-Champaign), Gregory Eyink (Johns Hopkins University) and Alexei Mailybaev (IMPA, Brazil).
This work was partially supported by grants from the Simons Foundation through the Targeted Grant “Revisiting the Turbulence Problem Using Statistical Mechanics” (Grant 663054 G.E., 662985 N.G. and 662960 B.H.).
Group A – PIs & Speakers
Business-class airfare for flights over 5 hours
Hotel accommodations for up to 3 nights
Reimbursement of Local Expenses
Group B – Out-of-town Participants
Hotel Accommodations for up to 3 nights
Reimbursement of Local Expenses
Group C – Local Participants
No funding provided besides hosted conference meals.
Group D – Remote Participants
A Zoom link will be provided.
For participants in Groups A & B driving to Manhattan, the James NoMad hotel offers valet parking. Please note there are no in-and-out privileges when using the hotel’s garage; therefore, participants are encouraged to walk or take public transportation to the Simons Foundation.
Participants in Groups A & B who require accommodations are hosted by the foundation for a maximum of three nights at The James NoMad Hotel. Any additional nights are at the attendee’s own expense. To arrange accommodations, please register at the link above.
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Reimbursement and Travel Policy
Any expenses not directly paid for by the Simons Foundation are subject to reimbursement based on the foundation’s travel policy. An email will be sent within a week following the conclusion of the meeting with further instructions on submitting your expenses via the foundation’s web-based expense reimbursement platform.
Receipts are required for any expenses over $25 USD and are due within 30 days of the conclusion of the meeting. Should you have any questions, please contact Emily Klein.