The explicitly analytical solution is derived for the dispersion relation of the flexural—gravity waves in a two-layer fluid with a uniform current. The upper fluid is covered by a thin plate with the presence of the elastic, compressive and inertial forces. The density of each of the two immiscible layers is constant. The fluids of finite depth are assumed to be inviscid and incompressible and the motion be irrotational. A linear system is established within the framework of potential theory. A new representation for the dispersion relation of flexural—gravity waves in a two-layer fluid is derived. The critical value for the compressive force is analytically determined. The dispersion relation for the capillary—gravity with an inertial surface in a two-layer fluid can be obtained in parallel. Some known dispersion relations can be recovered from the present solution.

中文翻译：

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压缩应力对均匀流动两层流体中弯曲重力波频散关系的影响

导出了针对具有均匀电流的两层流体中弯曲重力波的色散关系的明确解析解。上部流体被薄板覆盖，并存在弹性，压缩和惯性力。两个不混溶层的每一个的密度是恒定的。有限深度的流体被认为是不粘稠且不可压缩的，并且运动是不旋转的。在势能理论的框架内建立了线性系统。得出了弯曲重力波在两层流体中的色散关系的新表示。通过分析确定压缩力的临界值。可以并行获得两层流体中具有惯性表面的毛细管重力的色散关系。