Wave Energy Converter (WEC) & Marine Hydrodynamics Lab

Explore first-principles deep-water ocean wave mechanics, capture width ratios (CWR), power take-off (PTO) damping efficiencies, dynamic mooring line tension, and 25-year levelized offshore energy economics (LCOE).

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Archetype Presets:
Wave Power Flux ($J$)
-- kW/m
Deep-water crest density
Annual Generation (AEP)
-- GWh/yr
Net delivered grid power
Capacity Factor
--%
Wave climate distribution
Levelized Cost (LCOE)
$-- /MWh
25-year discounted basis
Project 25-Yr NPV
$--
Discounted net return
Internal Rate of Return
--%
Project equity IRR
Simple Payback
-- yrs
Unlevered CapEx recovery
Avoided CO2
-- t/yr
Grid emissions offset
Engineering & Ocean Parameters
Sea State & Metocean Climate
Conversion Hydrodynamics & Availability
Economics & PPA Tariff
Hydrodynamic & Technical Specs
Hydrodynamic Wave & Mooring Visualizer
Airy Linear Wave Field
5×5 Sea State Sensitivity Matrix (LCOE vs $H_s$ & $T_e$)
25-Year Pro-Forma Cash Flow Statement

First-Principles Wave Mechanics & Marine Energy Engineering

1. Airy Linear Wave Dynamics & Energy Flux

Ocean surface gravity waves convey concentrated kinetic and potential mechanical energy generated by prevailing offshore wind fields over vast ocean expanses (fetch). In deep-water regimes where water depth \(d > \frac{\lambda_0}{2}\), the dispersion relation simplifies to:

\(\lambda_0 = \frac{g T_e^2}{2\pi}, \quad C_0 = \frac{g T_e}{2\pi}\)

The time-averaged wave power flux per unit wavefront crest \(J\) is derived by integrating kinetic and potential energy density multiplied by wave group velocity \(C_g = \frac{1}{2} C_0\):

\(J = \frac{\rho g^2}{64\pi} H_s^2 T_e \approx 0.4904 \cdot H_s^2 T_e \quad \left[\frac{\text{kW}}{\text{m}}\right]\)

At an active North Atlantic deep-water berth (\(H_s = 3.2\text{ m}, T_e = 9.5\text{ s}\)), power density exceeds \(47.6\text{ kW}\) per linear meter of wavefront, representing one of the densest renewable energy reservoirs on Earth.

2. Capture Width Ratio (CWR) & Hydrodynamic Resonance

A wave energy converter absorbs power through radiation damping opposing wave excitation forces. The hydrodynamic capture width ratio expresses extraction efficiency relative to the device's physical frontal breadth \(B\):

\(\text{CWR} = \frac{P_{\text{absorbed}}}{J \cdot B}\)

Under classical Budal and Falnes limits, an unconstrained symmetrical heaving body tuned to natural resonance (\(\omega_0 = \sqrt{\frac{K}{M + A(\omega)}}\)) can achieve an absorption width equal to \(\frac{\lambda_0}{2\pi}\). This phenomenon, known as the antenna effect, enables compact resonant point absorbers to extract substantially more energy than their physical geometric footprint would dictate.

3. Survivability & Catenary Mooring Compliance

Marine survivability dictates that WECs withstand 100-year return extreme waves (\(H_{\text{max}} \approx 1.86 \cdot H_s\)). Mooring systems must resolve two competing requirements: maintaining adequate station-keeping to prevent cable fatigue while remaining sufficiently compliant to avoid catastrophic tension spikes during severe storm swells.

Knowledge Mastery Assessment: Marine Wave Energy Engineering

Frequently Asked Questions

Under Airy linear wave theory for deep water (where water depth exceeds half the wavelength), wave power flux per unit crest width J (kW/m) is governed by J = (rho * g^2 / (64 * pi)) * Hs^2 * Te. Here, rho is seawater density (1,025 kg/m3), g is gravitational acceleration (9.81 m/s2), Hs is significant wave height, and Te is the energy period. Deep-water wave energy flux scales quadratically with wave height and linearly with wave period.

The Capture Width Ratio (CWR) is the non-dimensional metric defining the hydrodynamic extraction efficiency of a wave energy converter. It represents the ratio of mechanical power absorbed by the floating or submerged body to the incident wave power passing through a crest width equal to the physical characteristic width of the device: CWR = P_absorbed / (J * B). Resonance tuning in point absorbers can produce apparent CWRs exceeding 30-40% due to wave diffraction and antenna radiation effects.

An Oscillating Water Column (OWC) utilizes a hollow chamber open to the ocean below the waterline and vented to the atmosphere through an air turbine. As incoming ocean waves rise and fall within the chamber, they compress and decompress the trapped air volume. Symmetrical airfoil Wells turbines rotate unidirectionally regardless of whether airflow is exhausting or inhaling, isolating mechanical bearings and electrical generators in dry air above the aggressive marine splash zone.

Marine wave energy arrays encounter substantial OPEX driven by dynamic positioning (DP) vessel charter day rates, tight weather operating windows (often limited to calm summer seas where Hs is under 1.5-2.0 meters), underwater subsea umbilical dynamic fatigue, biofouling, and catenary mooring tension cycles. Commercial utility-scale wave energy farms target levelized costs of $100-$150/MWh as array scaling, automated quick-release mooring, and serial component manufacturing mature.

Extreme storm sea states (where 100-year Hs can reach 1.8 to 2.2 times normal operating conditions) induce massive second-order wave drift forces and snap loads on mooring bridles. WEC mooring lines incorporate synthetic elastomeric tethers, catenary chain dampers, or submergence release mechanisms that allow devices to submerge into calmer sub-surface water during severe squalls, capping maximum peak mooring tension within safety margins.
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