[Paper Review] The Force of a Tsunami on a Wave Energy Converter

Laura O'Brien, Paul Christodoulides+3 more|arXiv (Cornell University)|Sep 10, 2012

Earthquake and Tsunami Effects2 references8 citations

TL;DR

This study investigates the hydrodynamic forces exerted by tsunamis on nearshore wave energy converters (WECs) using a linear 3D model based on potential flow theory. It finds that tsunami-induced loads on fixed plates are approximately 100 times smaller than those from typical storm swells, suggesting nearshore WECs can withstand tsunamis under linear assumptions, though nonlinear effects near the shore require further study.

ABSTRACT

With an increasing emphasis on renewable energy resources, wave power technology is fast becoming a realistic solution. However, the recent tsunami in Japan was a harsh reminder of the ferocity of the ocean. It is known that tsunamis are nearly undetectable in the open ocean but as the wave approaches the shore its energy is compressed creating large destructive waves. The question posed here is whether a nearshore wave energy converter (WEC) could withstand the force of an incoming tsunami. The analytical 3D model of Renzi & Dias (2012) developed within the framework of a linear theory and applied to an array of fixed plates is used. The time derivative of the velocity potential allows the hydrodynamic force to be calculated.

Motivation & Objective

• To assess the structural resilience of nearshore wave energy converters (WECs) against tsunami forces.
• To evaluate whether linear hydrodynamic theory is sufficient for predicting tsunami loads on WECs near the shore.
• To compare tsunami-induced loads with those from typical storm swells to assess relative risk.
• To identify the transition point from linear to nonlinear wave behavior near the coast.
• To highlight the need for further research on nonlinear effects, especially wave run-up and multiple wave impacts.

Proposed method

• Adopts a 3D linear potential flow model from Renzi & Dias (2012) to compute hydrodynamic forces on fixed plates.
• Calculates the time derivative of the velocity potential to determine the force via the jump in −ρΦt across the plate.
• Uses Green’s law to model tsunami amplification over a sloping seabed, relating amplitude and depth changes.
• Defines dimensionless parameters (ε, δ, γ, Ursell number) to assess the dominance of linear, nonlinear, and dispersive effects.
• Compares tsunami loading with that of a typical 3 m swell (5 s period) at 10.9 m depth using the same model.
• Performs numerical simulations with the VOLNA solver to examine nonlinear effects of multiple waves on dry-land-exposed plates.

Experimental results

Research questions

• RQ1 What is the magnitude of hydrodynamic force exerted by a tsunami on a fixed plate representing a nearshore WEC?
• RQ2 How does the tsunami load compare quantitatively to the load from a typical storm swell of similar amplitude?
• RQ3 At what depth does nonlinear wave behavior become significant for tsunami waves approaching the shore?
• RQ4 How do multiple tsunami waves, especially following a receding first wave, affect the structural load on a WEC?
• RQ5 Can linear theory adequately predict WEC loading near the shore, or are nonlinear effects critical for safety assessment?

Key findings

• The maximum pressure difference across an 18 m plate due to a tsunami is approximately 3 × 10³ N/m² (0.03 bar), and it is invariant with depth.
• The tsunami-induced load is approximately 100 times smaller than the load from a typical 3 m swell with a 5 s period, which reaches up to 3 × 10⁵ N/m² (3 bar).
• At a depth of 31 m, the Ursell number increases to ~10⁴, indicating that nonlinear effects become significant, marking the transition from linear to nonlinear wave dynamics.
• The force is highest at the center of the plate and zero at the edges, with no variation across depth due to the long wavelength of the tsunami.
• Numerical simulations with VOLNA show that a second wave impacting a WEC left on dry land after the first wave recedes can cause significant shock loading, potentially exceeding initial estimates.
• Resonant conditions between the beach slope and incident wavelength can amplify wave velocities, increasing the risk of structural damage under nonlinear dynamics.