Magnetohydrodynamic kink waves naturally form as a consequence of perturbations to a structured medium, for example, transverse oscillations of coronal loops. Linear theory has provided many insights into the evolution of linear oscillations, and results from these models are often applied to infer information about the solar corona from observed wave periods and damping times. However, simulations show that nonlinear kink waves can host the Kelvin–Helmholtz instability (KHI), which subsequently creates turbulence in the loop, dynamics that are beyond linear models. In this paper we investigate the evolution of KHI-induced turbulence on the surface of a flux tube where a nonlinear fundamental kink mode has been excited. We control our numerical experiment so that we induce the KHI without exciting resonant absorption. We find two stages in the KHI turbulence dynamics. In the first stage, we show that the classic model of a KHI turbulent layer growing at ∝t is applicable. We adapt this model to make accurate predictions of the damping of the oscillation and turbulent heating as a consequence of the KHI dynamics. In the second stage, the now dominant turbulent motions are undergoing decay. We find that the classic model of energy decay proportional to t ⁻² approximately holds and provides an accurate prediction of the heating in this phase. Our results show that we can develop simple models for the turbulent evolution of a nonlinear kink wave, but the damping profiles produced are distinct from those of linear theory that are commonly used to confront theory and observations.

中文翻译：

---

开尔文-亥姆霍兹不稳定引起的湍流的非线性波阻尼

磁流体动力扭结波是由于结构介质的扰动而自然形成的，例如冠状环的横向振荡。线性理论为线性振荡的演化提供了许多见解，这些模型的结果通常用于根据观测到的波周期和阻尼时间推断有关日冕的信息。然而，模拟表明，非线性扭结波可能会产生开尔文-亥姆霍兹不稳定性（KHI），从而在环路中产生湍流，其动力学超出了线性模型的范围。在本文中，我们研究了 KHI 引起的通量管表面湍流的演变，其中激发了非线性基本扭结模式。我们控制数值实验，以便在不激发共振吸收的情况下诱导 KHI。我们发现 KHI 湍流动力学分为两个阶段。在第一阶段，我们展示了以 ∝ 生长的 KHI 湍流层的经典模型t是适用的。我们采用该模型来准确预测 KHI 动力学导致的振荡阻尼和湍流加热。在第二阶段，目前占主导地位的湍流运动正在经历衰退。我们发现能量衰减的经典模型与t ⁻²近似成立并提供了该阶段加热的准确预测。我们的结果表明，我们可以为非线性扭结波的湍流演化开发简单的模型，但产生的阻尼曲线与通常用于对抗理论和观察的线性理论的阻尼曲线不同。