Abstract The evolution of interfacial waves is investigated for a stratified laminar-laminar flow in a plane channel using numerical simulations based on the Volume of Fluid (VOF) method. Different nonlinear instability mechanisms that can promote saturation or rapid amplification of interfacial waves are investigated. Controlled disturbances are introduced at the interface between the two fluids, to assess five different scenarios of nonlinear interactions including harmonic excitation, subharmonic resonance, interaction between a short and a long wave, and two kinds of modulated wavepackets. Present simulations suggest that the same non-resonant type of wave interaction dominates the nonlinear stages of evolution in all the scenarios, for the fluid properties and parameters covered in this work. This mechanism involves the amplification of harmonics by quadratic nonlinearities and leads to the finite-amplitude saturation of interfacial waves, which results in a wavy flow. Reduced order models based on interaction of few wavelengths and described by the Stuart–Landau equation are proposed for the prediction of the nonlinear flow dynamics of laminar liquid-liquid two-phase flows.

中文翻译：

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分层层流通道中界面波的非线性不稳定性

摘要 使用基于流体体积 (VOF) 方法的数值模拟研究了平面通道中分层层流的界面波的演变。研究了可以促进界面波饱和或快速放大的不同非线性不稳定机制。在两种流体之间的界面处引入受控扰动，以评估非线性相互作用的五种不同情况，包括谐波激励、次谐波共振、短波和长波之间的相互作用以及两种调制波包。目前的模拟表明，对于这项工作中涵盖的流体特性和参数，相同的非共振类型的波相互作用在所有场景中的非线性演化阶段都占主导地位。这种机制涉及二次非线性对谐波的放大，并导致界面波的有限幅值饱和，从而导致波状流。提出了基于少数波长相互作用并由 Stuart-Landau 方程描述的降阶模型，用于预测层流液-液两相流的非线性流动动力学。