Wave-Mud Interaction

Damping of the ocean surface waves as they propagate over and interact with the muddy seafloor plays an important role in coastal phenomena. Fishermen of southwest coast ofIndia in ”Chakara” feast celebrate the arrival of mud banks that damp large monsoon-driven waves and calm onshore waters resulting in a rich fish harvest.

image010

“1998 Airborne Data Acquisition and Registration (ADAR) image showing differential wave breaking due to shallow water mud deposits at the landward location of the field experiment. The experiment origin is signified by the plus sign.”
(from K.T.Hollandetal./ContinentalShelfResearch29(2009)503–514)

 

Due to the strong effect of the seafloor on the wave characteristics, particularly in very muddy regions like gulf of Mexico, the underlying mechanism and ability of prediction of coastal wave condition is of central interest. There are a number of models used to describe the mud in the wave attenuation problem. In general, these models are constitution relations for the mud. The mud nature, however, is very complicated and among these several models already existing none of them are capable of generally describing the damping phenomenon.  we came up with a visco-elastic three-parameter bottom model in which all complexities are in the coefficients (rather than the equations). We also developed a higher order spectral method based algorithm from which phase-resolved simulation of ocean waves can be performed (in a phase resolved simulation we model the ocean surface as is seen in real nature, as opposed to phase averaged model that only studies some long term averaged quantities of the ocean, such as the spectrum).  The phase -resolved tool along with our visco-elastic model has made a strong tool for the study of the linear damping and nonlinear interaction of waves over muddy shallow water.  Comparison of our direct simulation results with field observations and previous theories shows the effectiveness of our approach. We include the effect of nonlinearity, shoaling and frequency dependent mud damping together in a realistic ocean situation.

mud_mech1

Wave-mud interaction mechanisms: 1- One-Layer Resonant (Nonlinear) Mechanism

 

image011

Effect of nonlinearity on the wave damping over a shoaled shallow muddy coast of Louisiana (Observational setup of Elgar and Raubenheimer GRL 2009). dash-line is the initial spectrum upstream. Plus signs denote final spectrum observed. Solid lines show the direct simulation with and without taking into account for nonlinearities.

 

References:

– Alam, M.R., Liu, Y. and Yue, D.K.P., “Numerical Investigation of Broadband Wave Attenuation over Muddy Shoaling Seabeds”, Submitted to the Geophysical Research Letter (2009).

– Alam, M.R., Liu, Y. and Yue, D.K.P., “Numerical Investigation of Dissipation Mechanisms for Surface Wave Propagation over Muddy Seabed”, AGU Chapman Conference on Physics of Wave-Mud Interaction, Amelia Island, Florida, USA, 17-20 November 2008.

– Alam, M.R., Liu, Y. and Yue, D.K.P., “Broadband Waves over Muddy Seafloors” March meeting of American Geophysical Union: 2008 Ocean Sciences Meeting, From the Watershed to the Global Ocean, 2-7 March 2008 Orlando-Florida.