Clean Energy from First Principles

Wave Energy

Extracts kinetic and potential energy from ocean surface waves created by wind (itself driven by solar heating) using various converter technologies.

Fundamental Principle

Natural Asymmetry Exploited

Ocean waves represent a tertiary form of solar energy: the Sun heats Earth's surface unevenly, creating atmospheric pressure gradients that drive winds, which in turn transfer energy to the ocean surface through friction and pressure differentials. This energy accumulates in waves as they travel across vast ocean fetches, concentrating diffuse wind energy into a denser, more persistent form.

The key insight is energy density amplification: while solar radiation delivers ~100-200 W/m² on average and wind power density is typically 300-500 W/m² at good sites, wave power can reach 30-70 kW per metre of wave crest in energetic locations. This 5-30× concentration occurs because water is ~800× denser than air, and because wave energy accumulates over hundreds or thousands of kilometres of fetch.

Ultimate Source

Solar radiation drives atmospheric circulation, which drives wind, which drives waves. The global theoretical wave energy resource is estimated at 2-3 TW, with a technical potential of approximately 500 GW assuming 40% conversion efficiency along 2% of the world's coastlines exceeding 30 kW/m wave power density. This represents roughly 32,000 TWh/year of potential electricity generation.

Key Physics

Wave energy density:

E=116ρgH2E = \frac{1}{16} \rho g H^2

where ρ is water density (~1025 kg/m³ for seawater), g is gravitational acceleration (9.81 m/s²), and H is the significant wave height. The energy is equally partitioned between kinetic energy (water particle motion) and potential energy (surface displacement), as expected from the equipartition theorem.

Wave power (energy flux):

P=ρg264πHm02Te≈0.5⋅H2⋅T [kW/m]P = \frac{\rho g^2}{64\pi} H_{m0}^2 T_e \approx 0.5 \cdot H^2 \cdot T \text{ [kW/m]}

where H_{m0} is the significant wave height (metres), T_e is the energy period (seconds), and the simplified approximation gives power in kW per metre of wave front.

Critical relationships:

Wave formation physics:

Waves grow when wind speed exceeds wave phase velocity. Energy transfer occurs through:

  1. Pressure differentials between windward and leeward faces of wave crests
  2. Surface friction (shear stress) between moving air and water
  3. Resonant feedback as waves steepen

Wave height depends on:

Fully developed seas (maximum wave height for given wind speed) require fetch of hundreds of kilometres and duration of many hours to days.

Conversion Mechanism

Energy Capture

Wave energy converters (WECs) extract energy from one or more of the six degrees of freedom of wave-induced motion:

- **Heave**: Vertical up-down motion - **Surge**: Horizontal motion in wave direction - **Sway**: Horizontal motion perpendicular to wave direction - **Pitch**: Rotation about horizontal axis perpendicular to wave direction - **Roll**: Rotation about horizontal axis parallel to wave direction - **Yaw**: Rotation about vertical axis

Unlike wind turbines, which have converged on a dominant design (three-bladed horizontal axis), wave energy converters exhibit remarkable diversity. No single architecture has emerged as clearly superior, reflecting the complexity of the wave energy conversion problem.

Principal WEC Archetypes

1. Point Absorbers

Small floating or submerged bodies that absorb energy from waves in all directions. Their characteristic dimension is much smaller than the wavelength.

Operating principle: The buoy heaves (and possibly surges/pitches) in response to passing waves. Relative motion between the buoy and a reference (seabed, submerged plate, or internal mass) drives a power take-off system.

Examples: CorPower Ocean C4, Ocean Power Technologies PowerBuoy, Seabased

Characteristics:

2. Attenuators

Long, multi-segment floating structures oriented parallel to wave direction. Energy is extracted from the flexing motion between segments.

Operating principle: As waves pass along the device length, different segments rise and fall at different times, creating relative angular motion at hinged joints. Hydraulic rams at joints pump fluid through motors to generate electricity.

Examples: Pelamis (discontinued), DEXA

Characteristics:

3. Terminators

Devices oriented perpendicular to wave direction, presenting a barrier to incoming waves.

Operating principle: Intercepts wave front directly. Can use oscillating flaps, water columns, or overtopping mechanisms.

Examples: Oyster (oscillating wave surge converter), WaveRoller

Characteristics:

4. Oscillating Water Columns (OWC)

Partially submerged structures with an air chamber above a water column open to the sea below.

Operating principle: Wave action causes the internal water surface to oscillate, alternately compressing and expanding trapped air. This bidirectional airflow drives a self-rectifying air turbine (typically Wells turbine or impulse turbine).

Examples: Mutriku Wave Power Plant (Spain), Islay LIMPET (Scotland, decommissioned), OE Buoy

Characteristics:

5. Overtopping Devices

Structures that capture water from wave crests in an elevated reservoir, then release it through low-head hydro turbines.

Operating principle: Waves run up a ramp and overtop into a reservoir above mean sea level. The potential energy of elevated water drives turbines as it drains back to sea.

Examples: Wave Dragon

Characteristics:

6. Oscillating Wave Surge Converters (OWSC)

Bottom-hinged flaps that oscillate back and forth with the horizontal surge motion of waves in nearshore waters.

Operating principle: In shallow water, wave particle motion becomes predominantly horizontal (surge-dominant). A hinged flap captures this motion, driving hydraulic power take-off.

Examples: Oyster (Aquamarine Power, discontinued), WaveRoller (AW-Energy)

Characteristics:

Power Take-Off Systems

The power take-off (PTO) converts mechanical wave-induced motion to electricity:

Theoretical Limits

No Simple Betz-Equivalent Limit

Unlike wind turbines (Betz limit: 59.3%) or solar cells (Shockley-Queisser: 33%), wave energy has no single, simple theoretical efficiency limit. The physics is more complex because:

  1. Wave energy exists in multiple degrees of freedom simultaneously
  2. Devices can theoretically capture energy from a wave front wider than themselves
  3. Optimal control is non-causal (depends on future wave motion)
  4. Real seas are polychromatic (multiple frequencies) and multidirectional

Capture Width and Capture Width Ratio

The key performance metric is capture width (CW): the width of wave front from which the device extracts all energy, expressed in metres. The capture width ratio (CWR) normalizes this by device characteristic dimension:

$$CWR = \frac{\text{Absorbed power}}{\text{Wave power per metre} \times \text{Device width}}$$

Theoretical maximum capture widths for idealised point absorbers in regular waves:

For a 10-second wave (λ ≈ 156m), a heaving point absorber could theoretically capture energy from a 25m wide wave front, regardless of the device's actual size. This means CWR can exceed 100% for small devices.

Practical Efficiency Limits

Real-world constraints dramatically reduce achievable performance:

Hydrodynamic efficiency (wave to mechanical): 20-80% depending on device type and sea state

Power take-off efficiency: 70-90% for well-designed systems

Overall wave-to-wire efficiency: Typically 10-35%

Capture width ratio in real seas: 5-30% annual average (much lower than monochromatic theoretical limits)

Bandwidth Problem

A fundamental challenge is that WECs are resonant devices, most efficient at one frequency, while real seas contain a spectrum of frequencies. Strategies to broaden bandwidth include:

Optimal control requires prediction of future wave elevation, which is only partially achievable.

Practical Limitations

The Survivability-Efficiency Paradox

Wave energy devices must survive 100-year storms while extracting energy from average conditions. Storm waves can be 10-20× larger than typical waves, meaning forces scale 100-400× higher. This creates a fundamental tension:

The marine environment is extraordinarily harsh: saltwater corrosion, biofouling, fatigue from millions of load cycles, impacts from debris, and difficulty of access for maintenance.

Resource Variability

Spatial distribution:

Wave power varies enormously by location:

- Exceptional: 60-100 kW/m (Southern Ocean, exposed Atlantic coasts) - Good: 30-60 kW/m (Northwest Europe, Pacific coasts, southern Australia) - Moderate: 15-30 kW/m (Mediterranean, US East Coast) - Poor: <15 kW/m (Enclosed seas, equatorial regions)

The highest resources are at latitudes 40-60° where persistent westerly winds create long-fetch waves. However, these locations often have the harshest conditions.

Temporal variation:

  • Seasonal: Winter waves typically 2-3× summer waves in temperate regions
  • Synoptic (weather systems): Multi-day variations of factor 5-10×
  • Wave-by-wave: Factor 2-3× variation even in steady seas

Capacity factors for wave energy are typically 25-35%, comparable to wind but with different temporal patterns. Wave energy is more predictable than wind 24-48 hours ahead (waves integrate wind over time and space).

Installation and Maintenance

Marine operations are expensive and weather-dependent:

Mooring systems must withstand extreme loads while allowing device motion:

Technology Immaturity

Wave energy technology is far less mature than wind:

Many promising concepts have failed during sea trials (Pelamis, Oyster, Ocean Power Technologies' utility-scale projects). The "valley of death" between prototype and commercial deployment has claimed numerous companies.

Environmental Considerations

Potential impacts (generally considered manageable but requiring further study):

Environmental monitoring requirements add to project costs and timelines.

Scaling Characteristics

Device Scaling

Different WEC types scale differently:

Point absorbers: Limited scalability. Theoretical capture width is independent of device size for a given wavelength, so making devices larger does not proportionally increase power capture. Most point absorbers remain sub-MW scale (typical: 50-500 kW).

Attenuators: Scalable. Capture width increases with device length. MW-scale possible with devices >100m long.

Terminators: Scalable. Capture width increases with device width. MW-scale requires wide structures (>100m).

OWCs: Scalable. Larger chambers capture more energy. Fixed OWCs can be integrated into breakwaters at significant scale.

Array Effects

Wave farms (multiple devices) experience interactions:

Array gains (power per device in array vs. isolated device) can be >1.0 with careful design, but most real arrays show modest losses.

Power Density

Wave farms have low power density relative to offshore wind:

This reflects the distributed nature of wave energy and required spacing for survivability and moorings.

Current Status

Technology Readiness Level

Technology TRL Status
Oscillating water column (fixed) 7-8 Operational demonstration plants
Point absorbers 5-7 Multiple sea trials, pre-commercial
Oscillating wave surge converters 6-7 Full-scale prototypes tested
Attenuators 5-6 Concepts demonstrated, limited recent activity
Overtopping devices 5-6 Full-scale tested, not commercialized

Wave energy is 15-20 years behind offshore wind in development. Most devices remain at prototype or demonstration stage.

Global Deployment (2024)

Total ocean energy capacity: ~513 MW globally, but almost entirely tidal range:

Wave energy specifically: ~2-3 MW total installed globally

Notable wave energy installations:

2024 new deployments: ~1.6 MW across ocean energy (mostly tidal stream)

Pipeline: 165 MW of publicly funded ocean energy projects planned for deployment in Europe over next 5 years (majority is tidal stream; wave energy pipeline ~13 MW)

Costs

Current LCOE: $0.30-1.00/kWh or higher for prototype/demonstration projects

Cost breakdown challenges:

Cost reduction pathway:

For comparison:

Revenue support:

Leading Developers

Wave energy:

Test facilities:

Research Frontiers

Advanced control:

Novel concepts:

Materials and survivability:

System integration:

Market Outlook

Wave energy remains a long-term prospect rather than near-term commercial reality. Key milestones needed:

  1. Multi-MW arrays operating reliably for 3-5+ years
  2. LCOE demonstrated below $150/MWh
  3. Private investment without grant dependency
  4. Supply chain development
  5. Regulatory and permitting clarity

Industry projections:

The European pipeline of 165 MW over five years represents a critical test of commercialization potential. Success would catalyze broader deployment; further failures could set the industry back another decade.

Wave energy's ultimate role may be as a complement to wind and solar rather than a major contributor in its own right, valuable for: