Dynamics of local density perturbation in stably stratified fluid: Results of numerical experiments

Linear and nonlinear numerical models of dynamics of local density perturbation in a stably stratified medium are constructed. The influence of viscosity on the process of generation and propagation of internal waves generated by the local density perturbation in a pycnocline is evaluated. The problem on the dynamics of local density perturbation in the presence of wave background is considered.     

A cumulant analysis for non-Gaussian displacement distributions in Newtonian and non-Newtonian flows through porous media

We use displacement encoding pulsed field gradient (PFG) nuclear magnetic resonance to measure Fourier components S(q) of flow displacement distributions P(zeta) with mean displacement (zeta) for Newtonian and non-Newtonian flows through rocks and bead packs. Displacement distributions are non-Gaussian; hence, there are finite terms above second order in the cumulant expansion of ln(S(q)). We describe an algorithm for an optimal self-consistent cumulant analysis of data, which can be used to obtain the first three (central) moments of a non-Gaussian P(zeta), with error bars. The analysis is applied to Newtonian and non-Newtonian flows in rocks and beads. Flow with shear-thinning xanthan solution produces a 15.6+/-2.3% enhancement of the variance sigma(2) of displacement distributions when compared to flow experiments with water.     

Time-frequency analysis of the dispersive Rayleigh wave in stratified media

The dispersive characteristic of the Rayleigh wave propagating in a stratified media was analyzed by a time-frequency analysis method, the Reassignment of Smooth Pseudo-Wigner Ville Distribution (RSPWVD). Theoretical simulations and experiments were implemented for a homogeneous half-space and a two-layered half-space. It is indicated that the group velocity dispersion curves in different frequency ranges obtained by experimental result are all corresponding to the dominant modes in their surface displacement amplitudes. Such a mode identification of the multi-mode Rayleigh waves is required in inversing the medium parameters.     

A numerical analysis of chaotic behaviour in Bianchi IX models

In this paper we investigate the chaotic behaviour of the Bianchi IX cosmological models using techniques developed in the study of dynamical systems and chaotic behaviour. We numerically calculate the Lyapunov exponent, , and show that instead of converging to a constant value, it decreases steadily. We study this effect further by studying the Lyapunov exponent using short-time averages. We show that the usual method of calculating is invalid in the case of a cosmological model.     

An efficient numerical method for the equations of steady and unsteady flows of homogeneous incompressible Newtonian fluid

In the present paper, we present some numerical methods to solve the equations of steady and unsteady flows, such as those in the microcirculatory bed and large blood vessels (arteries and veins), respectively. In the case of steady flows, the method does not need neither any boundary conditions on pressure nor any small parameter, and the main computation consists of solving some Poisson equations. In the case of unsteady flows, the scheme uses a consistent Neumann boundary condition for the pressure Poisson equation. At each time step, a Poisson and heat equation are solved for the pressure and each velocity component, respectively. The accuracy and efficiency of scheme are checked by a set of numerical tests.     

Localised forced ignition of globally stoichiometric stratified mixtures: A numerical investigation

Localised forced ignition of globally stoichiometric stratified mixtures (i.e. < φ > =1.0) has been analysed here based on direct numerical simulations for different initial values of velocity and equivalence ratio fluctuations (i.e. u′ and φ′), and the Taylor micro-scale l_φ of equivalence ratio φ variation. The localised ignition is accounted for by a source term in the energy transport equation which deposits energy over a stipulated time interval. It has been found that combustion takes place predominantly under premixed mode in the case of successful ignition. The initial values of φ′ and l_φ have been found to have significant effects on the extent of burning of stratified mixtures following localised ignition. It has been found that an increase in u′(φ′) has adverse effects on the burned gas mass, whereas the effects of l_φ on the extent of burning are non-monotonic and dependent on φ′. Detailed physical explanations have been provided for the observed u′, φ′ and l_φ dependences on the extent of burning in stratified mixtures.     

Propagation and scattering of light in stratified media

The propagation and scattering of light in stratified media are considered. Based on the Maxwell equations, the present approaches to the solution of these problems are formulated in a unified way. The particular features of the wave propagation in stratified media are discussed. Scalar and vector fields are considered. Media with small-and large-scale regular inhomogeneities are examined. The construction of the Green’s function of the wave equation in a spatially homogeneous medium is discussed. Stratified isotropic and anisotropic media are analyzed. The scattering of light in a stratified medium is studied with emphasis on the Kirchhoff method, as this makes it possible to obtain calculation formulas in a form convenient for comparing the theory with the experiment. The propagation of waves in photonic crystals and the formation of forbidden zones in such objects are briefly considered.     

Dual solutions and stability analysis of flow and heat transfer of Casson fluid over a stretching sheet

The aim of the current study is to find out the dual solutions of the two-dimensional magnetohydrodynamic (MHD) flow of Casson fluid and heat transfer over the stretching sheet. The focus of the study is to examine the linear thermal radiation effects on dual solutions for both the steady and unsteady flow of Casson fluid over the stretching sheet under the influence of uniform magnetic field. The governing equations are formed as system of partial differential equations (PDEs). Using suitable transformations, the system of PDEs are converted into favorable nonlinear system of ordinary differential equations (ODEs). Simulations are performed in Maple 2015 to form the dual solutions in order to achieve the velocity, temperature, skin friction and heat transfer profiles of the Casson fluid over the stretching sheet. It is concluded that the dual solutions for the corresponding model are numerically stable. Furthermore, the upper branch solutions of the Casson fluid profiles are numerically stable as compared to the lower branch solutions. Results indicate that positive Eigen values of the MHD flow of Casson fluid provide stable profiles as compared to the negative Eigen values. It is believed that the current study would provide a base for the dual solution of the other types of the non-Newtonian fluid flows over various categories of surfaces.     

A beam summation algorithm for wave radiation and guidance in stratified media

A Gaussian beams summation (GBS) algorithm for tracking source excited wave fields in plane stratified media is presented. In the present application the medium is described by layers with constant gradient of the wave speed, and the GB propagators are calculated recursively in a closed form. The algorithm is calibrated for numerical efficacy and accuracy by defining simple physical criteria for choosing the expansion parameters (the beam collimation and the spectral discretization and truncation) that allow for sparse representation of the source-excited angular spectrum of beams. It is validated for a source-excited example in layered media, where it provides a smooth and physically meaningful solution under multipath and caustic conditions and remains accurate for long propagation ranges where phase error tends to accumulate.     

Disorder in ballistic systems: A numerical analysis

We present a numerical analysis of the single particle energy spectra of ballistic condensed matter systems and compare with recent theoretical results. We show that the presence even of weak disorder induces full chaoticity on time scales larger than the elastic disorder scattering time. To disentangle the effect of boundary, respectively disorder scattering on the spectral statistics, different types of correlation functions are introduced and discussed.     

A numerical simulation method for dissolution in porous and fractured media

We describe an algorithm for simulating reactive flows in porous media, in which the pore space is mapped explicitly. Chemical reactions at the solid–fluid boundaries lead to dissolution (or precipitation), which makes it necessary to track the movement of the solid–fluid interface during the course of the simulation. We have developed a robust algorithm for constructing a piecewise continuous (C₁) surface, which enables a rapid remapping of the surface to the grid lines. The key components of the physics are the Navier–Stokes equations for fluid flow in the pore space, the convection–diffusion equation to describe the transport of chemical species, and rate equations to model the chemical kinetics at the solid surfaces. A lattice-Boltzmann model was used to simulate fluid flow in the pore space, with linear interpolation at the solid boundaries. A finite-difference scheme for the concentration field was developed, taking derivatives along the direction of the local fluid velocity. When the flow is not aligned with the grid this leads to much more accurate convective fluxes and surface concentrations than a standard Cartesian template. A robust algorithm for the surface reaction rates has been implemented, avoiding instabilities when the surface is close to a grid point. We report numerical tests of different aspects of the algorithm and assess the overall convergence of the method.     

Numerical and analytical study of wave processes in periodic stratified media

We study the behaviour of the solutions of the Cauchy problem with discontinuous initial data for nonstandard linear partial differential equations modeling wave processes in periodic stratified media. Asymptotic formulas at large t are derived. The found asymptotic formulas are in a good agreement with the results of numerical experiments done by using the analytical computation system REDUCE 3.8.     

On the structure of internal waves excited by buoyant plumes in stratified fluid

Laboratory scale models of sewage disposal from submerged diffusers of the wastewater outfalls was carried out in the Large Thermostratified Tank of IAP RAS. It is shown that intensive interaction of internal waves occurs due to the interaction of turbulent buoyant plumes and a region of temperature bound (thermocline) and a stream propagates under a thermocline. A theoretical model of the field of internal waves is constructed for experimentally obtained velocity and density fields. It is demonstrated that the bimodal regime of internal wave excitation takes place with the first mode localized in the thermocline region and the second one in the stream. The mode excitation coefficients can be described well in the framework of self-induced internalwave generation by buoyant plumes.     

Nanoparticles superficial density of charge in electric double-layered magnetic fluid: A conductimetric and potentiometric approach

We analyze potentiometric and conductimetric measurements simultaneously performed on Electric Double-Layer Magnetic Fluid based on cobalt ferrite nanoparticles, in order to obtain the pH-dependence of the particle surface charge density. We propose a mechanism for the charging of the particle surface. This model considers the ferrofluid solution as a mixture of strong and weak diprotic acids. We show how an exact analytical treatment involving proton transfer between the particle surface and the bulk solution allows the construction of a speciation diagram of the charged superficial sites. The saturation value of the superficial density of charge is found to be equal to 0.326 ± 0.065 C m^-2. Received 9 May 2001 and Received in final form 17 July 2001     

The numerical simulation and analysis of three-dimensional seawater intrusion and protection projects in porous media

For the three-dimensional seawater intrusion and protection system, the model of dynamics of fluids in porous media and the modified upwind finite difference fractional steps schemes are put forward. Based on the numerical simulation of the practical situation in the Laizhou Bay Area of Shandong Province, predictive numerical simulation and analysis of the consequence of protection projects, underground dams, tidal barrage projects and the applied modular form of project adjustment have been finished. By using the theory and techniques of differential equation prior estimates, the convergence results have been got. Supported by the Major State Basic Research Program of China (Grant No. 19990328), the National Tackling Key Problem (Grant No. 2005020069), the National Natural Sciences Foundation of China (Grant Nos. 10771124 and 10372052), and the Doctorate Foundation of the Ministry of Education of China (Grant No. 20030422047)     

Regular and chaotic dynamics of a fountain in a stratified fluid

In the present paper, we study by direct numerical simulation (DNS) and theoretical analysis, the dynamics of a fountain penetrating a pycnocline (a sharp density interface) in a density-stratified fluid. A circular, laminar jet flow of neutral buoyancy is considered, which propagates vertically upwards towards the pycnocline level, penetrates a distance into the layer of lighter fluid, and further stagnates and flows down under gravity around the up-flowing core thus creating a fountain. The DNS results show that if the Froude number (Fr) is small enough, the fountain top remains axisymmetric and steady. However, if Fr is increased, the fountain top becomes unsteady and oscillates in a circular flapping (CF) mode, whereby it retains its shape and moves periodically around the jet central axis. If Fr is increased further, the fountain top rises and collapses chaotically in a bobbing oscillation mode (or B-mode). The development of these two modes is accompanied by the generation of different patterns of internal waves (IW) in the pycnocline. The CF-mode generates spiral internal waves, whereas the B-mode generates IW packets with a complex spatial distribution. The dependence of the amplitude of the fountain-top oscillations on Fr is well described by a Landau-type two-mode-competition model.     

Enhancement of turbulence in a stratified fluid by the presence of a shear field

Time-dependent solutions are obtained for turbulent flow in a stratified fluid in the presence of a shear field. Within the stated closure assumptions, it is shown that for certain shear fields that the turbulent intensity is enhanced.