论文标题
扬声器 - 线涡流中的分层prandtl斜坡流及其次要不稳定性
Speaker-wire vortices in stratified anabatic Prandtl slope flows and their secondary instabilities
论文作者
论文摘要
由于浮力在流动剪切上的正常成分的优势，静止的纵向涡旋在katabatic和nabatic prandtl斜率流中出现。在这里，我们进一步将这些纵向卷的自我配对视为独特的流程结构。反旋转涡流对的拓扑与扬声器 - 系列及其相互作用具有显着相似之处，是将流场进一步破坏和分解为较小结构的先驱。扬声器涡流本身可以保留其独特的拓扑，而无需重新连接或分手。对于固定的斜率角$α= 3^{\ Circ} $，并且以恒定的prandtl编号，我们分析说话者 - 线涡流的饱和状态，并根据其固定状态执行BI-Global线性稳定性分析。我们确定了基本和亚谐波的次要不稳定性的存在，具体取决于说话者 - 线涡流的基本状态的循环和横向波长。与在两个或偶数成对的情况下，与涡流动态相比，亚谐波模式相对于基本模式相对于基本模式的优势有助于解释单个涡流的相对稳定性。这些不稳定模式对于多种扬声器 - 旋转涡流的弯曲和合并至关重要，该模式对多种说话的涡流进行了弯曲和合并，从而破坏并导致更具动态的不稳定状态，最终朝着转移倾斜的方式，朝着转换倾斜度。通过直接数值模拟来证明此过程，我们能够跟踪这些不稳定性的非线性时间演变。
Stationary longitudinal vortical rolls emerge in katabatic and anabatic Prandtl slope flows due to the dominance of the normal component of the buoyancy force over flow shear. Here, we further identify 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 $α=3^{\circ}$ 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 explain the relative stability of a single vortex pair compared to the vortex dynamics in 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 direct numerical simulations with which we are able to track the nonlinear temporal evolution of these instabilities.
