Abstract
Fluid mud often exists in coastal areas with an interface separating it from its upper water layer. When a surface wave propagates over a bed covered with water and fluid mud, it will cause an interfacial wave of the mud-water interface, which damps the surface wave and results in mass transport of fluid mud. Most researches about wave attenuation and mass transport of fluid mud are based on the assumption that the mud-water interface is unbroken. This assumption excludes the breaking interfacial waves that are known as an important mechanism responsible for mass and momentum transport between the two fluids. When the surface wave is long, its velocity field, which also serves as basic flows, may be susceptible to the Kelvin-Helmholtz (K-H) instability if the shears at the interface are strong enough. In the present paper, the critical conditions for the K-H instability to occur for the mud-water interface is investigated via linear stability analysis and numerical simulation. It is found that, for a K-H instability to occur, the Stokes boundary layer thickness induced by a surface wave must be large enough to penetrate the fluid mud layer and produce a strong shear at the interface. Meanwhile, a critical condition is found for a long surface wave to cause breakup of mud-water interface through K-H instability. This is practically instructive for waterway and harbor construction and protection because it predicts that a thicker mud layer is harder to be taken away by a surface wave.
Highlights
Fluid mud is typically a mixture of fine cohesive clay particles, organic matters and water, and exhibits Newtonianlike behavior.1,2 In many real situations, the water body is stratified into two layers with a sharp interface, which is for the first time termed lutocline by Parker and Kirby.3 The typical density of fluid mud ranges from 1050 ∼ 1200kg/m3 and its dynamic viscosity varies from ten to thousands times that of water
Mud-water interface can be susceptible to the K-H instability if a surface wave is long enough. We have investigated this issue in the present paper by simplifying the wave inducing velocity fields to the oscillating two-layer Poiseuille flows
The linear stability analyses show that the ratio of the mud layer thickness and the Stokes boundary layer thickness in mud layer induced by surface waves plays a central role in determining the stability of the interface
Summary
Fluid mud is typically a mixture of fine cohesive clay particles, organic matters and water, and exhibits Newtonianlike behavior.1,2 In many real situations, the water body is stratified into two layers with a sharp interface, which is for the first time termed lutocline by Parker and Kirby.3 The typical density of fluid mud ranges from 1050 ∼ 1200kg/m3 and its dynamic viscosity varies from ten to thousands times that of water. We investigate the critical conditions for the breaking of mud-water interface by long surface waves in the present paper. For a viscous K-H instability to occur, a shorter disturbance wavelength is required to overcome the viscosity dissipation without consideration of the boundary layer thickness near the interface.
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