Related papers: Generalized fluid dynamics and the boundary condit…
We present general relativistic correction terms appearing in Newton's gravity to the second-order perturbations of cosmological fluids. In our previous work we have shown that to the second-order perturbations, the density and velocity…
The relativistic hydrodynamical equations are being examined with the aim of extracting the quantum-mechanical equations (the relativistic Klein-Gordon equation and the Schr\"odinger equation in the non-relativistic limit). In both cases it…
The classical equations of irrotational water waves have recently been reformulated as a system of two equations, one of which is an explicit non-local equation for the wave height and for the velocity potential evaluated on the free…
Vortices in fluids and superfluids are fundamental to phenomena ranging from Bose-Einstein condensates and superfluid films to neutron stars and hydrodynamic micro-rotors, where background geometry often plays an important role. Curvature…
This lecture provides some introduction to perfect fluid dynamics within the framework of general relativity. The presentation is based on the Carter-Lichnerowicz approach. It has the advantage over the more traditional approach of leading…
The Lagrangian description of fluid flow in relativistic cosmology is extended to the case of flow accelerated by pressure. In the description, the entropy and the vorticity are obtained exactly for the barotropic equation of state. In…
We study well-posedness of a velocity-vorticity formulation of the Navier--Stokes equations, supplemented with no-slip velocity boundary conditions, a no-penetration vorticity boundary condition, along with a natural vorticity boundary…
This article concerns the equations of motion of perfect incompressible fluids in a 3-D, smooth, bounded, simply connected domain. We suppose that the curl of the initial velocity field is a vortex patch, and examine the classical problems…
The classical Lorentz reciprocal theorem (LRT) was originally derived for slow viscous flows of incompressible Newtonian fluids under the isothermal condition. In the present work, we extend the LRT from simple to complex fluids with open…
We analyze the two-dimensional incompressible Navier-Stokes equations on a smooth, bounded domain with Navier boundary conditions. Starting from an initial vorticity in $L^p$ with $p>2$, we show strong convergence of the vorticity in the…
A composite representation of the turbulent boundary-layer velocity profile is proposed, which combines a recently determined accurate interpolation of the universal law of the wall with a simple analytical expression of the smooth…
We study a model describing the motion of the fluid in a lake, assuming inflow-outflow effects across the bottom, the porous coast and the inflows and outflows of rivers. We prove the global in time existence result for this model. The…
Interface between two phases of matter are ubiquitous in nature and technology. Determining the correct velocity condition at an interface is essential for understanding and designing of flows over a surface. We demonstrate that both the…
The Madelung equations offer a hydrodynamic description of quantum systems, from single particles to quantum fluids. In this formulation, the probability density is mapped onto the fluid density and the phase is treated as a scalar…
We extend the effective theory approach to the ideal fluid limit where the polarization of the fluid is non-zero. After describing and motivating the equations of motion, we expand them around the hydrostatic limit, obtaining the sound wave…
Extended theories are widely used in the literature to describe relativistic fluids. The motivation for this is mostly due to the causality issues allegedly present in the first order in the gradients theories. However, the decay of…
The motion of a two-dimensional buoyant vortex patch, i.e. a vortex patch with a uniform density different from the uniform density of the surrounding fluid, is analyzed in terms of evolution equations for the motion of its centroid,…
This paper presents a streamfunction-vorticity formulation for the Navier--Stokes and Euler equations on general surfaces. Notably, this includes non-simply connected surfaces, on which the harmonic components of the velocity field play a…
A new class of exact solutions of hydrodynamic equations for an incompressible fluid (gas) at the presence of a bulk sink and uprising vertical flows of matter is considered. The acceleration of the rotation velocity of classical…
On the basis of gauge principle in the field theory, a new variational formulation is presented for flows of an ideal fluid. The fluid is defined thermodynamically by mass density and entropy density, and its flow fields are characterized…