IX. Hydrodynamic Loads and Motion

At last, we have reached the critical topic of fluid-structure interaction, which enables us to assess how water impacts and applies forces to objects at or beneath the ocean surface. What forces act on boat hulls as they navigate stormy waters? How do dock pilings withstand years of relentless wave impact? How can we ensure a wind turbine’s structural integrity over decades of operation? This chapter equips us with the foundational tools to answer these questions, focusing on the various forces the ocean exerts on structures in marine environments.

We start by refreshing and building upon key dimensionless numbers crucial for categorizing fluid-body interactions in the ocean environment: Reynolds (Re), Froude (Fr), and Keulegan-Carpenter (KC) numbers. These numbers allow us to identify different flow regimes and help predict the types of forces that will be dominant in various conditions. With this background, we can effectively categorize the loads exerted on structures, distinguishing between static loads, such as gravity and steady currents, and dynamic loads from waves and other time-varying factors.

From here, we introduce Morison’s equation, a widely used formulation in ocean engineering for calculating the forces on submerged or partially submerged bodies. We expand upon Morison’s equation by introducing the Froude-Krylov force for modeling pressure forces on bodies due to incoming waves. We also delve into the concept of added mass, which represents the inertia of the fluid displaced by a moving structure, affecting the overall force response.

With Morison’s equation as a foundation, we discuss methods for selecting values for the drag coefficient CdC_dCd​ and inertia coefficient CmC_mCm​, examining the various factors that can influence these coefficients. This leads into a broader discussion on how to approach hydrodynamic load modeling in a linearized framework, covering the forces associated with static loads, wave radiation, and diffraction effects. We also revisit breaking waves, investigating the unique challenges involved in modeling the complex loads they impose and visualizing the impact of these forces graphically.

Finally, we introduce slamming coefficients to quantify the intense, short-duration loads that occur during wave impacts, providing several formulations for applying these coefficients in practical scenarios. This chapter concludes with an exploration of vortex-induced vibrations (VIV), which arise from periodic vortex shedding in fluid flow, leading to oscillatory loads and motions.

By the end of this chapter, you will have a comprehensive understanding of the forces acting on marine structures and the mathematical tools and frameworks used to predict these loads, equipping you to tackle real-world challenges in ocean engineering.

This chapter is a distillation of more detailed texts about water wave theory, the marine environment, and hydrodynamics, from the following:

• Apel, J.R. Principles of Ocean Physics. Academic Press, New York, 1987.
• Crapper, G.D. Introduction to Water Waves. Ellis Horwood Limited, New York, 1984.
• Lamb, H. Hydrodynamics. CJ Clay and Sons, Cambridge, 1895.
• Mei, C. The Applied Dynamics of Ocean Surface Waves. John Wiley and Sons, New York, 1982.
• Phillips, O.M. The Dynamics of the Upper Ocean. Cambridge University Press, Cambridge, 1977.
• Sarpkaya, T. Wave Forces on Offshore Structures. Cambridge University Press, Cambridge, 2010.
• Stoker, J.J. Water Waves: The Mathematical Theory with Applications. Interscience Publishers, Inc, New York, 1957.
• Whitham, G.B. Linear and Nonlinear Waves. John Wiley and Sons, New York, 1974.