Publications related to Boussinesq approximation (water waves)

A machine learning architecture for including wave breaking in envelope-type wave models

Wave breaking is a complex physical process about which open questions remain. For some applications, it is critical to include breaking effects in phase-resolved envelope-based wave models such as the non-linear Schr & ouml;dinger. A promising approach is ...

Pergamon-Elsevier Science Ltd2024

Nonlinear inviscid damping and shear-buoyancy instability in the two-dimensional Boussinesq equations

Michele Dolce

We investigate the long-time properties of the two-dimensional inviscid Boussinesq equations near a stably stratified Couette flow, for an initial Gevrey perturbation of size & epsilon;. Under the classical Miles-Howard stability condition on the Richardso ...

WILEY2023

Non-contact robotic manipulation of floating objects: exploiting emergent limit cycles

Josephine Anna Eleanor Hughes, Nana Obayashi

The study of non-contact manipulation in water, and the ability to robotically control floating objects has gained recent attention due to wide-ranging potential applications, including the analysis of plastic pollution in the oceans and the optimization o ...

Frontiers Media Sa2023

Mean flow modeling in high-order nonlinear Schrodinger equations

Debbie Eeltink

The evaluation and consideration of the mean flow in wave evolution equations are necessary for the accurate prediction of fluid particle trajectories under wave groups, with relevant implications in several domains, from the transport of pollutants in the ...

2023

Stochastic particle transport by deep-water irregular breaking waves

Debbie Eeltink

Correct prediction of particle transport by surface waves is crucial in many practical applications such as search and rescue or salvage operations and pollution tracking and clean-up efforts. Recent results by Deike et al. (J. Fluid Mech., vol. 829, 2017, ...

Cambridge University Press2023

Global Regularity For The Nonlinear Wave Equation With Slightly Supercritical Power

Maria Colombo, Silja Noëmi Aline Haffter

We consider the defocusing nonlinear wave equation ❑u D jujp ⠀1u in R3 ⠂ & UOELIG;0; 1/. We prove that for any initial datum with a scaling-subcritical norm bounded by M0 the equation is globally well-posed for p D 5 C i, where i 2 .0; ...

MATHEMATICAL SCIENCE PUBL2023

Dissipative Solitons and Switching Waves in Dispersion-Modulated Kerr Cavities

Tobias Kippenberg, Rui Ning Wang, Aleksandr Tusnin, Alisa Davydova, Miles Henry Anderson, Alexey Tikan

We theoretically and experimentally investigate the formation of dissipative coherent structures in Kerr nonlinear optical microresonators, whose spectrum encompasses an integrated dispersion that exceeds the cavity free-spectral range. We are able to acce ...

American Physical Society2023

High-order accurate well-balanced energy stable adaptive moving mesh finite difference schemes for the shallow water equations with non-flat bottom topography

Zhenying Zhang, Junming Duan

This paper proposes high-order accurate well-balanced (WB) energy stable (ES) adaptive moving mesh finite difference schemes for the shallow water equations (SWEs) with non flat bottom topography. To enable the construction of the ES schemes on moving mesh ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2023

Emergent nonlinear phenomena in a driven dissipative photonic dimer

Tobias Kippenberg, Rui Ning Wang, Hairun Guo, Mikhail Churaev, Junqiu Liu, Alexey Tikan, Kenichi Komagata

Collective effects leading to spatial, temporal or spatiotemporal pattern formation in complex nonlinear systems driven out of equilibrium cannot be described at the single-particle level and are therefore often called emergent phenomena. They are characte ...

NATURE RESEARCH2021

Koopman Analysis of Isolated Fronts and Solitons

Jeremy Peter Parker

A Koopman decomposition of a complex system leads to a representation in which nonlinear dynamics appear to be linear. The existence of a linear framework with which to analyze nonlinear dynamical systems brings new strategies for prediction and control, w ...

2020

Breaking of Internal Waves and Turbulent Dissipation in an Anticyclonic Mode Water Eddy

Bieito Fernandez Castro

A four-month glider mission was analyzed to assess turbulent dissipation in an anticyclonic eddy at the western boundary of the subtropical North Atlantic. The eddy (radius ≈ 60 km) had a core of low potential vorticity between 100–450 m, with maximum radi ...

2020

Symplectic dynamical low rank approximation of wave equations with random parameters

Fabio Nobile, Eleonora Musharbash, Eva Vidlicková

In this paper we propose a dynamical low-rank strategy for the approximation of second order wave equations with random parameters. The governing equation is rewritten in Hamiltonian form and the approximate solution is expanded over a set of 2S dynamical ...

2020

Brownian Swarm Dynamics and Burgers’ Equation with Higher Order Dispersion

Max-Olivier Hongler

he concept of ranked order probability distribution unveils natural probabilistic interpretations for the kink waves (and hence the solitons) solving higher order dispersive Burgers’ type PDEs. Thanks to this underlying structure, it is possible to propose ...

2020

Insights into the dynamics of the deep hypolimnion of Lake Geneva as revealed by long-term temperature, oxygen, and current measurements

Ulrich Lemmin

In order to identify or shed light on dominant long-term processes of the deep hypolimnion of Lake Geneva (309 m depth), time series of temperature and horizontal currents and profiles of temperature and oxygen, taken for over a decade in the deepest part ...

American Society of Limnology and Oceanography2020

Lower Hybrid Current Drive in High Aspect Ratio Tokamaks

Hoang-Trang Lam, Joan Decker, Xiaoxia Bai

A multi-machine study has been carried out to investigate the impact of a strongly bounded wave propagation domain on the Lower Hybrid current drive, a condition which occurs principally in high aspect ratio tokamaks. In this regime, the condition of kinet ...

SPRINGER2020

Control and stabilization of the periodic fifth order Korteweg-de Vries equation

Derek Lee Smith

We establish local exact control and local exponential stability of periodic solutions of fifth order Korteweg-de Vries type equations in H-s(& x1d54b;), s > 2. A dissipative term is incorporated into the control which, along with a propagation of regulari ...

2019

Advanced dispersion engineering of dispersive waves in Si3N4 microresonators

Tobias Kippenberg, Junqiu Liu, Maxim Karpov, Anton Lukashchuk, Fabien Gremion

We experimentally demonstrate the possibility of dispersive wave tuning via advanced dispersion engineering. We utilize hybridized modes of concentric coupled resonators for precise control of the dispersion profile. (C) 2019 The Author(s) ...

IEEE2019

Dual comb generation in a monochromatically driven crystalline microresonator

Tobias Kippenberg, Erwan Guillaume Albert Lucas, Wenle Weng

Recent works on Kerr frequency combs demonstrated the possibility to simultaneously generate multiple soliton states with different group velocities in a single microresonator, which could be beneficial for many applications utilizing dual-comb systems. In ...

SPIE-INT SOC OPTICAL ENGINEERING2019

Stable Manifold for the Critical Non-Linear Wave Equation: A Fourier Theory Approach

Gérôme Graf

I will try to explain, without going into too much detail, how one can consider a non-linear wave equation as a dynamical system and what it brings to the study of its solutions. We begin by considering our model case, the non-linear Klein-Gordon equation ...

EPFL2019

Polychromatic Cherenkov Radiation Induced Group Velocity Symmetry Breaking in Counterpropagating Dissipative Kerr Solitons

Tobias Kippenberg, Erwan Guillaume Albert Lucas, Wenle Weng

High-order-dispersion-induced dispersive waves emitted by dissipative Kerr solitons are frequently observed in microresonator frequency comb generation. Also known as soliton Cherenkov radiation, this type of dispersive wave plays a critical role in comb s ...

AMER PHYSICAL SOC2019