Fluid$-$Structure Interaction in Hydraulic Engineering: Discuss the theoretical aspects of fluid$-$structure interaction $($FSI$)$ in hydraulic engineering applications. Explain how FSI phenomena occur when fluid flow interacts with solid structures, leading to dynamic forces and deformation. Explore mathematical formulations, such as Navier$-$Stokes equations and structural equations of motion, used to model FSI problems numerically. Analyze the challenges associated with FSI analysis, including mesh coupling, time integration, and convergence issues, and discuss strategies to mitigate these challenges. Evaluate the significance of FSI theory in designing hydraulic structures, such as dams, spillways, and offshore platforms, to ensure their stability and performance under varying flow conditions.