SWAN-Mud: Engineering Model for Mud-Induced Wave Damping

Abstract

This paper describes the implementation of a new dispersion relation and energy-dissipation equation obtained from a viscous two-layer model schematization in the state-of-the-art wave forecasting model SWAN to simulate wave damping in coastal areas by fluid mud deposits. This new dispersion relation is derived for a nonviscous, nonhydrostatic upper layer and a viscous, hydrostatic lower layer, covering most conditions encountered in nature. An algorithm is developed for a robust numerical solution of this new implicit dispersion relation through proper starting values in the iteration procedure. The implementation is tested against a series of analytical solutions and three schematic test cases. Next, four dispersion relations published in the literature are evaluated and compared with the new dispersion relation. The solution of the dispersion relations forms a multidimensional space. Comparison of the various model solutions through one-dimensional graphs can therefore become quite misleading, as shown in the discussion of a two-dimensional representation of the solution space, explaining for instance the variation in ambient conditions at which maximum wave damping is to be expected. The various models have been developed for a variety of conditions, such as shallow and deep water and shallow and thick mud layers; the various models agree well in their domain of applicability, but they show significant deviations when used outside their domain. Because the ambient and mud conditions may vary considerable in space and time at a particular site, the use of the new model is advocated because it covers most water depths and fluid mud thicknesses encountered in nature. The strength of the new SWAN-mud model lies in its large-scale applicability, assessing the twodimensional evolution of wave fields in coastal areas. Therefore, the new implementation is evaluated with respect to the behavior of waves on a sloping seabed, representing real-world coasts. In all cases, the new SWAN-mud model behaves satisfactorily; a critical remaining issue, though, is the assessment of the relevant fluid mud parameters.

U.S. IOOS coastal and ocean modeling testbed: Evaluation of tide, wave, and hurricane surge response sensitivities to mesh resolution and friction in the Gulf of Mexico

“…Because the Louisiana shelf has a smooth muddy and silty bottom in lieu of a rougher sandy bottom, this study of Ike suggests that an appropriate value for the Gulf of Mexico LATEX shelf may be C fjon ¼ 0.019 m 2 =s 3 and that future consideration of C fjon values be region-specific and bottom-specific. In contrast to the smooth fine-grain bottom studied here, studies by Rogers and Holland [2009] and Kranenburg et al [2011] have shown that under relatively weak waves, fluid mud bottoms, which can vary greatly in rheologic characteristics, can also be highly dissipative and even alter the wave number.…”

“…In contrast to the smooth fine‐grain bottom studied here, studies by Rogers and Holland [] and Kranenburg et al . [] have shown that under relatively weak waves, fluid mud bottoms, which can vary greatly in rheologic characteristics, can also be highly dissipative and even alter the wave number.…”

Mechanisms of surface wave energy dissipation over a high‐concentration sediment suspension

“…Both complete solutions are based on the work of Kranenburg et al . [], and approximate solutions for an infinitely thick upper layer are presented. Several examples of velocity profiles and dissipation calculations are presented to illustrate the physics of the boundary layer viscous scaling in controlling the attenuation rates.…”

An experimental and numerical investigation on wave‐mud interactions

“…Significant attenuation of surface waves has been observed when the surface layer of the seabed is mainly composed of mud, such as off the coasts of Southwestern India [ Mathew et al ., ], Louisiana [ Sheremet and Stone , ; Elgar and Raubenheimer , ; Jaramillo et al ., ], Brazil [ Vinzon et al ., ; Rogers and Holland , ], South Korea [ Wells , ], and Surinam [ Wells and Coleman , ]. In the past few decades, many researchers have examined the physical processes and numerical modeling of wave‐mud interactions, including wave‐induced mud transport [e.g., Vinzon and Mehta , ; Traykovski et al ., , ; Hsu et al ., ; Jaramillo et al ., ; Safak et al ., ] and surface wave attenuation [e.g., Dalrymple and Liu , ; Winterwerp et al ., ; Elgar and Raubenheimer , ; Rogers and Holland , ; Kranenburg et al ., , among many others]. In some of these earlier numerical modeling studies, large wave dissipation was modeled through a two‐layer Newtonian‐type viscous model.…”