Related papers: Steady water waves with multiple critical layers: …
This paper considers two-dimensional gravity solitary waves moving through a body of density stratified water lying below vacuum. The fluid domain is assumed to lie above an impenetrable flat ocean bed, while the interface between the water…
This study describes a specific type of critical layer for near-inertial waves (NIWs) that forms when isopycnals run parallel to sloping bathymetry. Upon entering this slantwise critical layer, the group velocity of the waves decreases to…
Asymptotic multi-layer analyses and computation of solutions for turbulent flows over steady and unsteady monochromatic surface wave are reviewed, in the limits of low turbulent stresses and small wave amplitude. The structure of the flow…
We prove the existence of small steady periodic capillary-gravity water waves for general stratified flows, where we allow for stagnation points in the flow. We establish the existence of both laminar and non-laminar flow solutions for the…
For two-dimensional steady pure-gravity water waves with a unidirectional flow of constant favourable vorticity, we prove an explicit bound on the amplitude of the wave, which decays to zero as the vorticity tends to infinity. Notably, our…
This study analyzes steady periodic hydroelastic waves propagating on the water surface of finite depth beneath nonlinear elastic membranes. Unlike previous work \cite{BaldiT,BaldiT1,Toland,Toland1}, our formulation accommodates rotational…
We analytically study a scattering of long linear surface waves on stationary currents in a duct (canal) of constant depth and variable width. It is assumed that the background velocity linearly increases or decreases with the longitudinal…
Periodic travelling waves at the free surface of an incompressible inviscid fluid in two dimensions under gravity are numerically computed for an arbitrary vorticity distribution. The fluid domain over one period is conformally mapped from…
We investigate the properties of small-amplitude inertial waves propagating in a differentially rotating incompressible fluid contained in a spherical shell. For cylindrical and shellular rotation profiles and in the inviscid limit,…
In this article we consider irrotational gravity water waves with finite bottom. Our goal is two-fold. First, we represent the equations in holomorphic coordinates and discuss the local well-posedness of the problem in this context. Second,…
We consider three-dimensional inviscid irrotational flow in a two layer fluid under the effects of gravity and surface tension, where the upper fluid is bounded above by a rigid lid and the lower fluid is bounded below by a flat bottom. We…
Periodic water waves of permanent form traveling at constant speed, the so-called Stokes waves, are studied in water of fixed finite depth using methods previously used in water of infinite depth. We apply our methods to waves of varying…
Quantum vortices with more than a single circulation quantum are usually unstable and decay into clusters of smaller vortices. One way to prevent the decay is to place the vortex at the centre of a convergent (draining) fluid flow, which…
We consider the two-dimensional deep gravity-capillary water waves with point vortices. We first formulate the question in the holomorphic coordinates. Then, we derive an a priori energy estimate for water waves, and show that the water…
The formation of quantized vortices is a unifying feature of quantum mechanical systems, making it a premier means for fundamental and comparative studies of different quantum fluids. Being excited states of motion, vortices are normally…
We consider a two-dimensional, two-layer, incompressible, steady flow, with vorticity which is constant in each layer, in an infinite channel with rigid walls. The velocity is continuous across the interface, there is no surface tension or…
We consider a multi-fluid system with several free interfaces. For this system we prove existence of three-dimensional steady gravity-capillary waves with non-zero vorticity. We obtain non-zero vorticity by prescribing the relative velocity…
We construct large families of two-dimensional travelling water waves propagating under the influence of gravity in a flow of constant vorticity over a flat bed. A Riemann-Hilbert problem approach is used to recast the governing equations…
We prove that stable fluid equilibria with trivial homology on curved, reflection-symmetric periodic channels must posses "islands", or cat's eye vortices. In this way, arbitrarily small disturbances of a flat boundary cause a change of…
Near the critical point, isothermal interfacial zones are investigated starting from a non-local density of energy. From the equations of motion of thermocapillary fluids, we point out a new kind of adiabatic waves propagating along the…