A spatially resolved stochastic weighted particle method for inception–coagulation– advection problems is presented. Convergence to a deterministic limit is briefly studied. Numerical experiments are carried out for two problems with very different coagulation kernels. These tests show the method to be robust and confirm the convergence properties. The robustness of the weighted particle method...

In this paper, the exponential B-spline functions are used for the numerical solution of the advection-diffusion equation. Two numerical examples related to pure advection in a finitely long channel and the distribution of an initial Gaussian pulse are employed to illustrate the accuracy and the efficiency of the method. Obtained results are compared with some early studies.

This paper revisits the classical problem of convectively driven one-dimensional (parallel) flow along an infinite vertical plate. We consider flows induced by an impulsive (step) change in plate temperature and by a sudden application of a plate heat flux. Provision is made for pressure work and vertical temperature advection in the thermodynamic energy equation, processes that are generally n...

The Colorado Plateau, surrounded by a ring of mountains, has the meteorological characteristics of a basin. Deep, persistent potential temperature inversions form in this basin in winter. The formation, maintenance, and dissipation of these inversions are investigated using two to four times daily radiosonde data from the winter and early spring of 1989–90. In winter, inversion evolution is for...

An explanation of the origin of intermittency in the fully developed turbulence remains one of the main open problems of theoretical hydrodynamics. Quantitatively, intermittency is measured by deviations from Kolmogorov’s scaling of the velocity correlators. Below, we shall describe a recent progress in the understanding of intermittency in a simple system describing the passive advection of a ...

Liquid microdroplets represent a convenient system for studies of mixing by chaotic advection in discrete microscopic volumes. The mixing properties of the flows in microdroplets are governed by their symmetries, which give rise to invariant surfaces serving as barriers to transport. Thorough mixing via chaotic advection requires destruction of all such invariant surfaces. To illustrate this id...

We consider convective systems in a bounded domain, in which viscous fluids described by the Stokes system are coupled using the Boussinesq approximation to a reaction-advection-diffusion equation for the temperature. We show that the resulting flows possess relaxation-enhancing properties in the sense of [12]. In particular, we show that solutions of the nonlinear problems become small when th...

We solve for the structure of a hot accretion disc with unsaturated thermal Comptonisation of soft photons and with advection, generalizing the classical model of Shapiro et al. The upper limit on the accretion rate due to advection constrains the luminosity to < ∼ 0.15y 3/5 α 7/5 of the Eddington limit, where y and α are the Compton and viscosity parameters, respectively. The characteristic te...

Eigenmode projection has been used in analysis of the two-dimensional numerical solution of electron temperature gradient ETG turbulence. The secondary Kelvin–Helmholtz instability KHI that breaks up the primary ETG structure at the onset of saturation is found to be associated with strong excitation of damped eigenmodes and strong energy damping. While the KHI structure induces some fine scale...