发表机构
University of Michigan; Los Alamos National Laboratory–Michigan SPARC（密歇根大学; 洛斯阿拉莫斯国家实验室-密歇根SPARC）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文从不可压缩变密度方程直接推导可混溶瑞利-泰勒不稳定性的线性稳定性表述，统一了经典理论，揭示了扩散在有限施密特数下的稳定作用及非布辛涅斯克耦合的影响。
AI 中文摘要
我们提出了可混溶瑞利-泰勒不稳定性线性稳定性的表述，保留了粘性、菲克质量扩散和非布辛涅斯克效应。本表述并非采用Duff、Harlow和Hirt（1962）的扩散修正，也不依赖于Chandrasekhar（1961）的粘性特征值问题，而是直接从不可压缩变密度控制方程推导而来。这两种方法均可作为极限情况被恢复，从而扩展了Morgan、Likhachev和Jacobs（2016）的工作。控制方程允许存在一个随时间演化的自相似扩散基态，其中误差函数密度剖面伴随有由非无散约束所要求的非零垂直基态速度。线性化产生了一个针对垂直速度和密度扰动的简化耦合表述，适用于理论分析和计算。在准稳态近似下，我们表明该表述在施密特数无穷大的极限下简化为经典的粘性不可混溶理论，并恢复了Chandrasekhar特征值问题。在有限施密特数下，扩散改变了增长率谱及其高波数结构。在谱截止之外，我们确立了标度关系 $\omega_r \sim -\lambda_m k^2$，其中 $\lambda_m$ 由局部分层运动粘度和参考扩散尺度之间的竞争决定。通过隔离扩散效应，我们表明其稳定影响随密度分层增强而减弱。浮力产生变为双峰并转向轻流体一侧，而压力产生增长到可与浮力相抗衡，并在分层的重侧充当能量源。这些结果共同阐明了经典扩散修正何时仍然适用，以及何时必须保留扩散和非布辛涅斯克耦合。
英文摘要
We present a formulation for the linear stability of the miscible Rayleigh-Taylor instability, retaining viscosity, Fickian mass diffusion, and non-Boussinesq effects. Rather than adopting the diffusive corrections of Duff, Harlow, and Hirt (1962) or relying on the viscous eigenvalue problem of Chandrasekhar (1961), the present formulation is derived directly from the incompressible variable-density governing equations. Both approaches are recovered as limiting cases, extending Morgan, Likhachev, and Jacobs (2016). The governing equations admit a time-evolving self-similar diffusive base state in which an error-function density profile is accompanied by a nonzero vertical base velocity required by the non-solenoidal constraint. Linearization yields a reduced coupled formulation for the vertical velocity and density perturbations, suitable for both theoretical analysis and computation. Within the quasi-steady-state approximation, we show that the formulation reduces, in the infinite-Schmidt-number limit, to the classical viscous immiscible theory and recovers the Chandrasekhar eigenvalue problem. At finite Schmidt number, diffusion alters the growth-rate spectrum and its high-wavenumber structure. Beyond the spectral cutoff we establish the scaling $ω_r \sim -λ_m k^2$, where $λ_m$ is determined by the competition between the locally stratified kinematic viscosity and the reference diffusive scale. By isolating the effect of diffusion, we show that its stabilizing influence weakens with increasing density stratification. Buoyancy production becomes bimodal and shifts toward the lighter-fluid side, while pressure production grows to rival buoyancy and acts as an energy source on the heavier side of stratification. Together, these results clarify when classical diffusive corrections remain applicable and when diffusion and non-Boussinesq coupling must be retained.
Comments36 pages, 19 figures
