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We investigate wind wave growth by direct numerical simulations solving for the two phase Navier-Stokes equations. We consider ratio of the wave speed $c$ to wind friction velocity $u_*$ from $c/u_*=$ 2 to 8, i.e. in the slow to…

Fluid Dynamics · Physics 2022-11-08 Jiarong Wu , Stéphane Popinet , Luc Deike

We introduce a numerical strategy to study the evolution of 2D water waves in the presence of a plunging jet. The free-surface Navier-Stokes solution is obtained with a finite but small viscosity. We observe the formation of a surface…

Fluid Dynamics · Physics 2024-05-01 Alan Riquier , Emmanuel Dormy

We investigate the spectral instability of a $2\pi/\kappa$ periodic Stokes wave of sufficiently small amplitude, traveling in water of unit depth, under gravity. Numerical evidence suggests instability whenever the unperturbed wave is…

Analysis of PDEs · Mathematics 2023-10-09 Vera Mikyoung Hur , Zhao Yang

Fluid flows are typically studied by solving the Navier--Stokes equation. One of the fundamental assumptions of this equation is Stokes' hypothesis. This hypothesis assumes bulk viscosity, to be identically zero. The Stokes' hypothesis is a…

Fluid Dynamics · Physics 2023-03-16 Bhanuday Sharma , Rakesh Kumar

This paper considers two-dimensional steady solitary waves with constant vorticity propagating under the influence of gravity over an impermeable flat bed. Unlike in previous works on solitary waves, we allow for both internal stagnation…

Analysis of PDEs · Mathematics 2021-10-12 Susanna V. Haziot , Miles. H. Wheeler

We propose and analyse a novel, fully discrete numerical algorithm for the approximation of the generalised Stokes system forced by transport noise -- a prototype model for non-Newtonian fluids including turbulence. Utilising the Gradient…

Numerical Analysis · Mathematics 2024-12-20 Jerome Droniou , Kim-Ngan Le , Jörn Wichmann

In order to generalize the well-known spanwise-oscillating-wall technique for drag reduction, non-sinusoidal oscillations of a solid wall are considered as a means to alter the skin-friction drag in a turbulent channel flow. A series of…

Starting with the pioneering computations of Stokes in 1847, the search of traveling waves in fluid mechanics has always been a fundamental topic, since they can be seen as building blocks to determine the long time dynamics (which is a…

Analysis of PDEs · Mathematics 2025-09-15 Roberto Feola , Riccardo Montalto , Shulamit Terracina

Identification and extraction of vortical structures and of waves in a disorganised flow is a mayor challenge in the study of turbulence. We present a study of the spatio-temporal behavior of turbulent flows in the presence of different…

Fluid Dynamics · Physics 2015-11-09 P. Clark di Leoni , P. J. Cobelli , P. D. Mininni

We study the Stokes phenomenon via hyperfunctions for the solutions of the 1-dimensional complex heat equation under the condition that the Cauchy data are holomorphic on $\mathbb{C}$ but a finitely many singular or branching points with…

Analysis of PDEs · Mathematics 2018-05-30 Bożena Tkacz

We study the Stokes phenomenon for the solutions of the 1-dimensional complex heat equation and its generalizations with meromorphic initial data. We use the theory of Borel summability for the description of the Stokes lines, the…

Analysis of PDEs · Mathematics 2016-09-13 Sławomir Michalik , Bożena Podhajecka

Nonlinear hydroelastic waves along a compressed ice sheet lying on top of a two-dimensional fluid of infinite depth are investigated. Based on a Hamiltonian formulation of this problem and by applying techniques from Hamiltonian…

Analysis of PDEs · Mathematics 2025-01-15 Philippe Guyenne , Adilbek Kairzhan , Catherine Sulem

We prove that all irrotational planar periodic traveling waves of sufficiently small-amplitude are spectrally unstable as solutions to three-dimensional inviscid finite-depth gravity water-waves equations.

Analysis of PDEs · Mathematics 2025-07-31 Ziang Jiao , L. Miguel Rodrigues , Changzhen Sun , Zhao Yang

The geometric phase techniques for swimming in viscous flows express the net displacement of a swimmer as a path integral of a field in configuration space. This representation can be transformed into an area integral for simple swimmers…

Fluid Dynamics · Physics 2021-04-13 Lyndon Koens , Eric Lauga

Wave steepness is a key geometric variable for describing breaking occurrence and its consequences, including energy dissipation and air entrainment. Using three laboratory campaigns under varying spectral conditions and co-flowing wind…

Fluid Dynamics · Physics 2026-05-29 Rui Cao , Enrique M. Padilla , Xu Chen , Adrian H. Callaghan

We study the dynamics of the interface given by two incompressible viscous fluids in the Stokes regime filling a 2D horizontally periodic strip. The fluids are subject to the gravity force and the density difference induces the dynamics of…

Analysis of PDEs · Mathematics 2023-01-03 Francisco Gancedo , Rafael Granero-Belinchón , Elena Salguero

Solutions to the Stokes equations written in terms of a small number of hydrodynamic image singularities have been a useful tool in theoretical and numerical computations for nearly fifty years. In this article, we extend the catalogue of…

Fluid Dynamics · Physics 2020-07-07 Alexander Chamolly , Eric Lauga

In two-dimensional forced Navier-Stokes turbulence, energy cascades to the largest scales in the system to form a pair of coherent vortices known as the Bose condensate. We show, both numerically and analytically, that the energy…

Fluid Dynamics · Physics 2012-04-03 Chi-kwan Chan , Dhrubaditya Mitra , Axel Brandenburg

For many biological systems that involve elastic structures immersed in fluid, small length scales mean that inertial effects are also small, and the fluid obeys the Stokes equations. One way to solve the model equations representing such…

Numerical Analysis · Mathematics 2019-07-24 Ondrej Maxian , Wanda Strychalski

We present a numerical study of spatially quasi-periodic traveling waves on the surface of an ideal fluid of infinite depth. This is a generalization of the classic Wilton ripple problem to the case when the ratio of wave numbers satisfying…

Fluid Dynamics · Physics 2021-04-07 Jon Wilkening , Xinyu Zhao