Generalised unsteady plume theory
Generalised unsteady plume theory
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广义非定常羽流理论
DOI：
10.1017/jfm.2016.72
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发表时间：
2016
影响因子：
3.7
通讯作者：
M. van Reeuwijk
中科院分区：
文献类型：
--
作者：
John Craske;M. van Reeuwijk
我们开发了一个广义的非定常羽流理论，并将其与一个新的直接数值模拟（DNS）数据集的统计非定常湍流羽流合奏。本文所描述的理论框架概括了以前的模型，并揭示了非定常羽流物理学的几个基本方面。该框架使人们能够理解的结构的控制积分方程取决于假设的纵向速度，湍流和压力的径向依赖。因此，由Scase和休伊特（J. Fluid Mech.，第697卷，2012年，pp. 455-480）被示出为关于速度分布的非物理假设的结果。该框架表明，这些不适定的非定常羽流模型是退化的情况下，其中一个比较大的一组适定的模型，可以从广义的非定常羽流方程，我们得到。绘制DNS的羽流的结果进行瞬时阶跃变化的源浮力通量，我们使用的框架中的诊断能力，调查所得行波的属性。一般来说，控制积分方程是双曲型的，在“礼帽”模型的极限情况下变成抛物线型，并且行波可以根据调用以关闭积分方程的特定假设而被分类为惰性的、纯的或强制的。从DNS数据的观测指导下，我们使用的框架中的预测能力，开发一个相对简单的，准确的和良好的非定常羽流模型，是基于高斯速度分布的假设。一个纯直边羽流，这是从DNS观察到的关键功能相一致的解析解。
We develop a generalised unsteady plume theory and compare it with a new direct numerical simulation (DNS) dataset for an ensemble of statistically unsteady turbulent plumes. The theoretical framework described in this paper generalises previous models and exposes several fundamental aspects of the physics of unsteady plumes. The framework allows one to understand how the structure of the governing integral equations depends on the assumptions one makes about the radial dependence of the longitudinal velocity, turbulence and pressure. Consequently, the ill-posed models identified by Scase & Hewitt (J. Fluid Mech., vol. 697, 2012, pp. 455–480) are shown to be the result of a non-physical assumption regarding the velocity profile. The framework reveals that these ill-posed unsteady plume models are degenerate cases amongst a comparatively large set of well-posed models that can be derived from the generalised unsteady plume equations that we obtain. Drawing on the results of DNS of a plume subjected to an instantaneous step change in its source buoyancy flux, we use the framework in a diagnostic capacity to investigate the properties of the resulting travelling wave. In general, the governing integral equations are hyperbolic, becoming parabolic in the limiting case of a ‘top-hat’ model, and the travelling wave can be classified as lazy, pure or forced according to the particular assumptions that are invoked to close the integral equations. Guided by observations from the DNS data, we use the framework in a prognostic capacity to develop a relatively simple, accurate and well-posed model of unsteady plumes that is based on the assumption of a Gaussian velocity profile. An analytical solution is presented for a pure straight-sided plume that is consistent with the key features observed from the DNS.