Related papers: Irreversibility in an ideal fluid
A suitable expression for hydrodynamic impulse in a compressible fluid is deduced. The development of appropriate impulse formulation for compressible Euler equations confirms the propriety of the hydrodynamic impulse expression for a…
We address an experimental investigation of evaporation waves. These waves appear when a liquid contained in a vertical glass tube is suddenly depressurized from a high initial pressure down to the atmospheric one. The state of the liquid…
We study the motion of an incompressible, inviscid two-dimensional fluid in a rotating frame of reference. There the fluid experiences a Coriolis force, which we assume to be linearly dependent on one of the coordinates. This is a common…
Helical symmetry is invariance under a one-dimensional group of rigid motions generated by a simultaneous rotation around a fixed axis and translation along the same axis. The key parameter in helical symmetry is the step or pitch, the…
The flow of fluid confined between a heated rotating cylinder and a cooled stationary cylinder is a canonical experiment for the study of heat transfer in engineering. The theoretical treatment of this system is greatly simplified if the…
An equation describing the irreversible evolution of the local density of a continuous medium without involving any statistical hypotheses and assumptions is derived. The derivation is based on the smoothing of the microscopic dynamic…
In this paper we consider the Hamiltonian formulation of the equations of incompressible ideal fluid flow from the point of view of optimal control theory. The equations are compared to the finite symmetric rigid body equations analyzed…
Irreversible aggregation is an archetypal example of a system driven far from equilibrium by sources and sinks of a conserved quantity (mass). The source is a steady input of monomers and the evaporation of colliding particles with a small…
The breakup of a jet of a viscous fluid with viscosity $\mu _{1}$ immersed into another viscous fluid with viscosity $\mu _{2}$ is considered in the limit when the viscosity ratio $\lambda =\mu _{1}/\mu _{2}$ is close to zero. We show that,…
It was shown in \cite{bloch2000optimal} that an optimal control formulation for incompressible ideal fluid flow yields Euler's equations. In this paper, we consider a variational obstacle-avoidance formulation for incompressible ideal flows…
The breakup of a fluid jet into droplets has long fascinated natural scientists, with early research dating back to the 19th century. Infinitesimal perturbations to a jet grow because of surface tension, which eventually leads to breakup of…
In the variational principle leading to the Euler equation for a perfect fluid, we can use the method of undetermined multiplier for holonomic constraints representing mass conservation and adiabatic condition. For a dissipative fluid, the…
Bubbles at a free surface surface usually burst in ejecting myriads of droplets. Focusing on the bubble bursting jet, prelude for these aerosols, we propose a simple scaling for the jet velocity and we unravel experimentally the intricate…
Many natural and technical processes deal with the turbulent mixing and heat transfer in the jet of mutually immiscible liquids, which represent an important class of the modern multiphase systems dynamics. The differential equations for…
Turbulent flows governed by the Navier-Stokes equations (NSE) generate an out-of-equilibrium time irreversible energy cascade from large to small scales. In the NSE, the energy transfer is due to the nonlinear terms that are formally…
We consider the motion of a rigid body due to the pressure of a surrounded two-dimensional irrotational perfect incompressible fluid, the whole system being confined in a bounded domain with an impermeable condition on a part of the…
From everyday experience, we all know that a solid edge can deflect a liquid flowing over it significantly, up to the point where the liquid completely sticks to the solid. Although important in pouring, printing and extrusion processes,…
Active matter describes systems whose constituents convert energy from their surroundings into directed motion, such as bacteria or catalytic colloids. We establish a thermodynamic law for dilute suspensions of interacting active particles…
In Part I of the paper, we prove non-uniqueness of the solution to the Cauchy problem of the Euler equations of an ideal incompressible fluid in dimension two with vorticity in some Lebesgue space. The radially symmetric external force is…
We consider the free-boundary motion of two perfect incompressible fluids with different densities $\rho_+$ and $\rho_-$, separated by a surface of discontinuity along which the pressure experiences a jump proportional to the mean curvature…