Related papers: Hydrodynamic Nambu Brackets derived by Geometric C…
A systematic method to derive the Hamiltonian and Nambu form for the shallow water equations, using the conservation for energy and potential enstrophy, is presented. Different mechanisms, such as vortical flows and emission of gravity…
Motivated by a geometric method employed for the derivation of the Nambu bracket for ideal two-dimensional incompressible hydrodynamics, we reconstruct the reduced magnetohydrodynamic (RMHD) model by a priori imposition of its conservation…
So far fluid mechanical Nambu brackets have mainly been given on an intuitive basis. Alternatively an algorithmic construction of such a bracket for the two-dimensional vorticity equation is presented here. Starting from the Lie--Poisson…
A Nambu-Poisson formulation of the system of three ordinary differential equations describing dynamics of three vortexes of the ideal two-dimensional hydrodynamics is given. The system is integrated by quadratures.
On the basis of the intimate relation between Nambu dynamics and the hydrodynamics, the hydrodynamics on a non-commutative space (obtained by the quantization of space), proposed by Nambu in his last work, is formulated as ``hydrodynamics…
Some turbulent flows self-organize into large-scale structures, rather than breaking up into ever-smaller scales. Underpinning this phenomenon is the existence of two sign-definite quantities which are conserved by the dynamics.…
The dynamics of an ideal wave triad with real amplitudes has a well-known Nambu representation with energy and enstrophy as conservation laws. Here we derive Nambu representations for systems with constant forcings. These equations have…
A geometric formulation of a generalization of Nambu mechanics is proposed. This formulation is carried out, wherever possible, in analogy with that of Hamiltonian systems. In this formulation, a strictly nondegenerate constant 3-form is…
A framework is developed based on the concepts of {\it divorticity} ${\textbf B}$($\equiv\nabla\times\bfo$, $\bfo$ being the vorticity) and $\textit{dihelicity} g \lp \equiv\bfv\cdot\textbf{B}\rp$ for discussing the theoretical structure…
We consider relativistic hydrodynamics in the limit where the number of spatial dimensions is very large. We show that under certain restrictions, the resulting equations of motion simplify significantly. Holographic theories in a large…
The constraints imposed on hydrodynamics by the structure of gauge and gravitational anomalies are studied in two dimensions. By explicit integration of the consistent gravitational anomaly, we derive the equilibrium partition function at…
The Nambu Bracket quantization of the Hydrogen atom is worked out as an illustration of the general method. The dynamics of topological open branes is controlled classically by Nambu Brackets. Such branes then may be quantized through the…
One field of fluid dynamics concerns the search for variational principles. So far, the Hamiltonian view and Riemannian geometry has been applied to find geodesics for hydrodynamic systems. Compared to Riemannian geometry sub-Riemannian…
This paper describes a multidimensional hydrodynamic code which can be used for studies of relativistic astrophysical flows. The code solves the special relativistic hydrodynamic equations as a hyperbolic system of conservation laws based…
A water monolayer squeezed between two solid planes experiences strong out-of-plane confinement effects while expanding freely within the plane. As a consequence, the transport of such two-dimensional water combines hydrodynamic and…
Dipole-conserving fluids serve as examples of kinematically constrained systems that can be understood on the basis of symmetry. They are known to display various exotic features including glassylike dynamics, subdiffusive transport, and…
Hydrodynamics on non-commutative space is studied based on a formulation of hydrodynamics by Y. Nambu in terms of Poisson and Nambu brackets. Replacing these brackets by Moyal brackets with a parameter $\theta$, a new hydrodynamics on…
The hydrodynamic equations for a model of a confined quasi-two-dimensional gas of smooth inelastic hard spheres are derived from the Boltzmann equation for the model, using a generalization of the Chapman-Enskog method. The heat and…
We formulate a quantum theory of vorticity (hydro)dynamics on a general two-dimensional bosonic lattice. In the classical limit of a bosonic condensate, it reduces to conserved plasma-like vortex-antivortex dynamics. The nonlocal…
We conduct a numerical study of relativistic viscous fluid dynamics in the Density Frame for one-dimensional fluid flows. The Density Frame is a formulation of relativistic viscous hydrodynamics that is first-order in time, requires no…