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arXiv 1903.08151physics.flu-dyn
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含时加速度三维界面相干结构的Rayleigh-Taylor不稳定动力学

On the Rayleigh-Taylor unstable dynamics of 3D interfacial coherent structures with time-dependent acceleration

Desmond L. Hill, Aklant K. Bhowmick, Snezhana I. Abarzhi

摘要:

瑞利-泰勒不稳定性(RTI)发生在一系列工业和自然过程中。尽管绝大多数现有的研究都考虑了恒定加速度,但RTI在大多数情况下是由可变加速度驱动的。在这里,我们专注于RTI与幂律时间依赖的加速度驱动,并通过应用群论方法找到解决这个经典的非线性边值问题。我们推断,动力学是由加速度项和解决方案严重依赖于时间依赖性的值大于$-2$的加速度指数。我们发现,在早期的动力学,RTI的增长率依赖于加速参数和初始条件。对于后期动力学,我们将界面动力学与界面剪切函数联系起来,得到了连续族的正则渐近解和非线性RTI的不变性质。基本上界面和多尺度特征的动力学也被证明。在体相中速度场是势场,由于界面剪切作用,在界面处出现涡结构。从动力学的不变性性质可以看出,多尺度特征是明显的。我们还实现了良好的协议与现有的观察和制定新的基准,为未来的实验工作。

英文摘要:

Rayleigh-Taylor instability (RTI) occurs in a range of industrial and natural processes. Whereas the vast majority of existing studies have considered constant acceleration, RTI is in most instances driven by variable acceleration. Here we focus on RTI driven by acceleration with a power-law time-dependence, and by applying a group theoretic method find solutions to this classical nonlinear boundary value problem. We deduce that the dynamics is dominated by the acceleration term and that the solutions depend critically on the time dependence for values of the acceleration exponent greater than $-2$. We find that in the early-time dynamics, the RTI growth-rate depends on the acceleration parameters and initial conditions. For the later-time dynamics, we link the interface dynamics with an interfacial shear function, and find a continuous family of regular asymptotic solutions and invariant properties of nonlinear RTI. The essentially interfacial and multi-scale character of the dynamics is also demonstrated. The velocity field is potential in the bulk, and vortical structures appear at the interface due to interfacial shear. The multi-scale character becomes clear from the invariance properties of the dynamics. We also achieve excellent agreement with existing observations and elaborate new benchmarks for future experimental work.

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