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In this paper, we numerically study the wave turbulence of surface gravity waves in the framework of Euler equations of the free surface. The purpose is to understand the variation of the scaling of the spectra with wavenumber $k$ and…
Two-dimensional potential flows of an ideal fluid with a free surface are considered in situations when shape of the bottom depends on time due to external reasons. Exact nonlinear equations describing surface waves in terms of the so…
This paper investigates the three-dimensional axisymmetric compressible Navier-Stokes equations under slip boundary conditions in a cylindrical domain excluding the axis. For initial density allowed to vanish, we establish the global…
In the present paper, microcanonical measures for the dynamics of three dimensional (3D) axially symmetric turbulent flows with swirl in a Taylor-Couette geometry are defined, using an analogy with a long-range lattice model. We compute the…
A single incompressible, inviscid, irrotational fluid medium bounded by a free surface and varying bottom is considered. The Hamiltonian of the system is expressed in terms of the so-called Dirichlet-Neumann operators. The equations for the…
For ideal fluid flow with zero surface tension and gravity, it remains unknown whether local singularities on the free surface can develop in well-posed initial value problems with smooth initial data. This is so despite great advances over…
Turbulence modeling remains a longstanding challenge in fluid dynamics. Recent advances in data-driven methods have led to a surge of novel approaches aimed at addressing this problem. This work builds upon our recent work [Phys. Rev.…
The two-dimensional free-boundary problem describing steady gravity waves with vorticity on water of finite depth is considered. Bounds for stream functions as well as free-surface profiles and the total head are obtained under the…
This paper presents a sharp free surface method for fully nonlinear flow of two immiscible phases for wave propagation problems in the Finite Volume framework. The method resolves a sharp interface between two phases by combining the…
This paper presents a three-dimensional analytical study of the intrinsic free vibration of an elastic multilayered hollow sphere interacting with an exterior non-Newtonian fluid medium. The fluid is assumed to be characterized by a…
Confinement effects by rigid boundaries in the dynamics of ideal fluids are considered from the perspective of long-wave models and their parent Euler systems, with the focus on the consequences of establishing contacts of material surfaces…
We study a three-dimensional incompressible viscous fluid in a horizontally periodic domain with finite depth whose free boundary is the graph of a function. The fluid is subject to gravity and generalized forces arising from a surface…
There has been significant recent interest in the study of water waves coupled with non-zero vorticity. We derive analytical approximations for the exponentially-small free-surface waves generated in two-dimensions by one or several…
We study the exact controllability for spatially periodic water waves with surface tension, by localized exterior pressures applied to free surfaces. We prove that in any dimension, the exact controllability holds within arbitrarily short…
We describe traveling waves in a basic model for three-dimensional water-wave dynamics in the weakly nonlinear long-wave regime. Small solutions that are periodic in the direction of translation (or orthogonal to it) form an…
We study the propagation of monochromatic surface waves on a turbulent flow. The flow is generated in a layer of liquid metal by an electromagnetic forcing. This forcing creates a quasi two-dimensional (2D) turbulence with strong vertical…
Steady fluid flows have very special topology. In this paper we describe necessary and sufficient conditions on the vorticity function of a 2D ideal flow on a surface with or without boundary, for which there exists a steady flow among…
We establish the existence and uniqueness of smooth solutions with large vorticity and weak solutions with vortex sheets/entropy waves for the steady Euler equations for both compressible and incompressible fluids in arbitrary infinitely…
We report an experimental and numerical study of turbulent fluid motion in a free surface. The flow is realized experimentally on the surface of a tank filled with water stirred by a vertically oscillating grid positioned well below the…
This paper presents a pioneering investigation into the existence of traveling wave solutions for the two-dimensional Euler equations with constant vorticity in a curved annular domain, where gravity acts radially inward. This configuration…