Related papers: A conservation theorem for the f plane
It is shown that the Euler hydrodynamics for vortical flows of an ideal fluid coincides with the equations of motion of a charged {\it compressible} fluid moving due to a self-consistent electromagnetic field. Transition to the Lagrangian…
It is well known that a superfluid rotates by forming an array of quantized vortices. A relativistic formulation for superfluid vortex dynamics is required for a range of problems in astrophysics and cosmology, from neutron star interiors…
Motivated by the works of Cheskidov, Lopes Filho, Nussenzveig Lopes and Shvydkoy in [8, Commun. Math. Phys. 348: 129-143, 2016] and Chen and Yu in [5, J. Math. Pures Appl. 131: 1-16, 2019], we address how the $L^p$ control of vorticity…
The connection between symmetries and conservation laws as made by Noether's theorem is extended to the context of causal variational principles and causal fermion systems. Different notions of continuous symmetries are introduced. It is…
We consider an Einstein-aether type Lorentz-violating theory of gravity in which the aether vector field $V_{\mu }$ is represented as the gradient of a scalar field $\phi $, $V_{\mu }=\nabla _{\mu }\phi $. A self interacting potential for…
The conservation of helicity in ideal barotropic fluids is discussed from a group theoretical point of view. A new symmetry group is introduced i.e. the alpha group of translations. It is proven via the Noether theorem that this group…
Scalar fields, $\phi_i$ can be coupled non-minimally to curvature and satisfy the general criteria: (i) the theory has no mass input parameters, including the Planck mass; (ii) the $\phi_i$ have arbitrary values and gradients, but undergo a…
It is known that the energy of a weak solution to the Euler equation is conserved if it is slightly more regular than the Besov space $B^{1/3}_{3,\infty}$. When the singular set of the solution is (or belongs to) a smooth manifold, we…
We report direct evidence of a secondary flow excited by the Earth rotation in a water-filled spherical container spinning at constant rotation rate. This so-called {\it tilt-over flow} essentially consists in a rotation around an axis…
The water bottle flip experiment is a recreational, non-conventional illustration of the conservation of angular moment. When a bottle partially filled with water is thrown in a rotational motion, water redistributes throughout the bottle,…
Given that observations seem to favour a \index{density parameter} $\Omega_0<1$, corresponding to an open universe, we consider gauge\hs invariant perturbations of non\hs flat Robertson\hs Walker universes filled with a general imperfect…
Helmholtz theorem states that, in ideal fluid, vortex lines move with the fluid. Another Helmholtz theorem adds that strength of a vortex tube is constant along the tube. The lines may be regarded as integral surfaces of a 1-dimensional…
In order to address the difficulties of classical fluid kinematics in describing vorticity and the paradox of linear correlation between viscous force and vorticity in the Navier-Stokes equations, the study examines the inherent…
Elastic turbulence (ET), observed in flows of sufficiently elastic polymer solution at small inertia, is characterized by chaotic motions and power-law scaling of energy spectrum ($E$) in both wavenumber ($k$) and frequency ($\omega$):…
We show that for any variational symmetry of the problem of the calculus of variations on time scales there exists a conserved quantity along the respective Euler-Lagrange extremals.
For the model of a compressible barotropic fluid on a two dimensional rotating Riemmanian manifold we discuss a special class of smooth solutions having a form of a steady non-singular vortex moving with a bearing field. The model can be…
The entropy based flux-limiting (EFL) scheme is a novel approach designed to accurately resolve shocks and discontinuities in special and general relativistic hydrodynamics. By adaptively adjusting the numerical fluxes, the EFL method…
An action in which the Ricci scalar is nonminimally coupled with a scalar field and contains higher order curvature invariant terms carries a conserved current under certain conditions that decouples geometric part from the scalar field.…
Many definitions of moist potential vorticity (PV) have been proposed to extend the dry theory of Ertel PV. None of the moist PV definitions seem to have all of the desirable properties of the dry Ertel PV. For instance, dry PV is not only…
In this paper, we propose a Hamiltonian regularization of scalar conservation laws, which is parametrized by $\ell > 0$ and conserves an $H^1$ energy. We prove the existence of global weak solutions for this regularization. Furthermore, we…