This study investigates the energy budget of a viscoelastic planar liquid sheet in the presence of gas velocity oscillations. The energy budget is studied in different unstable regions, and the results are very different from those obtained for steady basic flow. The work done by surface tension and aerodynamic forces is periodic, leading to the growth of standing waves on liquid sheets. The positive work done by aerodynamic forces is the main cause of the instability, as for steady basic flow. However, treating the negative work of the surface tension as an increment in the surface energy is an effective means of determining the instability mechanisms. The unsteady basic flow causes the rate of change in the work done by viscosity and elasticity to vary periodically. An increase in elasticity and a decrease in deformation retardation promote the instability by increasing the work done by the gas medium, with reduced dissipation only as a secondary factor. This effect is more significant in parametric unstable regions than in the Kelvin–Helmholtz unstable region.

中文翻译：

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存在气体速度振荡的粘弹性平面液体片的能量收支

这项研究调查了在存在气体速度振荡的情况下粘弹性平面液体薄板的能量收支。在不同的不稳定区域研究能量收支，其结果与稳定基本流量获得的结果截然不同。表面张力和空气动力所完成的工作是周期性的，导致液体板上的驻波增加。与稳定的基本流量一样，由空气动力完成的积极工作是不稳定的主要原因。但是，将表面张力的负功视为表面能的增加是确定不稳定机制的有效手段。不稳定的基本流动使通过粘度和弹性完成的功的变化率周期性地变化。弹性的增加和变形延迟的减少通过增加气体介质的功来促进不稳定性，而耗散的减少仅是次要因素。在参数不稳定区域中，此效果比在Kelvin–Helmholtz不稳定区域中更显着。