We investigate the dissipation of linear, two-dimensional, interfacial waves in a setting comprising three fluids (an upper fluid of semi-infinite depth, a middle fluid-layer of finite thickness, and a lower fluid of semi-infinite depth) separated by two distinct interfaces, which we consider to be elastic. We derive analytic expressions for the dissipation rate of capillary-gravity waves in such a system, in both the barotropic and baroclinic modes of propagation. Using the dissipation rate model formulated herein, we conduct parametric studies of barotropic gravity waves in an air–oil–water system. We consider six different wavenumbers within the range of 0.0165 m⁻¹ (corresponding to ocean swell) to 44.5 m⁻¹ (corresponding to a typical laboratory gravity wave) and investigate the effects of three major mechanisms of loss of energy, which are the dissipation due to the (i) dynamics in the upper fluid (air), (ii) elastic interfaces, and (iii) viscous middle fluid (oil) layer of finite thickness. For waves with wavenumbers of 0.0165 m⁻¹ and 0.04 m⁻¹, the dominant mechanism for the energy loss is that due to the dynamics in air. For waves with wavenumbers of 1 m⁻¹ and 4 m⁻¹, the oil layer acts to increase the dissipation rates significantly but only when its thickness is beyond a threshold value. For waves with wavenumbers of 36.2 m⁻¹ and 44.5 m⁻¹, the elastic interfaces cause significant increases in the dissipation rates, when their elasticities change from a value of 0.01 N/m to 0.0225 N/m. The three-fluid model developed herein is applicable to capillary-gravity waves propagating in a generic fluid system with arbitrary values for the densities, viscosities, interfacial elasticities, and with an arbitrary value for the middle fluid-layer thickness within an upper limit. This model is useful in predicting the dissipation rates of waves on the ocean surface, which is (in general) covered with biofilms and oil layers of thicknesses ranging from a few μm to a few mm, and in predicting the dissipation rates of waves such as swell, for which the dynamics in the upper fluid (air) are important.

中文翻译：

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界面毛细管重力波消散的三流体模型

我们研究了在由以下三种流体分开的流体（一个半无限深度的上部流体，一个有限厚度的中间流体层和一个半无限深度的下部流体）的环境中线性二维界面波的耗散。两个截然不同的界面，我们认为它们是弹性的。我们在正压和斜压两种传播模式下推导了这种系统中毛细管重力波的耗散率的解析表达式。使用本文制定的耗散率模型，我们对空气-油-水系统中的正重力流进行了参数研究。我们考虑在0.0165 m ^-1（对应于海浪）至44.5 m ^-1范围内的六个不同波数（对应于典型的实验室重力波）并研究三种主要的能量损失机制的影响，这些机制是（i）上部流体（空气）的动力学，（ii）弹性界面和（iii）引起的耗散。 ）有限厚度的粘性中间流体（油）层。对于波数为0.0165 m ^-1和0.04 m ^-1的波，能量损失的主要机理是由于空气动力学引起的。对于波数为1 m ^-1和4 m ^-1的波，仅当油层的厚度超过阈值时，油层才会显着提高耗散率。对于波数为36.2 m ^-1和44.5 m ^-1的波当弹性界面的弹性值从0.01 N / m更改为0.0225 N / m时，弹性界面会导致耗散率显着提高。本文开发的三流体模型适用于在通用流体系统中传播的毛细管重力波，其密度，粘度，界面弹性具有任意值，并且中间流体层厚度在上限内具有任意值。该模型可用于预测在海洋表面（通常被生物膜和油层覆盖，厚度从几微米到几毫米不等）覆盖的海浪的消散率，以及预测诸如对于膨胀，上部流体（空气）的动力学很重要。