Relative Importance Of Advection Research Articles

Lopsided dust rings in transition disks

Context. Particle trapping in local or global pressure maxima in protoplanetary disks is one of the new paradigms in the theory of the first stages of planet formation. However, finding observational evidence for this effect is not easy. Recent work suggests that the large ring-shaped outer disks observed in transition disk sources may in fact be lopsided and constitute large banana-shaped vortices. Aims. We wish to investigate how effective dust can accumulate along the azimuthal direction. We also want to find out if the size- sorting resulting from this can produce a detectable signatures at millimeter wavelengths. Methods. To keep the numerical cost under control we develop a 1+1D method in which the azimuthal variations are treated sepa- rately from the radial ones. The azimuthal structure is calculated analytically for a steady-state between mixing and azimuthal drift. We derive equilibration time scales and compare the analytical solutions to time-dependent numerical simulations. Results. We find that weak, but long-lived azimuthal density gradients in the gas can induce very strong azimuthal accumulations of dust. The strength of the accumulations depends on the P\'eclet number, which is the relative importance of advection and diffusion. We apply our model to transition disks and our simulated observations show that this effect would be easily observable with ALMA and in principle allows to put constraints on the strength of turbulence and the local gas density.

Semianalytical Self-Similar Solution of Bent-Over Jet in Cross-Flow

The flow and scalar field in the cross section of a bent-over momentum jet in cross-flow has been investigated via a 2D numerical solution of the governing equations with similarity transformation. The semianalytical model employs a free shear layer model for turbulent closure and the assumption of a constant velocity in the direction of the cross-flow; the entire solution depends solely on a dimensionless turbulent mixing parameter λ that measures the relative importance of advection and diffusion. The computed streamlines and vorticity field clearly indicate a vortex-pair flow for all λ. The shape of the scalar distribution, however, grows from a circular cell to a kidney-shaped double peak structure. Using a value of λ = 55, the computed jet trajectory and spreading and the cross-sectional shape are in good agreement with the experiments, although the dilution is somewhat overpredicted. The results suggest a free shear layer model of e = 0.0272Wml*, where e, Wm, and l* are the eddy viscosity, maximum v...

The roles of advection and diffusion in planar magnetic merging solutions

Since cosmic plasmas are highly conducting, large-scale magnetic fields are tied almost completely to the velocity field of the fluid. Only in localized regions of strong current density can the magnetic field slip through the plasma, allowing magnetic energy to be converted into ohmic heating or the kinetic energy of mass motion. Here we contrast the roles of advection and resistive diffusion in three different steady-state two-dimensional models for magnetic energy conversion: magnetic annihilation, reconnective diffusion and a kinematic model based on the classical magnetic reconnection picture. First we examine the diagnostic of ‘field-line slippage’ and show that it provides a useful indicator of the relative importance of advection and diffusion in each solution. We then quantify the energy release characteristics of the different models by examining the ratio of ohmic heat to kinetic energy generation.

Eulerian-Lagrangian localized adjoint methods for systems of nonlinear advective-diffusive-reactive transport equations

The contamination of groundwater by various hazardous materials has emerged as a primary environmental issue. The pollution of oil reservoirs is a closely related problem in that microorganisms are involved in the contaminant process. The mathematical models that describe these phenomena involve a set of nonlinear advective-diffusive-reactive transport equations, which may involve reactions with all the species and are themselves coupled to growth equations for the subsurface bacterial population. In this article, we discuss and compare different mathematical models, present Eulerian-Lagrangian localized adjoint methods (ELLAM) and combine them with specific linearization techniques to solve these nonlinear transport systems. The derived numerical schemes systematically adapt to the changing features of governing equations. The relative importance of advection, diffusion and reaction is directly incorporated into the schemes by judicious choice of the test functions in the variational formulations. Numerical experiments are presented to show the potential of these methods.

Why Is the Deep Sinking Narrow?

Narrowness of downwelling and broadness of upwelling are ubiquitous features of numerical and laboratory simulations of oceanic thermal overturning and are evidenced by the global ocean distributions of tracers, heat, and salt. By varying the relative size of the upwelling and downwelling in a pipe model based upon that of Stommel, it is shown that this structure has two interesting energetic properties: 1) broad upwelling allows the maximum amount of overturning for a given forcing by allowing the deepest penetration of heat and hence the largest baroclinic pressure gradient and 2) the narrow sinking region solution has the minimum potential energy because the deep is filled with the coldest possible water formed beneath the coldest boundary condition. The spinup of a two-dimensional model from diffusive equilibrium (with an initial symmetric overturning) to advective-diffusive-convective steady state shows that the asymmetry develops as baroclinic pressure gradients weaken preferentially on the upwelling side of the overturning while the flow of fluid modified by the boundary condition away from the surface tends to maintain pressure gradients in the downwelling branch. In steady-state solutions, the asymmetry develops as the relative importance of advection is increased by decreasing the diffusivity.

Colloidal silica transport through structured, heterogeneous porous media

In order to better understand factors controlling the migration of inorganic colloids through heterogeneous porous media, the transport of colloidal silica through columns containing a single preferred flow path was investigated. The preferred flow path, which consisted of a tubule of coarse-grained sand, was embedded in a matrix of fine-grained sand. The relative importance of advection, dispersion, deposition (removal of particles from suspension), entrainment (resuspension of deposited particles), and mass exchange between the two pore water regions was evaluated by comparing experimental data to calculations of a two-dimensional advection-dispersion model. Results of this comparison indicate that silica movement could be understood in terms of advective-dispersive transport in the preferred flow path and surrounding matrix with small interaction between the adjacent regions. Deposition of silica was found to follow a first-order kinetic process and was at least partially reversible.