Lattice Boltzmann equations (LBE) are a useful tool for simulating the incompressible Navier-Stokes equations. However, LBE actually simulate compressible but usually isothermal fluid at some small finite Mach number. There has been recent interest in using larger, still subsonic, numbers, which viscous terms resulting momentum equation depart appreciably from those In particular, constraint implies nonzero "bulk" viscosity addition to usual shear viscosity. This difficulty arises level of...

A scaling theory of long-wavelength electrostatic turbulence in a magnetised, weakly collisional plasma (e.g., ITG turbulence) is proposed, with account taken both the nonlinear advection perturbed particle distribution by fluctuating ExB flows and its phase mixing, which caused streaming particles along mean magnetic field and, linear problem, would lead to Landau damping. It found that it possible construct consistent very little free energy leaks into high velocity moments function,...

Magnetohydrodynamics couples the Navier–Stokes and Maxwell equations to describes flows in electrically conducting fluids. The divergence of magnetic field must vanish, but numerical algorithms typically do not preserve this condition exactly. Artifacts can then arise solutions, such as spurious forces parallel field. These artifacts be alleviated by using extended sets Maxwell’s that include charges currents hence are invariant under duality rotations interchange electric fields. eight-wave...

Lattice Boltzmann equations for the isothermal Navier-Stokes have been constructed systematically using a truncated moment expansion of equilibrium distribution function from continuum kinetic theory. Applied to shallow water equations, with its different equation state, same approach yields discrete equilibria that are subject grid scale computational instability. Different and stable were previously by Salmon [J. Marine Res. 57, 503 (1999)]. The two sets differ through nonhydrodynamic or...

Starting from Hamilton's principle on a rotating sphere, we derive series of successively more accurate β-plane approximations. These are Cartesian approximations to motion in spherical geometry that capture the change with latitude angle between rotation vector and local vertical. Being derived using principle, different each conserve energy, angular momentum potential vorticity. They differ their treatments locally horizontal component vector, is usually neglected under traditional...

This paper derives a set of two-dimensional equations describing thin inviscid fluid layer flowing over topography in frame rotating about an arbitrary axis. These retain various terms involving the locally horizontal components angular velocity vector that are discarded usual shallow water equations. The obliquely derived both by averaging three-dimensional and from averaged Lagrangian columnar motion using Hamilton’s principle. They share same conservation properties as equations, for...

Abstract The thermal shallow water equations provide a depth-averaged description of motions in fluid layer that permits horizontal variations material properties. They typically arise through an equivalent barotropic approximation two-layer system, with spatially varying density contrast due to evolving temperature field the active layer. We formalize previous derivation quasi-geostrophic (QG) theory these equations, by performing direct asymptotic expansion for small Rossby number. then...

We study Landau damping in the 1+1D Vlasov-Poisson system using a Fourier-Hermite spectral representation. describe propagation of free energy phase space forwards and backwards propagating Hermite modes recently developed for gyrokinetics [Schekochihin et al. (2014)]. The change electric field corresponds to net flux via evolution equation. In linear damping, decay forward modes; nonlinear initial is followed by growth characterised generation term. content increases exponentially until...

Conventional shallow water theory successfully reproduces many key features of the Jovian atmosphere: a mixture coherent vortices and stable, large-scale, zonal jets whose amplitude decreases with distance from equator. However, both freely decaying forced-dissipative simulations equations in parameter regimes invariably yield retrograde equatorial jets, while Jupiter itself has strong prograde jet. Simulations by Scott Polvani [“Equatorial superrotation atmospheres,” Geophys. Res. Lett. 35,...

We present lattice Boltzmann simulations of rarefied flows driven by pressure drops along two-dimensional microchannels. Rarefied effects lead to non-zero cross-channel velocities, and nonlinear variations in the channel. Both are absent uniform body forces. obtain second-order accuracy for two components velocity relative asymptotic solutions compressible Navier–Stokes equations with slip boundary conditions. Since common formulations cannot capture Knudsen layers, we replace usual discrete...

We derive equations to describe the flow of multiple superposed layers inviscid, incompressible fluids with constant densities over prescribed topography in a rotating frame. Motivated by geophysical applications, these incorporate complete Coriolis force. do not make widely used ‘traditional approximation’ that omits contribution force from locally horizontal part rotation vector. Our derivation is performed averaging governing Euler each layer, and two different forms Hamilton's...

The Hamiltonian structure of the inhomogeneous layer models for geophysical fluid dynamics devised by Ripa [Geophys. Astrophys. Fluid Dyn. 70, 85 (1993)] involves same Poisson bracket as a formulation shallow water magnetohydrodynamics in velocity, height, and magnetic flux function variables. This becomes Lie–Poisson semidirect product Lie algebra under change variables, giving simple direct proof Jacobi identity place Ripa’s long outline proof. has appeared before compressible relativistic...

Numerical simulations with previous formulations of the quantum lattice Boltzmann (QLB) scheme in three spatial dimensions showed significant lack isotropy. In two or more QLB approach relies upon operator splitting to decompose time evolution into a sequence applications one-dimensional along coordinate axes. Each application must be accompanied by rotation wave function basis chiral eigenstates aligned relevant axis. The previously observed isotropy was due an inconsistency these...

SUMMARY This paper describes the development of a lattice Boltzmann (LB) model for binary gas mixture, and applications to channel flow driven by density gradient with diffusion slip occurring at wall. LB methods single component gases typically use non‐physical equation state in which relationship between pressure varies according scaling used. is fundamentally unsuitable extension multi‐component systems containing differing molecular masses. Substantial variations species densities...

Transfer of free energy from large to small velocity-space scales by phase mixing leads Landau damping in a linear plasma. In turbulent drift-kinetic plasma, this transfer is statistically nearly canceled an inverse due “anti-phase-mixing” modes excited stochastic form plasma echo. Fluid moments (density, velocity, and temperature) are thus approximately energetically isolated the higher distribution function, so ineffective as dissipation mechanism when collisionality small.

Shallow water magnetohydrodynamics (SWMHD) is a recently proposed model for thin layer of incompressible, electrically conducting fluid. The velocity and magnetic field are taken to be nearly two dimensional, with approximate magnetohydrostatic balance in the perpendicular direction, leading reduced two-dimensional model. SWMHD equations have been found previously admit unphysical cusp-like singularities finite amplitude magnetogravity waves. This paper extends Hamiltonian formulation...

Shallow water magnetohydrodynamics is a recently proposed model for thin layer of incompressible, electrically conducting fluid. The velocity and magnetic field are taken to be nearly two dimensional, with approximate magnetohydrostatic balance in the perpendicular direction. In this paper Hamiltonian description, ubiquitous noncanonical Lie–Poisson bracket barotropic magnetohydrodynamics, derived by integrating three-dimensional energy density Specialization dimensions yields an elegant...