Linear stability of katabatic Prandtl slope flows with ambient wind forcing
Linear stability of katabatic Prandtl slope flows with ambient wind forcing
复制标题
下降普朗特斜坡流与环境风力的线性稳定性
DOI：
10.1017/jfm.2019.1047
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发表时间：
2020
影响因子：
3.7
通讯作者：
Senocak, Inanc
中科院分区：
文献类型：
--
作者：
Xiao, Cheng-Nian;Senocak, Inanc
我们研究了无限宽的均匀冷却的平面上，由于上方均匀的下坡风场的附加强迫作用下，katabatic坡面流动的稳定性。我们采用Prandtl(Lykosov&Gutman 1972)的坡面流原始模型的扩展形式来推导基流，这是稳定性分析中一个有趣的基本状态，因为它不能简化为独立于外部参数的单一普遍形式。我们对这一基本状态进行了线性模态分析，证明了对于固定的普朗特数和坡角，两个独立的无量纲参数足以描述流动的稳定性。其中一个参数是我们在肖和Senocak(2019)中引入的层结微扰数。第二个参数到目前为止还是未知的，可以解释为高空环境风的动能与由于背景层结的粘性和稳定作用而产生的阻尼值之比。对于固定的普朗特数，根据倾斜角的大小和前述的无量纲数，可以出现不稳定的定常横模和行波纵模。环境风对基流稳定性的影响是复杂的，在一定的参数范围内，环境风既可以是稳定的，也可以是不稳定的。我们的结果有力地反证了目前仅依靠梯度Richardson数来描述层状大气坡面流动的动态稳定性的做法。
We investigate the stability of katabatic slope flows over an infinitely wide and uniformly cooled planar surface subject to an additional forcing due to a uniform downslope wind field aloft. We adopt an extension of Prandtl's original model for slope flows (Lykosov & Gutman 1972) to derive the base flow, which constitutes an interesting basic state in stability analysis because it cannot be reduced to a single universal form independent of external parameters. We apply a linear modal analysis to this basic state to demonstrate that for a fixed Prandtl number and slope angle, two independent dimensionless parameters are sufficient to describe the flow stability. One of these parameters is the stratification perturbation number that we have introduced in Xiao & Senocak (2019). The second parameter, which we will henceforth designate the wind forcing number, is hitherto uncharted and can be interpreted as the ratio of the kinetic energy of the ambient wind aloft to the damping due to viscosity and stabilizing effect of the background stratification. For a fixed Prandtl number, stationary transverse and travelling longitudinal modes of instabilities can emerge, depending on the value of the slope angle and the aforementioned dimensionless numbers. The influence of ambient wind forcing on the base flow's stability is complicated as the ambient wind can be both stabilizing as well as destabilizing for a certain range of the parameters. Our results constitute a strong counter-evidence against the current practice of relying solely on the gradient Richardson number to describe the dynamic stability of stratified atmospheric slope flows.
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影响因子：
4.3
作者：
KONDO, J;SATO, T
通讯作者：
SATO, T
下降风：现场案例研究
影响因子：
8.9
作者：
P. Manins;B. Sawford
通讯作者：
B. Sawford
沿着浸没在稳定分层流体中的垂直板的不稳定对流驱动流
影响因子：
3.7
作者：
Alan Shapiro;E. Fedorovich
通讯作者：
E. Fedorovich
DOI：
10.1175/jam-2182.1
发表时间：
2005-01-01
期刊：
JOURNAL OF APPLIED METEOROLOGY
影响因子：
--
作者：
Haiden, T;Whiteman, CD
通讯作者：
Whiteman, CD
影响因子：
4.3
作者：
J. Doran;T. W. Horst;C. Whiteman
通讯作者：
C. Whiteman