Speaker-wire vortices in stratified anabatic Prandtl slope flows and their secondary instabilities
Speaker-wire vortices in stratified anabatic Prandtl slope flows and their secondary instabilities
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分层无热量普朗特斜率流中的扬声器线涡流及其二次不稳定性
DOI：
10.1017/jfm.2022.508
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发表时间：
2022
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
静止的纵向涡卷出现在下降和上升的普朗特斜坡流在浅的斜坡作为一个不稳定的结果时，施加的表面浮力通量相对于背景分层足够大。在这里，我们确定这些纵向辊的自配对作为一个独特的流动结构。反向旋转涡对的拓扑结构与扬声器线有着惊人的相似之处，它们之间的相互作用是流场进一步不稳定和分解成更小结构的前兆。就其本身而言，扬声器线涡流保持其独特的拓扑结构，而没有任何涡流重连或分裂。对于一个固定的倾斜角，并在一个恒定的普朗特数，我们分析了扬声器线涡的饱和状态，并进行了双全局线性稳定性分析的基础上，他们的稳态。我们建立的基础和次谐波二次不稳定性依赖于扬声器线涡的基态的流通和横向波长的存在。次谐波模式相对于基本模式的优势，有助于解释一个单一的涡对的涡动力学相比，在两个或偶数对的存在下的相对稳定性。这些不稳定模式对于多个扬声器线涡流的弯曲和合并至关重要，这些涡流破裂并导致更动态的不稳定状态，最终为向湍流过渡铺平道路。这个过程是通过三维流动模拟，我们能够跟踪这些不稳定性的非线性时间演化证明。
Stationary longitudinal vortical rolls emerge in katabatic and anabatic Prandtl slope flows at shallow slopes as a result of an instability when the imposed surface buoyancy flux relative to the background stratification is sufficiently large. Here, we identify the self-pairing of these longitudinal rolls as a unique flow structure. The topology of the counter-rotating vortex pair bears a striking resemblance to speaker-wires and their interaction with each other is a precursor to further destabilization and breakdown of the flow field into smaller structures. On its own, a speaker-wire vortex retains its unique topology without any vortex reconnection or breakup. For a fixed slope angle and at a constant Prandtl number, we analyse the saturated state of speaker-wire vortices and perform a bi-global linear stability analysis based on their stationary state. We establish the existence of both fundamental and subharmonic secondary instabilities depending on the circulation and transverse wavelength of the base state of speaker-wire vortices. The dominance of subharmonic modes relative to the fundamental mode helps to explain the relative stability of a single vortex pair compared to the vortex dynamics in the presence of two or an even number of pairs. These instability modes are essential for the bending and merging of multiple speaker-wire vortices, which break up and lead to more dynamically unstable states, eventually paving the way for transition towards turbulence. This process is demonstrated via three-dimensional flow simulations with which we are able to track the nonlinear temporal evolution of these instabilities.
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