The unsteady dynamics of planar liquid sheet flows, interacting with unconfined gaseous environments located on both sides of the liquid phase, is numerically investigated by means of the Volume-of-Fluid (VOF) technique for supercritical regimes. The global behavior of the non-parallel flow is analyzed by perturbing the initial steady configuration by means of a Gaussian bump in the transverse velocity component of relatively small amplitude, thereby exciting sinuous modes. To gain more physical insights into the fluid system, a theoretical linear one-dimensional model is also developed. A physical interpretation of this model relates the sheet dynamics to transverse vibrations of tensional string forced by terms containing the lateral velocity and subjected to a total damping coefficient, which can assume negative values. The VOF simulation satisfactorily confirms that the velocity impulse perturbation splits into two wave fronts traveling downstream with the theoretical wave velocities. A good agreement is found in comparing the crossing times over the entire domain length of such waves with the almost constant spacing between the frequencies of the eigenvalue spectrum. Surface tension plays a stabilizing role, and for relatively high values of density ratio rρ of gaseous-to-liquid phases, the sheet becomes unstable. It is argued that the distribution of transverse velocity component of the gaseous phase represents the forcing term, which leads the system toward the instability when, for relatively high rρ, the total damping becomes negative. An analogy seems to exist between the global unstable behavior exhibited by the liquid sheet as rρ increases and the shear-induced global instability found by Tammisola et al. [Surface tension-induced global instability of planar jets and wakes,” J. Fluid Mech. 713, 632–658 (2012)] in the presence of surface tension. However, for the gravitational sheet, the surface tension is stabilizing.

中文翻译：

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通过流体体积模拟的薄液体片的全局特征模式

通过用于超临界状态的流体体积 (VOF) 技术对与位于液相两侧的无约束气态环境相互作用的平面液体层流的非定常动力学进行了数值研究。非平行流的全局行为是通过在相对较小幅度的横向速度分量中的高斯颠簸扰动初始稳定配置来分析的，从而激发正弦模式。为了获得对流体系统的更多物理见解，还开发了理论线性一维模型。该模型的物理解释将片材动力学与张力弦的横向振动联系起来，该振动由包含横向速度的项强制并受到总阻尼系数的影响，总阻尼系数可以假设为负值。VOF 模拟令人满意地证实了速度脉冲扰动分裂成两个波前，以理论波速度向下游传播。在比较此类波在整个域长度上的交叉时间与特征值谱频率之间几乎恒定的间隔时，发现了一个很好的一致性。表面张力起稳定作用，对于相对较高的气液相密度比 rρ 值，片材变得不稳定。有人认为，气相横向速度分量的分布代表了强迫项，当相对较高的 rρ 总阻尼变为负时，这导致系统趋于不稳定。随着 rρ 增加，液体层表现出的全局不稳定行为与 Tammisola 等人发现的剪切引起的全局不稳定性之间似乎存在类比。[表面张力引起的平面射流和尾流的全局不稳定性，”J. Fluid Mech。713, 632–658 (2012)] 在存在表面张力的情况下。然而，对于引力片，表面张力是稳定的。