Determination Of Drag And Inertia Coefficients By An Analytical Model
Authors: MARLIER GARANC , BOUCHETTE FREDERIC , MEULE SAMUEL , CERTAIN RAPHAEL , JOUVENEL JEAN-YVES 
Published: May 2024

Hard structures like dykes or groins have been recognized for their negative environmental impact and limited durability in the face of climate change (Sutton-Grier et al., 2015). The concept of Shore Soft Engineering (SSE) has allowed ecological considerations to be embedded in the design of coastal protection (Hartig et al., 2011). Among emerging defense structures, nature-based solutions are built with natural materials and rely on physical properties and mechanisms observed in nature. They aim to protect, manage and restore ecosystems while providing some benefit to the human-being and biodiversity (Cohen-Shacham et al., 2016); they offer an interesting alternative to hard structures. However, implementing these solutions in urbanized coastal areas where ecosystems are vulnerable can be challenging. Another alternative approach is using biomimetic solutions, which can provide the functions of natural systems like seagrass, dunes, or coral through robust human-made constructions. Natural habitats exist in a variety of more or less complex forms, ranging from rigid (mangroves, coral) to flexible (seagrass) (Mullarney and Henderson, 2018); and they drive changes in the current profile, in wave dissipation or in sediment motion. Understanding how to mimic these systems, in particular their internal geometry and hydrodynamic effects, is challenging. This complexity makes the development of biomimetic solutions difficult (Perricone et al., 2023). In this context, this study strictly focuses on wave dissipation by flexible systems.
Wave dissipation by natural habitats has been extensively studied through laboratory experiments (Houser et al., 2015) and in-situ measurements (Bradley and Houser, 2009). The pioneer analytical model (Dalrymple et al., 1984) depicted aquatic vegetation as rigid cylinders; however, the rigidity assumption fails to capture the inherent flexibility of plants. Alternative strategies emerged to account for this flexibility, such as using an empirical drag coefficient (Mendez and Losada, 2004) or introducing an effective length, representing the length that a rigid cylinder would have to dissipate the same wave height as flexible cylinders (Luhar and Nepf, 2016). However, to define this effective length or an empirical drag coefficient, it is necessary to carry out in-situ measurements. Numerous analytical models based on force balance (Luhar and Nepf, 2016; Leclercq and de Langre, 2018) have been developed to represent the movement of flexible vegetation like seagrass. These models depict the flexible vegetation as a series of segmented rigid stems attached to each other and subjected to oscillating flows. Some models attempt to link stem motion with wave dissipation to integrate this coupling into numerical models (Yin et al., 2022). However, these models still require unknown quantities such as drag and inertial coefficients. The present study aims to develop an analytical model for determining drag and inertial coefficients based solely on the geometry, the structure flexibility and wave forcing. At last, the method could help better represent the dissipation into numerical simulations without the need for prior parametrization.