Irregular Wave Transformation On Mud Profiles
Including The Fluidization Of Mud Layer
Key Words: Irregular Wave, Mud Layer, Fluidization
Introduction
Wave attenuation and mud mass transport are two major phenomena of wave-mud interactionthat have received the most attentions during past decades. There have also been some effortsto formulate the fluidization of mud, based on the characteristics of the wave and undisturbedmud layer. Recently, the effect of irregularity has also been included in a number of studies(eg, [1], [2]). However, the fluidization of mud layer under irregular waves and theattenuation of irregular waves on mud profiles have not been studied yet.
The present study offers a numerical cross-shore wave-mud interaction model that can beused to predict fluid mud thickness and irregular wave transformation along soft mud profiles.
Fluidization of Mud Layer
It is assumed that a water layer is sitting on top of a stratified two-layered mud bed, where theupper one is a generalized visco-elastic (VE) layer and the lower stationary layer is elastic [3].
Simulating the behavior of the fluidized mud layer, the thickness of the fluid mud layer isrelated to the resulting strains due to the imposed wave height.
Wave spectral method is used to extend the fluidization model to irregular waves.
Considering the periodic response of the imposed shear strain, the maximum shear strain ofan irregular wave can be calculated by superimposing of maximum shear strains of regularwave components
(1) =
Where is the maximum shear strain of nthwave component.Comparing the maximum shear strain at the top of the elastic bed with the yield strain, the thickness of the fluidizedmud layer is determined.
Wave-Fluid Mud Interaction Model
The governing equations for the fluid system, i.e. the fluidized mud layer and water layer, arelinearizedNavier-Stokes equations and the continuity equation which are solved assumingVE behavior for fluid mud. The wave attenuation rate, ki, is calculated by this model.
Irregular Wave Transformation
Assuming the exponential decay of wave height over a horizontal mud bed, the energydissipation rate of mud bottom, εDm, is related to the wave attenuation rate, ki, as [4].
εDm =-d/dx(E)=2E (2)
Where E = ρgH 2 /8 is the wave energy per unit surface area, ρ is the water density and Cg is the group velocity. After the breaking line, εD reflects both dissipation effects of wave breaking and fluid mud. Comparing the amplitudes of the wave components the modeling wavwspevtra at x = x jis calculated.
Model Performance
Fig. 1 shows one example of the measured and calculated wave spectra at a site offshore ofthe town of Alleppey in Kerala, India, where the measurements are at two stations with adistance of about 300 m [5]. As it is observed, the measured wave spectrum is in goodagreement with the numerical simulations.
Fig. 1) Measured and simulated wave spectra at Alleppey in Kerala, India [5]
Results
The model results show that dissipation will be occurred according to presence of fluid mud layer in the area of study. This can be seen according to the comparison of measured data and numerical simulation. Irregular wave data will significantly change the thickness of fluid mud layer according to the wave length and especially wave energy.
This phenomenon can be seen in the outputs and in comparison to the measures data there is only a small difference that depends on wave's period.
References
[1] Soltanpour, M., Shibayama, T., Masuya, Y., Sabzevari, I. (2004), Wave Attenuation and MudMass Transport under Irregular Waves, Proc. 29th Coastal Eng. Conf., ASCE, pages 1851-1860.
[2] Zhang, Q. H., Zhao, Z. D. (1999), Wave-Mud Interaction: Wave Attenuation and Mud MassTransport, Coastal Sediments “99”, pages 1867-1880.
[3] Foda, M. A., Hunt, J. R. and Chou, H. T. (1993), A Nonlinear Model for The Fluidization ofMarine Mud by Waves. American Geophysical Union, Journal of Geophysical Research, Vol.
58, No. C4, pages 7039-7047.
[4] Soltanpour, M., Shibayama, T., Noma, T. (2003), Cross-shore Mud Transport and BeachDeformation Model, Coastal Engineering Journal, Vol. 45, No. 3, pages 363-387.
[5] Mathew, J. (1992), Wave-Mud Interaction in Mud banks, Ph.D. dissertation, Cochin University ofScience and Technology, Cochin, Kerala, India.