The destabilizing effect of boundary slip on Bénard convection

We investigate the influence of slip boundary conditions on the onset of Bénard convection in an infinite fluid layer. It is shown that the critical Rayleigh number is a decreasing function of the slip length, and therefore boundary slip is seen to have a destabilizing effect. Chebyshev‐tau and compound matrix formulations for solving the eigenvalue problem are presented. Copyright © 2005 John Wiley & Sons, Ltd.     

Detecting instabilities in flows of viscoelastic fluids

There is a growing interest in developing numerical tools to investigate the onset of physical instabilities observed in experiments involving viscoelastic flows, which is a difficult and challenging task as the simulations are very sensitive to numerical instabilities. Following a recent linear stability analysis carried out in order to better understand qualitatively the origin of numerical instabilities occurring in the simulation of flows viscoelastic fluids, the present paper considers a possible extension for more complex flows. This promising method could be applied to track instabilities in complex (i.e. essentially non‐parallel) flows. In addition, results related to transient growth mechanism indicate that it might be responsible for the development of numerical instabilities in the simulation of viscoelastic fluids. Copyright © 2003 John Wiley & Sons, Ltd.     

“Slow” active control of combustion instabilities by modification of liquid fuel spray properties

This paper describes an experimental investigation of the feasibility of using “slow” active control approaches, which “instantaneously” change liquid fuel spray properties, to suppress combustion instabilities. The objective of this control approach was to break up the feedback between the combustion process heat release and combustor pressure oscillations that drive the instability by changing the characteristics of the combustion process (e.g., the characteristic combustion time). To demonstrate the feasibility of such control, this study used a proprietary fuel injector (Nanomiser^TM), which can vary its fuel spray properties, to investigate the dependence of acoustics–combustion process coupling, i.e., the driving of combustion instabilities, upon the fuel spray properties. This study showed that by changing the spray characteristics it is possible to significantly damp combustion instabilities. Furthermore, using combustion zone chemiluminescence distributions, which were obtained by Abel’s deconvolution synchronized with measured acoustic data, it has been shown that the instabilities were mostly driven midway between the combustor centerline and wall, a short distance downstream from the flame holder, where the mean axial flow velocity is approximately zero in the vortex near the flame holder. The results of this study strongly suggest that a “slow” active control system that employs controllable fuel injectors could be effectively used to prevent the onset of detrimental combustion instabilities.     

随机环境下的对称零程过程的大偏差原理

利用相对熵方法及鞅方法给出了随机环境下的对称零程过程的经验测度的收敛速度函数.     

Influence of Relative Permeability on the Stability Characteristics of Immiscible Flow in Porous Media

Relative permeability functions for immiscible displacements in porous media show a wide range of profiles. Although, this behavior is well known, its impact on the stability of the displacement process is unexplored. Our analysis clearly demonstrates for the first time that the viscous instability characteristics of two-phase flows are governed not only by their end point values, but are strongly dependent on the actual profile of relative permeability functions. Linear stability analysis predicts the capacity of the flow to develop large scale fingers which can result in substantial bypassing of the resident fluid. It is observed that relative permeability functions attributed to drainage processes yield a more unstable displacement as compared to functions related to imbibition processes. Moreover, instability is observed to increase for those relative permeability functions which result from increased wettability of the wetting fluid. High accuracy numerical simulations show agreement with these predictions and demonstrate how large amplitude viscous fingers result in significant bypassing for certain relative permeability functions. In the nonlinear regime, the finger amplitude grows at a rate ∝ t^1/2 initially, drops to t^1/4 at a later time and finally grows ∝ t. The basic mechanisms of finger interaction, however, are not substantially influenced by relative permeability functions.     

快度中心区强子物质输运系数和粘滞流体演化

用Chapman-Enskog方法计算了相对论性重离子碰撞快度中心区产生的π介子物质的输运系数,并建立了相应的粘滞流体力学方程,进而讨论了粘滞对π介子物质演化过程的影响.结果表明,粘滞将减缓快度中心区π介子物质的冷却速度.     

Lax Pairs for Equations Describing Compatible Nonlocal Poisson Brackets of Hydrodynamic Type and Integrable Reductions of the Lamé Equations

We solve the problem of describing compatible nonlocal Poisson brackets of hydrodynamic type. We prove that for nonsingular pairs of compatible nonlocal Poisson brackets of hydrodynamic type, there exist special local coordinates such that the metrics and the Weingarten operators of both brackets are diagonal. The nonlinear evolution equations describing all nonsingular pairs of compatible nonlocal Poisson brackets of hydrodynamic type are derived in these special coordinates, and the integrability of these equations is proved using the inverse scattering transform. The Lax pairs with a spectral parameter for these equations are found. We construct various classes of integrable reductions of the derived equations. These classes of reductions are of an independent differential-geometric and applied interest. In particular, if one of the compatible Poisson brackets is local, we obtain integrable reductions of the classical Lamé equations describing all orthogonal curvilinear coordinate systems in a flat space; if one of the compatible brackets is generated by a constant-curvature metric, the corresponding equations describe integrable reductions of the equations for orthogonal curvilinear coordinate systems in a space of constant curvature.     

One-dimensional harmonic lattice caricature of hydrodynamics: Second approximation

The long-time behavior of an infinite chain of coupled harmonic oscillators is studied. In addition to a limiting hydrodynamic (Euler-type) equation, the next approximation is investigated. The corresponding equation is derived.     

Front propagation in certain one-dimensional exclusion models

Recent results on two interacting particle systems on are summarized, the asymmetric simple exclusion process and the branching exclusion process.