Book review of ENCYCLOPEDIA OF NONLINEAR SCIENCE,edited by Alwyn Scott,Routledge, Taylor and Francis Group, 2005, VII +1053 pp., 135, $225 hardback (ISBN 1-57958-385-7).

We present three-dimensional (3D) solutions of the magnetohydrostatic equations in the co-rotating frame of reference outside a magnetized rigidly rotating cylinder. We make no symmetry assumption for the magnetic field, but to be able to make analytical progress we neglect outflows and specify a particular form for the current density. The magnetohydrostatic equations can then be reduced to a single linear partial differential equation for a pseudo-potential U, from which the magnetic field can be calculated by differentiation. The equation for U can be solved by standard methods. The solutions can also be used to determine the plasma pressure, density and temperature as functions of all three spatial coordinates. Despite the obvious limitations of this approach, it can, for example, be used as a simple tool to create 3D models for the closed field line regions of rotating magnetospheres without rotational symmetry.     

Long waves due to a symmetrical wind stress on the surface of a rotating ocean

Abstract

The problem of unsteady long waves generated by any horizontal and symmetrically distributed, time-periodic surface wind on a rotating ocean is analysed for large times and distances. Uniform asymptotic estimates of the surface displacement in the unsteady state are obtained. The steady-state wave and velocity fields at any distance are also determined. Some characteristics of the unsteady and steady motions are described. Also noted are the features that distinguish the motion from its one-dimensional analogue for which a non-uniform analysis in the unsteady state along with a large-distance form of the surface elevation are already known.     

旋转电极法研究盐类溶解─LiCl、NaCl、KCl在水中的溶解动力学

利用旋转盘装置结合离子选择电极研究了ＬｉＣｌ、ＮａＣｌ、ＫＣｌ在２０℃～３５℃水中溶解动力学，得到了溶解动力学方程．     

大气中的包络Rossby孤立波——纬度效应的作用

本文进一步对旋转正压大气中的包络Rossby孤立波进行了研究，结果发现当Rossby波的波数m（m为纬向波数）满足1≤m≤2时，旋转正压大气中才存在包络Rossby孤立波，并且只有m＝2的包络Rossby孤立波才具有阻塞高压的结构。我们还对这种m＝２的包络Rossby孤立波随纬度变化的持续性进行了计算，得到了许多结果。     

The long-time decay of rotating homogeneous flows over variable topography

The long-time decay of rotating, homogeneous flows over variable topography is analyzed by means of laboratory experiments and numerical simulations. The influence of the topography on the flow evolution is associated with stretching and squeezing effects on fluid columns as they experience changes in depth, and with viscous effects produced by the boundary condition at the solid bottom of the tank. In particular, experiments with a sine-shaped topography in one of the horizontal directions are analyzed by using two different basic flows. First, the evolution of dipolar vortices drifting across the topography while slowly decaying, is examined. The second set of experiments considers the evolution and decay of an initially circular vortex transforming into a tripolar structure. The experiments are well represented by numerical simulations based on a quasi-two-dimensional formulation with variable topography.     

Baroclinic nonlinear exchanges of energy and potential enstrophy in the quasi-geostrophic two-layer model

Abstract

Merilees and Warn's (1975) nonlinear interaction analysis of two-dimensional nondivergent flow is extended to examine the quasi-geostrophic two-layer model. Two sets of triads exist in this model (Salmon, 1978). The purely barotropic triads are the same as the triads examined by Merilees and Warn. Baroclinic-barotropic triads are found to exchange more energy or potential enstrophy with smaller or larger scales depending on the scale of motion as compared with the internal Rossby deformation radius and the relative wavenumber position of baroclinic and barotropic components.     

Equilibrium Structures of Rotationally and Tidally Distorted Polytropic Models of Stars

We propose suitable modifications in the concept of Roche equipotentials to account for the effect of mass distribution inside a star. The Kippenhahn and Thomas (1970) approach is used to incorporate the effects of rotational and tidal forces in the equations of stellar structure. The proposed method is applied to compute structures of certain rotationally and tidally distorted polytropic models.     

Laboratory experiments on along-slope flows in homogeneous and stratified rotating fluids

Laboratory experiments have been carried out for the flow along isobaths of simulated shelf-continental slope geometry. Cases of both homogeneous and linearly stratified fluids are considered and the background flows are sufficiently strong to have the flow near the bottom boundary range from transitional to fully turbulent. The background motions are impulsively started and flows with a coast on the right (spin-down) and on the left (spin-up) are considered. The homogeneous spin-down and spin-up processes are smooth in the sense that no vortical structures were found to be of the order of the slope width or larger. Flows reach equilibrium more quickly for spin-down cases, and this is attributed to secondary flows forced by the basin geometry. All of the stratified experiments exhibited large-scale instabilities as evidenced by the generation of slope and basin scale eddy structures and a much slower decay than their homogeneous counterparts.     

Konzentrationsprofile in Rotationsscheibenreaktoren und deren Modellierung am Beispiel des anaeroben Acetatabbaus mit experimenteller Überprüfung

Concentration Profiles in Rotating Disc Reactors. Their Mathematical Model for the Anaerobic Digestion of Acetic Acid Including an Experimental Verification This paper presents rotating disc reactors for aerobic and anaerobic wastewater treatment. Unlike the activated sludge or contact processes, this reactor allows higher concentrations of biomass and lesser danger of the reactor becoming blocked. The reduced backmixing within the reactor leads to axial concentration profiles when continuously operated. These are presented for various biological processes. The axial concentration profiles generated during the continuous anaerobic degradation of acetic acid are measured and described by a mathematical model. A refined dispersion model is created on the basis of tracer experiments taking into account the actual construction of the reactor as well as the physical conditions in it. To determine the biodegradation a Haldane kinetics is used, in which the undissociated acetic acid is the substrate. The model takes into consideration all the local parameters (pH value, concentration of acetic acid, biomass, and ion activity). The difficult measurement of the concentration of the active biomass which is immobilized on the disk is accomplished by carrying out batch experiments. The results of the experiments are 22 concentration profiles with influent DOC concentrations from 200 to 2000 mg L^–1 which were measured and modelled. Some examples are shown to illustrate the influence of the ion activity and the refinement of the dispersion model.