Surface tension driven flow on a thin reaction front

Surface tension driven convection affects the propagation of chemical reaction fronts in liquids. The changes in surface tension across the front generate this type of convection. The resulting fluid motion increases the speed and changes the shape of fronts as observed in the iodate-arsenous acid reaction. We calculate these effects using a thin front approximation, where the reaction front is modeled by an abrupt discontinuity between reacted and unreacted substances. We analyze the propagation of reaction fronts of small curvature. In this case the front propagation equation becomes the deterministic Kardar-Parisi-Zhang (KPZ) equation with the addition of fluid flow. These results are compared to calculations based on a set of reaction-diffusion-convection equations.     

Laminar flame and acoustic waves in two-dimensional flow

The complete system of fluid dynamics equations describing the development of instability of a reaction front in a two-dimensional flow in reversed time are reduced to a closed system of equations of front dynamics by using Lagrangian variables and integrals of motion. The system can be used to analyze processes behind the front without solving the complete system of fluid dynamics and chemical kinetics equations. It is demonstrated how the gas density disturbances induced by the moving front can be described in the adiabatic approximation.     

The action principle for generalized fluid motion including gyroviscosity

A general set of fluid equations that allow for energy-conserving momentum transport by gyroscopic motion of fluid elements is obtained. The equations are produced by a class of action principles that yield a large subset of the known fluid and magnetofluid models, including gyroviscosity. Analysis of the action principle yields broad, model-independent results regarding the conservation laws of energy and linear and angular momenta. The formalism is illustrated by studying fluid models with intrinsic angular momentum that may appear in the contexts of condensed matter, biological, and other areas of physics.     

Stability of convective patterns in reaction fronts: a comparison of three models

Autocatalytic reaction fronts generate density gradients that may lead to convection. Fronts propagating in vertical tubes can be flat, axisymmetric, or nonaxisymmetric, depending on the diameter of the tube. In this paper, we study the transitions to convection as well as the stability of different types of fronts. We analyze the stability of the convective reaction fronts using three different models for front propagation. We use a model based on a reaction-diffusion-advection equation coupled to the Navier-Stokes equations to account for fluid flow. A second model replaces the reaction-diffusion equation with a thin front approximation where the front speed depends on the front curvature. We also introduce a new low-dimensional model based on a finite mode truncation. This model allows a complete analysis of all stable and unstable fronts.     

Dynamic Transition in a Two-Component Fluid in the Supercooled State

A mode-coupling model has been proposed to study the dynamics of a dense binary fluid. The present model includes a correct set of slow variables, which are consistent with the corresponding conservation laws. From the equations of fluctuating hydrodynamics for slow variables, a coupled set of nonlinear equations for various time-dependent correlations of density fluctuations are obtained. In the long-time limit, a self-consistent solution of these equations shows a dynamic transition, which occurs at a much higher density than predicted by the other existing models for the same systems. Our model brings the theoretical prediction for dynamic transition in better agreement with the simulation results for these systems. We have considered a hard sphere binary mixture to make a direct comparison of our results with the predictions of models studied in earlier works.     

Rotating cylindrically symmetric Kaluza-Klein fluid model

Kaluza-Klein field equations for stationary cylindrically symmetric fluid models in standard Einstein theory are formulated and a set of physically viable solutions is reported. This set is believed to be the first such Kaluza-Klein solutions and it includes the Kaluza-Klein counterpart of Davidson’s solution describing spacetime of a perfect fluid in rigid rotation about a regular axis.     

Global Solutions to a Reactive Boussinesq System with Front Data on an Infinite Domain

We prove the existence of global solutions to a coupled system of Navier–Stokes, and reaction-diffusion equations (for temperature and mass fraction) with prescribed front data on an infinite vertical strip or tube. This system models a one-step exothermic chemical reaction. The heat release induced volume expansion is accounted for via the Boussinesq approximation. The solutions are time dependent moving fronts in the presence of fluid convection. In the general setting, the fronts are subject to intensive Rayleigh-Taylor and thermal-diffusive instabilities. Various physical quantities, such as fluid velocity, temperature, and front speed, can grow in time. We show that the growth is at most for large time t by constructing a nonlinear functional on the temperature and mass fraction components. These results hold for arbitrary order reactions in two space dimensions and for quadratic and cubic reactions in three space dimensions. In the absence of any thermal-diffusive instability (unit Lewis number), and with weak fluid coupling, we construct a class of fronts moving through shear flows. Although the front speeds may oscillate in time, we show that they are uniformly bounded for large t. The front equation shows the generic time-dependent nature of the front speeds and the straining effect of the flow field. Received: 15 January 1996 / Accepted: 2 September 1997     

低温回热器模型REGEN

回热器是低温制冷机的核心组件,完成回热器的热设计与结构设计等于说完成了回热式低温制冷机设计的主体。通过建立回热器内流体与回热填料的质量方程、动量方程和能量方程并求解可确定制冷机的理论设计性能指标。运用解析方法求解回热器数学物理模型相当困难,因此广泛采用数值求解方法。总结了目前国际上主流的回热器物理数学模型,介绍并比较回热器性能仿真软件REGEN、Sage和DeltaE,重点介绍REGEN的原理、特点、功能和应用等方面,并指出其不足之处和发展方向。     

Irregular wakes in reaction-diffusion waves

Reaction-diffusion equations have proved to be highly successful models for a wide range of biological and chemical systems, but chaotic solutions have been very rarely documented. We present a new mechanism for generating apparently chaotic spatiotemporal irregularity in such systems, by analysing in detail the bifurcation structure of a particular set of reaction-diffusion equations on an infinite one-dimensional domain, with particular initial conditions. We show that possible solutions include travelling fronts which leave behind either regular or irregular spatiotemporal oscillations. Using a combination of analytical and numerical analysis, we show that the irregular behaviour arises from the instability of oscillations induced by the passage of the front. Finally, we discuss the generality of this mechanism as a way in which spatiotemporal irregularities can arise naturally in reaction-diffusion systems.     

Hamiltonian fluid reductions of electromagnetic drift-kinetic equations for an arbitrary number of moments

We present an infinite family of Hamiltonian electromagnetic fluid models for plasmas, derived from drift-kinetic equations. An infinite hierarchy of fluid equations is obtained from a Hamiltonian drift-kinetic system by taking moments of a generalized distribution function and using Hermite polynomials as weight functions of the velocity coordinate along the magnetic guide field. Each fluid model is then obtained by truncating the hierarchy to a finite number N+1$N+1$ of equations by means of a closure relation. We show that, for any positive N$N$, a linear closure relation between the moment of order N+1$N+1$ and the moment of order N$N$ guarantees that the resulting fluid model possesses a Hamiltonian structure, thus respecting the Hamiltonian character of the parent drift-kinetic model. An orthogonal transformation is identified which maps the fluid moments to a new set of dynamical variables in terms of which the Poisson brackets of the fluid models become a direct sum and which unveils remarkable dynamical properties of the models in the two-dimensional (2D) limit. Indeed, when imposing translational symmetry with respect to the direction of the magnetic guide field, all models belonging to the infinite family can be reformulated as systems of advection equations for Lagrangian invariants transported by incompressible generalized velocities. These are reminiscent of the advection properties of the parent drift-kinetic model in the 2D limit and are related to the Casimirs of the Poisson brackets of the fluid models. The Hamiltonian structure of the generic fluid model belonging to the infinite family is illustrated treating a specific example of a fluid model retaining five moments in the electron dynamics and two in the ion dynamics. We also clarify the connection existing between the fluid models of this infinite family and some fluid models already present in the literature.     

On the method of inverse scattering problem and Bäcklund transformations for supersymmetric equations

Supersymmetric Liouville and sine-Gordon equations are studied. We write down for these models the system of linear equations for which the method of inverse scattering should be applicable. Expressions for an infinite set of conserved currents are explicitly given. Supersymmetric Bäcklund transformations and generalized conservation laws are constructed.     

关于色散流体的介电方程

指出了在宏观推导运动流体的非局域型材料关系时，所涉及到的局部静止坐标必须随同流体一起转动．为了确定它与实验室坐标之间的关系，描述流体状态的场变量，除平动速度外，还应有三个空间角度．这些角变量满足一组一般的偏微分方程．尽管本文的内容是针对简单的弛豫时间模型而给出的，其物理方法可适用于推导洛伦兹协变的、含任何复杂的色散和非线性项的材料方程 关键词：     

Rarefactive ion-acoustic electrostatic solitary structures in nonthermal plasmas

An investigation has been made of ion-acoustic solitary waves in an unmagnetized nonthermal plasma whose constituents are an inertial ion fluid and nonthermally distributed electrons. The properties of stationary solitary structures are briefly studied by the pseudo-potential approach, which is valid for arbitrary amplitude waves, and by the reductive perturbation method which is valid for small but finite amplitude limit. The time evolution of both compressive and rarefactive solitary waves, which are found to coexist in this nonthermal plasma model, is also examined by solving numerically the full set of fluid equations. The temporal behaviour of positive (compressive) solitary waves is found to be typical, i.e., the positive initial disturbance breaks up into a series of solitary waves with the largest in front. However, the behaviour of negative (rarefactive) solitary waves is quite different. These waves appear to be unstable and produce positive solitary waves at a later time. The relevancy of this investigation to observations in the magnetosphere of density depressions is briefly pointed out. Received 12 October 1999     

Symmetry in the problem on wave-flow modes of a thin viscous-fluid layer

It is shown that a suitable transformation in the transverse-coordinate shift makes the set of equations describing the flow of viscous fluid films in the long-wavelength approximation invariant with respect to the reflection transformation. When constructing the flow models with the Galerkin spectral method, this symmetry in the equation for the longitudinal velocity stimulates its representation with the help of a set of functions symmetric with respect to the transverse coordinate.     

Fluid motion and molecular reorientation in a homeotropically orientated nematic liquid-crystal cell

The linearized Ericksen-Leslie differential equations, which couple fluid motion and director reorientation to each other, are reduced to a set of time varying differential equations for two pulsed optical waves incident at an angle upon a homeotropically orientated liquid-crystal cell. The differential equations are solved by a numerical method. The fluid velocity and the director angle are plotted as a function of space and time. It is shown that the reaction of fluid motion upon director reorientation is small.     

A nonlinear theory for the motion of hydrodynamic discontinuity surfaces

The complete system of hydrodynamic equations that describe the free surface of an inviscid fluid, a tangential discontinuity, and the development of the hydrodynamic instability of a reaction front is reduced to a closed system of surface equations using Lagrangian variables, special integrals of motion, and their analogues. The vorticity is shown to play a fundamental role in the pattern of motion of hydrodynamic discontinuities, imparting a differential form to the equations. In the isentropic approximation, it is demonstrated how to take into account the fluid density oscillations caused by this motion. The derived system of equations is consistent with the previously known analytical solutions obtained in special cases.     

A study of spectral element and discontinuous Galerkin methods for the Navier–Stokes equations in nonhydrostatic mesoscale atmospheric modeling: Equation sets and test cases

We present spectral element (SE) and discontinuous Galerkin (DG) solutions of the Euler and compressible Navier–Stokes (NS) equations for stratified fluid flow which are of importance in nonhydrostatic mesoscale atmospheric modeling. We study three different forms of the governing equations using seven test cases. Three test cases involve flow over mountains which require the implementation of non-reflecting boundary conditions, while one test requires viscous terms (density current). Including viscous stresses into finite difference, finite element, or spectral element models poses no additional challenges; however, including these terms to either finite volume or discontinuous Galerkin models requires the introduction of additional machinery because these methods were originally designed for first-order operators. We use the local discontinuous Galerkin method to overcome this obstacle. The seven test cases show that all of our models yield good results. The main conclusion is that equation set 1 (non-conservation form) does not perform as well as sets 2 and 3 (conservation forms). For the density current (viscous), the SE and DG models using set 3 (mass and total energy) give less dissipative results than the other equation sets; based on these results we recommend set 3 for the development of future multiscale research codes. In addition, the fact that set 3 conserves both mass and energy up to machine precision motives us to pursue this equation set for the development of future mesoscale models. For the bubble and mountain tests, the DG models performed better. Based on these results and due to its conservation properties we recommend the DG method. In the worst case scenario, the DG models are 50% slower than the non-conservative SE models. In the best case scenario, the DG models are just as efficient as the conservative SE models.     

Accelerating flames in tubes—an analysis

Flame acceleration in tubes is studied. A tube filled with flammable mixture is closed at one end and open to the atmosphere at its second end. When ignition takes place near the closed end, it is well-known from experiments that the flame may accelerate, oscillate and eventually reach considerable speeds. A one-dimensional analysis is presented, based upon the assumption that the flame front propagates at a speed that is small compared to the speed of sound. The analysis leads to a construction of the complete unsteady solution. Results from the analysis and from a numerical simulation are compared. They are similar enough to validate the analysis. The tube acoustics are set in motion by the expansion of the fluid due to ignition at the closed end. Subsequently, both spectrum and amplitude evolve because of the motion of the temperature interface, and because of forcing by the flame front, which the analysis precisely quantifies. Oscillations in the front position are strong enough to result in flow reversal. In addition, the induced periodic acoustic acceleration of the temperature and density interface will periodically make the flame front Rayleigh–Taylor unstable, which should result in the dramatic increase in the propagation speed seen in experiments.     

A steady-state fluid model of the coaxial plasma gun

The plasma layer in a coaxial plasma gun is considered as a shock front driven by expanding magnetic fields. Analytical steady-state solutions of the fluid equations yield the plasma properties, allowing the scaling of plasma focus devices.