二维Navier-Stokes流中的快速化学反应：初始区
Fast chemical reaction in two-dimensional Navier-Stokes flow: Initial regime
摘要：
本文研究了二维双周期Navier-Stokes流中的无限快双分子化学反应。化学计量量的反应物最初通过无限梯度分离。重点放在反应的初始阶段，其特征在于反应物之间的明确定义的一维材料接触线。特别注意的是反应物的扩散的效果。这项研究是平流层下部等熵混合的理想框架，其动机是为了更好地了解气候化学模型中分辨率对平流层化学的影响。采用拉格朗日拉伸理论的方法，我们涉及理论上的系综平均的长度的接触线，沿它的梯度和空间平均反应物浓度（这里称为化学速度）的下降率的模量的联合统计的有限时间李雅普诺夫指数与两个等价的时间。李雅普诺夫指数的倒数度量了拉格朗日包裹在混沌轨道上直到有限时间t的拉伸时间尺度，而第一等效时间度量了它在t之前的最近过去，第二等效时间度量了轨道的早期部分。我们表明，化学速度的尺度像扩散的平方根，其时间演化是由罕见的大事件在有限时间李雅普诺夫指数分布。光滑的初始梯度的情况下进行了讨论。的理论结果进行了测试与合奏的直接数值模拟（DNS）使用伪谱模型。
英文摘要：
This paper studies an infinitely fast bimolecular chemical reaction in a two-dimensional bi-periodic Navier-Stokes flow. The reactants in stoichiometric quantities are initially segregated by infinite gradients. The focus is placed on the initial stage of the reaction characterized by a well-defined one dimensional material contact line between the reactants. Particular attention is given to the effect of the diffusion of the reactants. This study is an idealized framework for isentropic mixing in the lower stratosphere and is motivated by the need to better understand the effect of resolutionon stratospheric chemistry in Climate-Chemistry Models. Adopting a Lagrangian stretching theory approach, we relate theoretically the ensemble mean of the length of the contact line, of the gradients along it and of the modulus of the rate of decrease of the space averaged reactant concentrations (here called the chemical speed) to the joint statistics of the finite time Lyapunov exponent with two equivalent times. The inverse of the Lyapunov exponent measures the stretching time scale of a Lagrangian parcel on a chaotic orbit up to a finite time t, while the first equivalent time measures it in the recent past before t and the second equivalent time in the early part of the trajectory. We show that the chemical speed scales like the square root of the diffusion and that its time evolution is determined by rare large events in the finite time Lyapunov exponent distribution. The case of smooth initial gradients is also discussed. The theoretical results are tested with an ensemble of direct numerical simulations (DNS) using a pseudospectral model.
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