Related papers: Canonical scale separation in two-dimensional inco…
This work makes analytic progress in the deterministic study of turbulence in Hamiltonian systems by identifying two types of energy cascade solutions and the corresponding large- and small-scale structures they generate. The first cascade…
Vortices are the hallmarks of hydrodynamic flow. Recent studies indicate that strongly-interacting electrons in ultrapure conductors can display signatures of hydrodynamic behavior including negative nonlocal resistance, Poiseuille flow in…
Classical hydrodynamics is a remarkably versatile description of the coarse-grained behavior of many-particle systems once local equilibrium has been established. The form of the hydrodynamical equations is determined primarily by the…
We consider attractive irreducible conservative particle systems on $\mathbb{Z}$, without necessarily nearest-neighbor jumps or explicit invariant measures. We prove that for such systems, the hydrodynamic limit under Euler time scaling…
We present a formal, approximate model for singularity formation in classical fluid dynamics in three dimensions. The construction utilizes an approximation of local two-dimensionality to study an anti-parallel hairpin vortex structure with…
We present a novel canonical description of the incompressible fluid dynamics. This description uses the dynamical constraints, in our case reflecting "incompressibility" assumption, and leads to replacement of usual hydrodynamical Poisson…
We prove the conservation of energy for weak and statistical solutions of the two-dimensional Euler equations, generated as strong (in an appropriate topology) limits of the underlying Navier-Stokes equations and a Monte Carlo-Spectral…
We analyse the multiscale properties of energy-conserving upwind-stabilised finite element discretisations of the two-dimensional incompressible Euler equations. We focus our attention on two particular methods: the Lie derivative…
Phase separation of binary fluids quenched by contact with cold external walls is considered. Navier-Stokes, convection-diffusion, and energy equations are solved by lattice Boltzmann method coupled with finite-difference schemes. At high…
Conventional wisdom holds that macroscopic classical phenomena naturally emerge from microscopic quantum laws. However, despite this mantra, building direct connections between these two descriptions has remained an enduring scientific…
We present an efficient and highly scalable geometric method for two-dimensional ideal fluid dynamics on the sphere. The starting point is Zeitlin's finite-dimensional model of hydrodynamics. The efficiency stems from exploiting a…
A decomposition of the energy and helicity fluxes in a turbulent hydrodynamic flow is proposed. The decomposition is based on the projection of the flow to a helical basis that allows to investigate separately the role of interactions among…
We present a formalism for Newtonian multi-fluid hydrodynamics derived from an unconstrained variational principle. This approach provides a natural way of obtaining the general equations of motion for a wide range of hydrodynamic systems…
We derive a new formulation of the compressible Euler equations exhibiting remarkable structures, including surprisingly good null structures. The new formulation comprises covariant wave equations for the Cartesian components of the…
We present theoretical and numerical evidence to show that self-defocusing nonlinear optical propagation can be used to compute Euler fluid dynamics and possibly Navier-Stokes fluid dynamics. In particular, the formation of twin vortices…
Introducing a Clebsch-like parameterization, we have formulated a canonical Hamiltonian system on a symplectic leaf of reduced magnetohydrodynamics. An interesting structure of the equations is in that the Lorentz-force, which is a…
Quantum liquids in two dimensions represent interesting dynamical quantum systems for several reasons, among them the possibility of the existence of infinite hidden symmetries, such as conformal symmetry or the symmetry associated with…
We present a combined experimental and theoretical investigation of the formation and decay kinetics of vortices in two dimensional, compressible quantum turbulence. We follow the temporal evolution of a quantum fluid of exciton polaritons,…
The geometric nature of Euler fluids has been clearly identified and extensively studied over the years, culminating with Lagrangian and Hamiltonian descriptions of fluid dynamics where the configuration space is defined as the…
In the Seiberg-Witten limit, the low-energy dynamics of N weakly coupled identical open strings on a D3-brane can behave as two-dimensional incompressible hydrodynamics. Classical vortices are frozen in the fluid and described by an action…