3.2.1 Static equilibrium
The first set of models contained in IH-SET are those that reproduce the static equilibrium position of a beach. A beach reaches its static equilibrium at its limit of erosion or greatest indentation (Hsu and Evans, 1989). To reach this state, no further littoral drifts are present and the net sediment transport rate decreases, eventually ceasing altogether (González and Medina, 2001). Static equilibrium models are categorized by the plane on which the beach position is mapped, as beach profile models map the beach slope as viewed from the side, while beach planform models map the beach’s shoreline as viewed from above. Both types of models can be incredibly useful in coastal engineering applications, especially as static equilibrium positions are modified by natural and anthropological changes over time causing erosion.
3.2.1.1. Beach Profile
Several researchers have proposed empirical formulations to replicate static equilibrium conditions for the beach profile. These proposals vary in complexity; some focus on a single-section profile (e.g., Dean 1991), while others introduce two-section models (e.g., Bernabeu, 1999), and even three-section models (e.g., Requejo et al., 2008). These formulations are designed to better capture variations in natural beach profile morphology.
The following are the beach profile models included in IH-SET, each developed to represent static equilibrium conditions for the beach profile.
3.2.1.2. Beach Planform
In terms of beach planform, various empirical formulations have been proposed to capture static equilibrium shapes. These include the logarithmic spiral (e.g., Silvester, 1960), parabolic (e.g., Hsu and Evans, 1989; González and Medina, 2001; Elshinnawy et al., 2022), and hyperbolic tangent models (e.g., Moreno and Kraus, 1999). While these analytical approaches are advantageous due to their simplicity and general applicability, they may not accurately represent sites with bathymetric irregularities or obstacles, such as reefs or rocky slabs. In such cases, the model proposed by Gainza et al. (2018) provides a more suitable approach.
The following are the beach planform models included in IH-SET, each developed to represent static equilibrium conditions for the beach planform.
