Abstract: Equilibrium beach formulations are useful tools for diagnosing and managing coastal engineering problems, providing solutions for beach erosion problems. Headland Bay Beaches (HBBs) can be used as equilibrium coastal systems for stabilizing coastlines and mitigating erosion problems. These embayed beaches may exist in a state of static or dynamic equilibrium. Throughout the literature, several equations can be found for obtaining the Static Equilibrium Planform (SEP) of Headland Bay Beaches (HBBs) with almost negligible net littoral drift rates. However, the formulations used to define the Dynamic Equilibrium Planform (DEP) of embayed beaches with specific net sediment transport rates are scarce, and based on a limited number of studies. This paper proposes a new derived formula for obtaining the planform shape of HBBs in dynamic equilibrium conditions. The formula represents a general form of the Parabolic Bay Shape Equation (PBSE) with modified coefficients as a function of both the wave obliquity (?) and the net littoral drift rate passing through the bay (Q). The angular difference (?d) between the direction of the mean wave energy flux at the diffraction point of the headland and the beach orientation down-coast is also incorporated in the proposed formula. The model was verified against natural HBBs in dynamic equilibrium with different net littoral drift rates along the Brazilian coast, producing good results.

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