Key Insights
The European wind power industry is experiencing robust growth, driven by the EU's ambitious renewable energy targets and increasing concerns about climate change. A CAGR of 6.11% from 2019 to 2024 suggests a significant expansion, and this momentum is expected to continue through 2033. Key drivers include supportive government policies, falling turbine costs, technological advancements leading to higher efficiency and larger capacity turbines, and the increasing competitiveness of wind energy against fossil fuels. The onshore segment currently dominates, but offshore wind is experiencing rapid expansion fueled by substantial investment and technological breakthroughs enabling deeper water installations. Germany, the UK, France, and other leading European nations are at the forefront of this expansion, each with significant installed capacity and ongoing projects. However, challenges remain, including grid infrastructure limitations, permitting complexities, and public acceptance concerns in certain regions. The competitive landscape is dominated by major players like Siemens Gamesa, Vestas, Orsted, EDF, and GE, with a mix of equipment suppliers and wind farm operators actively shaping the market. The continued growth is contingent upon overcoming regulatory hurdles, securing consistent investment, and addressing community concerns regarding visual impact and potential environmental effects.
The market's segmentation by location (onshore and offshore) highlights distinct growth trajectories. While onshore wind continues to be a significant contributor, offshore wind projects are witnessing accelerated growth due to increasing technological feasibility and government support. Leading companies are investing heavily in research and development to improve turbine technology, reduce costs, and expand operational capacity in deeper waters. This investment is also driving innovation in other supporting industries, such as grid integration solutions. Further analysis suggests that the regional distribution of wind power capacity is uneven, with certain countries benefiting from advantageous geographical conditions and supportive regulatory frameworks. The forecast period, 2025-2033, projects continued expansion, though the exact rate might fluctuate depending on factors such as fluctuating energy prices, changes in government policies, and the pace of technological advancements. The overall outlook for the European wind power industry remains positive, positioning it as a vital component of the continent's energy transition.
Europe Wind Power Industry: A Comprehensive Market Report (2019-2033)
This comprehensive report provides an in-depth analysis of the Europe wind power industry, covering market size, growth drivers, challenges, key players, and future outlook. The study period spans 2019-2033, with 2025 serving as the base and estimated year. The forecast period is 2025-2033, and the historical period is 2019-2024. This report is crucial for industry stakeholders, investors, and anyone seeking to understand the dynamics of this rapidly evolving sector.

Europe Wind Power Industry Market Concentration & Innovation
The European wind power market exhibits a moderately concentrated structure, with a few dominant players and numerous smaller participants. Key players such as Siemens Gamesa Renewable Energy and Vestas Wind Systems AS hold significant market share, driven by their technological advancements, economies of scale, and global reach. The market share of these leading companies, estimated at xx% in 2025, underscores their influence on market pricing and innovation.
Mergers and acquisitions (M&A) play a critical role in shaping the industry landscape. Recent years have witnessed significant M&A activity, with deal values totaling an estimated xx Million in 2024. These transactions often aim to consolidate market positions, acquire technological capabilities, or expand geographical reach. Regulatory frameworks, including EU renewable energy targets and national support schemes, significantly influence market dynamics. Innovation is driven by the continuous pursuit of higher efficiency, lower costs, and improved grid integration, fostering development in areas such as larger turbine sizes, floating offshore wind technology, and smart grid integration. The industry faces competition from other renewable sources, such as solar power, but its advantages in terms of scalability and predictability ensure continued growth. End-user trends show an increasing demand for clean energy, driving the expansion of wind power across diverse sectors, including utilities, corporations, and households.
Europe Wind Power Industry Industry Trends & Insights
The European wind power industry is experiencing robust growth, driven by supportive government policies, declining technology costs, and increasing environmental awareness. The market is estimated to reach xx Million in 2025, growing at a Compound Annual Growth Rate (CAGR) of xx% during the forecast period (2025-2033). This growth is fueled by several factors:
- Increased Renewable Energy Targets: Stringent EU and national targets for renewable energy integration are driving significant investments in wind power capacity expansion.
- Technological Advancements: Continuous innovation in turbine technology, such as larger rotor diameters and improved blade designs, is increasing energy efficiency and reducing the levelized cost of energy (LCOE).
- Falling Costs: Economies of scale and technological advancements have significantly reduced the cost of wind energy, making it increasingly competitive with conventional energy sources.
- Corporate Sustainability Initiatives: Large corporations are increasingly incorporating renewable energy into their operations to meet sustainability goals, further boosting demand.
- Consumer Preferences: Growing public awareness of climate change and support for clean energy are creating a favorable market environment for wind power.
Market penetration of wind power in the European electricity mix is projected to reach xx% by 2033, reflecting the significant contribution of wind energy to the region’s decarbonization efforts. The competitive landscape is marked by intense rivalry amongst leading manufacturers, developers, and operators, further driving innovation and cost reductions.

Dominant Markets & Segments in Europe Wind Power Industry
The European wind power market demonstrates robust growth across both onshore and offshore segments. However, the offshore wind segment is experiencing particularly rapid expansion, driven by its high capacity factor and proximity to large population centers.
Offshore Wind: The leading markets for offshore wind energy are found in the North Sea region, particularly in the UK, Germany, and Denmark.
- Key Drivers:
- Favorable wind resources and grid infrastructure.
- Governmental support schemes and subsidies.
- Technological advancements in floating offshore wind technology, enabling development in deeper waters.
- Large-scale projects attracting significant investments.
Onshore Wind: Onshore wind continues to be a significant contributor to the European renewable energy mix, with several countries demonstrating strong growth. Germany and Spain, for instance, are known for their considerable onshore wind capacity.
- Key Drivers:
- Extensive land availability suitable for wind farm development.
- Mature technology and established supply chains.
- Declining technology costs and increasing competitiveness.
- Regional support schemes and incentives.
While offshore wind is experiencing faster growth currently, onshore wind maintains a larger share of the overall European wind power capacity, showcasing the complementary roles of both segments in meeting the region's energy demands.
Europe Wind Power Industry Product Developments
Recent product innovations have focused on increasing turbine capacity, improving efficiency, and reducing operational costs. Larger turbine sizes, more advanced blade designs, and improved control systems are enhancing energy output and lowering LCOE. The integration of smart grid technologies and digitalization enhances grid stability and enables better management of renewable energy supply. These advancements are driving market competitiveness, enabling wind power to compete effectively with conventional power sources.
Report Scope & Segmentation Analysis
This report segments the European wind power market primarily by location: onshore and offshore.
Onshore Wind: This segment encompasses wind farms located on land. The onshore wind market is characterized by a relatively mature technology, extensive infrastructure, and widespread adoption across various European countries. Growth in this segment is projected to be xx Million by 2033, driven by ongoing policy support, declining technology costs, and increasing demand for renewable energy.
Offshore Wind: This segment includes wind farms located in marine environments. The offshore wind market is experiencing rapid expansion, driven by high wind resources and technological advancements in floating wind technology. The growth of this segment is expected to be xx Million by 2033, fueled by substantial investments and supportive policy frameworks.
Key Drivers of Europe Wind Power Industry Growth
Several key factors are driving the growth of the European wind power industry:
- Stringent Renewable Energy Targets: The EU and individual member states have ambitious renewable energy targets, necessitating significant wind power capacity additions.
- Falling Technology Costs: Continuous technological advancements have dramatically reduced the cost of wind energy, making it increasingly competitive with fossil fuels.
- Supportive Policy Frameworks: Government incentives, subsidies, and feed-in tariffs are encouraging private investment and accelerating wind power development.
- Increasing Environmental Awareness: Growing public concern over climate change and the need for clean energy solutions fuels demand for wind power.
Challenges in the Europe Wind Power Industry Sector
The European wind power industry faces several challenges:
- Grid Integration Challenges: Integrating large amounts of intermittent renewable energy into existing grids requires significant infrastructure upgrades and smart grid technologies.
- Permitting and Regulatory Hurdles: Complex permitting processes and regulatory uncertainties can delay project development and increase costs.
- Supply Chain Constraints: The industry faces potential bottlenecks in the supply of key components, particularly during periods of rapid expansion.
- Competition from other Renewables: Competition from other renewable energy sources, such as solar PV, requires ongoing innovation to maintain competitiveness.
Emerging Opportunities in Europe Wind Power Industry
The European wind power industry presents several emerging opportunities:
- Offshore Wind Expansion: Significant potential exists for further offshore wind development, particularly in deeper waters with floating wind technology.
- Hybrid Projects: Combining wind power with energy storage technologies can enhance grid stability and improve the reliability of renewable energy supply.
- Green Hydrogen Production: Using wind power to produce green hydrogen offers significant opportunities for decarbonizing various sectors.
- Digitalization and Smart Grids: Integrating smart grid technologies and data analytics can optimize grid management and improve the efficiency of wind farms.
Leading Players in the Europe Wind Power Industry Market
- Siemens Gamesa Renewable Energy
- Vestas Wind Systems AS
- Orsted AS
- EDF SA
- General Electric Company
- E.ON SE
- Acciona Energia SA
Key Developments in Europe Wind Power Industry Industry
- November 2021: Google signed a 12-year Corporate Power Purchase Agreement (CPPA) for 50 MW of wind power from Ørsted's offshore wind farm in the German North Sea, underscoring the growing corporate demand for renewable energy.
- August 2022: EDF Renewables and Budimex signed a memorandum of understanding for a 50/50 partnership to develop offshore wind farms in Poland, highlighting the expansion of offshore wind into new markets.
Strategic Outlook for Europe Wind Power Industry Market
The European wind power industry is poised for sustained growth, driven by supportive policies, technological advancements, and increasing environmental awareness. The forecast period will witness significant capacity additions, particularly in the offshore wind segment. The industry's continued innovation, focus on cost reduction, and successful grid integration will be key to unlocking its full potential and contributing significantly to Europe's clean energy transition.
Europe Wind Power Industry Segmentation
-
1. Location
- 1.1. Onshore
- 1.2. Offshore
Europe Wind Power Industry Segmentation By Geography
- 1. Germany
- 2. United Kingdom
- 3. France
- 4. Italy
- 5. Spain
- 6. Rest of Europe

Europe Wind Power Industry REPORT HIGHLIGHTS
Aspects | Details |
---|---|
Study Period | 2019-2033 |
Base Year | 2024 |
Estimated Year | 2025 |
Forecast Period | 2025-2033 |
Historical Period | 2019-2024 |
Growth Rate | CAGR of 6.11% from 2019-2033 |
Segmentation |
|
Table of Contents
- 1. Introduction
- 1.1. Research Scope
- 1.2. Market Segmentation
- 1.3. Research Methodology
- 1.4. Definitions and Assumptions
- 2. Executive Summary
- 2.1. Introduction
- 3. Market Dynamics
- 3.1. Introduction
- 3.2. Market Drivers
- 3.2.1. 4.; Increasing Investments in Offshore Wind Power Projects4.; Supportive Government Policies
- 3.3. Market Restrains
- 3.3.1. 4.; Increasing Adopting of Alternative Clean Energy Sources (Ex
- 3.4. Market Trends
- 3.4.1. Offshore Segment to Witness Significant Growth in the Market
- 4. Market Factor Analysis
- 4.1. Porters Five Forces
- 4.2. Supply/Value Chain
- 4.3. PESTEL analysis
- 4.4. Market Entropy
- 4.5. Patent/Trademark Analysis
- 5. Europe Wind Power Industry Analysis, Insights and Forecast, 2019-2031
- 5.1. Market Analysis, Insights and Forecast - by Location
- 5.1.1. Onshore
- 5.1.2. Offshore
- 5.2. Market Analysis, Insights and Forecast - by Region
- 5.2.1. Germany
- 5.2.2. United Kingdom
- 5.2.3. France
- 5.2.4. Italy
- 5.2.5. Spain
- 5.2.6. Rest of Europe
- 5.1. Market Analysis, Insights and Forecast - by Location
- 6. Germany Europe Wind Power Industry Analysis, Insights and Forecast, 2019-2031
- 6.1. Market Analysis, Insights and Forecast - by Location
- 6.1.1. Onshore
- 6.1.2. Offshore
- 6.1. Market Analysis, Insights and Forecast - by Location
- 7. United Kingdom Europe Wind Power Industry Analysis, Insights and Forecast, 2019-2031
- 7.1. Market Analysis, Insights and Forecast - by Location
- 7.1.1. Onshore
- 7.1.2. Offshore
- 7.1. Market Analysis, Insights and Forecast - by Location
- 8. France Europe Wind Power Industry Analysis, Insights and Forecast, 2019-2031
- 8.1. Market Analysis, Insights and Forecast - by Location
- 8.1.1. Onshore
- 8.1.2. Offshore
- 8.1. Market Analysis, Insights and Forecast - by Location
- 9. Italy Europe Wind Power Industry Analysis, Insights and Forecast, 2019-2031
- 9.1. Market Analysis, Insights and Forecast - by Location
- 9.1.1. Onshore
- 9.1.2. Offshore
- 9.1. Market Analysis, Insights and Forecast - by Location
- 10. Spain Europe Wind Power Industry Analysis, Insights and Forecast, 2019-2031
- 10.1. Market Analysis, Insights and Forecast - by Location
- 10.1.1. Onshore
- 10.1.2. Offshore
- 10.1. Market Analysis, Insights and Forecast - by Location
- 11. Rest of Europe Europe Wind Power Industry Analysis, Insights and Forecast, 2019-2031
- 11.1. Market Analysis, Insights and Forecast - by Location
- 11.1.1. Onshore
- 11.1.2. Offshore
- 11.1. Market Analysis, Insights and Forecast - by Location
- 12. Germany Europe Wind Power Industry Analysis, Insights and Forecast, 2019-2031
- 13. France Europe Wind Power Industry Analysis, Insights and Forecast, 2019-2031
- 14. Italy Europe Wind Power Industry Analysis, Insights and Forecast, 2019-2031
- 15. United Kingdom Europe Wind Power Industry Analysis, Insights and Forecast, 2019-2031
- 16. Netherlands Europe Wind Power Industry Analysis, Insights and Forecast, 2019-2031
- 17. Sweden Europe Wind Power Industry Analysis, Insights and Forecast, 2019-2031
- 18. Rest of Europe Europe Wind Power Industry Analysis, Insights and Forecast, 2019-2031
- 19. Competitive Analysis
- 19.1. Market Share Analysis 2024
- 19.2. Company Profiles
- 19.2.1 2 Siemens Gamesa Renewable Energy
- 19.2.1.1. Overview
- 19.2.1.2. Products
- 19.2.1.3. SWOT Analysis
- 19.2.1.4. Recent Developments
- 19.2.1.5. Financials (Based on Availability)
- 19.2.2 Equipment Suppliers
- 19.2.2.1. Overview
- 19.2.2.2. Products
- 19.2.2.3. SWOT Analysis
- 19.2.2.4. Recent Developments
- 19.2.2.5. Financials (Based on Availability)
- 19.2.3 3 Vestas Wind Systems AS*List Not Exhaustive
- 19.2.3.1. Overview
- 19.2.3.2. Products
- 19.2.3.3. SWOT Analysis
- 19.2.3.4. Recent Developments
- 19.2.3.5. Financials (Based on Availability)
- 19.2.4 2 Orsted AS
- 19.2.4.1. Overview
- 19.2.4.2. Products
- 19.2.4.3. SWOT Analysis
- 19.2.4.4. Recent Developments
- 19.2.4.5. Financials (Based on Availability)
- 19.2.5 Wind Farm Operators
- 19.2.5.1. Overview
- 19.2.5.2. Products
- 19.2.5.3. SWOT Analysis
- 19.2.5.4. Recent Developments
- 19.2.5.5. Financials (Based on Availability)
- 19.2.6 3 EDF SA
- 19.2.6.1. Overview
- 19.2.6.2. Products
- 19.2.6.3. SWOT Analysis
- 19.2.6.4. Recent Developments
- 19.2.6.5. Financials (Based on Availability)
- 19.2.7 1 General Electric Company
- 19.2.7.1. Overview
- 19.2.7.2. Products
- 19.2.7.3. SWOT Analysis
- 19.2.7.4. Recent Developments
- 19.2.7.5. Financials (Based on Availability)
- 19.2.8 4 E ON SE
- 19.2.8.1. Overview
- 19.2.8.2. Products
- 19.2.8.3. SWOT Analysis
- 19.2.8.4. Recent Developments
- 19.2.8.5. Financials (Based on Availability)
- 19.2.9 1 Acciona Energia SA
- 19.2.9.1. Overview
- 19.2.9.2. Products
- 19.2.9.3. SWOT Analysis
- 19.2.9.4. Recent Developments
- 19.2.9.5. Financials (Based on Availability)
- 19.2.1 2 Siemens Gamesa Renewable Energy
List of Figures
- Figure 1: Europe Wind Power Industry Revenue Breakdown (Million, %) by Product 2024 & 2032
- Figure 2: Europe Wind Power Industry Share (%) by Company 2024
List of Tables
- Table 1: Europe Wind Power Industry Revenue Million Forecast, by Region 2019 & 2032
- Table 2: Europe Wind Power Industry Volume Thousand Forecast, by Region 2019 & 2032
- Table 3: Europe Wind Power Industry Revenue Million Forecast, by Location 2019 & 2032
- Table 4: Europe Wind Power Industry Volume Thousand Forecast, by Location 2019 & 2032
- Table 5: Europe Wind Power Industry Revenue Million Forecast, by Region 2019 & 2032
- Table 6: Europe Wind Power Industry Volume Thousand Forecast, by Region 2019 & 2032
- Table 7: Europe Wind Power Industry Revenue Million Forecast, by Country 2019 & 2032
- Table 8: Europe Wind Power Industry Volume Thousand Forecast, by Country 2019 & 2032
- Table 9: Germany Europe Wind Power Industry Revenue (Million) Forecast, by Application 2019 & 2032
- Table 10: Germany Europe Wind Power Industry Volume (Thousand) Forecast, by Application 2019 & 2032
- Table 11: France Europe Wind Power Industry Revenue (Million) Forecast, by Application 2019 & 2032
- Table 12: France Europe Wind Power Industry Volume (Thousand) Forecast, by Application 2019 & 2032
- Table 13: Italy Europe Wind Power Industry Revenue (Million) Forecast, by Application 2019 & 2032
- Table 14: Italy Europe Wind Power Industry Volume (Thousand) Forecast, by Application 2019 & 2032
- Table 15: United Kingdom Europe Wind Power Industry Revenue (Million) Forecast, by Application 2019 & 2032
- Table 16: United Kingdom Europe Wind Power Industry Volume (Thousand) Forecast, by Application 2019 & 2032
- Table 17: Netherlands Europe Wind Power Industry Revenue (Million) Forecast, by Application 2019 & 2032
- Table 18: Netherlands Europe Wind Power Industry Volume (Thousand) Forecast, by Application 2019 & 2032
- Table 19: Sweden Europe Wind Power Industry Revenue (Million) Forecast, by Application 2019 & 2032
- Table 20: Sweden Europe Wind Power Industry Volume (Thousand) Forecast, by Application 2019 & 2032
- Table 21: Rest of Europe Europe Wind Power Industry Revenue (Million) Forecast, by Application 2019 & 2032
- Table 22: Rest of Europe Europe Wind Power Industry Volume (Thousand) Forecast, by Application 2019 & 2032
- Table 23: Europe Wind Power Industry Revenue Million Forecast, by Location 2019 & 2032
- Table 24: Europe Wind Power Industry Volume Thousand Forecast, by Location 2019 & 2032
- Table 25: Europe Wind Power Industry Revenue Million Forecast, by Country 2019 & 2032
- Table 26: Europe Wind Power Industry Volume Thousand Forecast, by Country 2019 & 2032
- Table 27: Europe Wind Power Industry Revenue Million Forecast, by Location 2019 & 2032
- Table 28: Europe Wind Power Industry Volume Thousand Forecast, by Location 2019 & 2032
- Table 29: Europe Wind Power Industry Revenue Million Forecast, by Country 2019 & 2032
- Table 30: Europe Wind Power Industry Volume Thousand Forecast, by Country 2019 & 2032
- Table 31: Europe Wind Power Industry Revenue Million Forecast, by Location 2019 & 2032
- Table 32: Europe Wind Power Industry Volume Thousand Forecast, by Location 2019 & 2032
- Table 33: Europe Wind Power Industry Revenue Million Forecast, by Country 2019 & 2032
- Table 34: Europe Wind Power Industry Volume Thousand Forecast, by Country 2019 & 2032
- Table 35: Europe Wind Power Industry Revenue Million Forecast, by Location 2019 & 2032
- Table 36: Europe Wind Power Industry Volume Thousand Forecast, by Location 2019 & 2032
- Table 37: Europe Wind Power Industry Revenue Million Forecast, by Country 2019 & 2032
- Table 38: Europe Wind Power Industry Volume Thousand Forecast, by Country 2019 & 2032
- Table 39: Europe Wind Power Industry Revenue Million Forecast, by Location 2019 & 2032
- Table 40: Europe Wind Power Industry Volume Thousand Forecast, by Location 2019 & 2032
- Table 41: Europe Wind Power Industry Revenue Million Forecast, by Country 2019 & 2032
- Table 42: Europe Wind Power Industry Volume Thousand Forecast, by Country 2019 & 2032
- Table 43: Europe Wind Power Industry Revenue Million Forecast, by Location 2019 & 2032
- Table 44: Europe Wind Power Industry Volume Thousand Forecast, by Location 2019 & 2032
- Table 45: Europe Wind Power Industry Revenue Million Forecast, by Country 2019 & 2032
- Table 46: Europe Wind Power Industry Volume Thousand Forecast, by Country 2019 & 2032
Frequently Asked Questions
1. What is the projected Compound Annual Growth Rate (CAGR) of the Europe Wind Power Industry?
The projected CAGR is approximately 6.11%.
2. Which companies are prominent players in the Europe Wind Power Industry?
Key companies in the market include 2 Siemens Gamesa Renewable Energy, Equipment Suppliers, 3 Vestas Wind Systems AS*List Not Exhaustive, 2 Orsted AS, Wind Farm Operators, 3 EDF SA, 1 General Electric Company, 4 E ON SE, 1 Acciona Energia SA.
3. What are the main segments of the Europe Wind Power Industry?
The market segments include Location.
4. Can you provide details about the market size?
The market size is estimated to be USD XX Million as of 2022.
5. What are some drivers contributing to market growth?
4.; Increasing Investments in Offshore Wind Power Projects4.; Supportive Government Policies.
6. What are the notable trends driving market growth?
Offshore Segment to Witness Significant Growth in the Market.
7. Are there any restraints impacting market growth?
4.; Increasing Adopting of Alternative Clean Energy Sources (Ex: Solar. Hydro).
8. Can you provide examples of recent developments in the market?
November 2021: Google signed up for 50 MW of wind power to be delivered from an offshore wind farm built by Danish energy giant Ørsted in the German North Sea. The 12-year Corporate Power Purchase Agreement (CPPA) will contribute to Google's commitment to operating all data centers with carbon-free energy by 2030.
9. What pricing options are available for accessing the report?
Pricing options include single-user, multi-user, and enterprise licenses priced at USD 4750, USD 5250, and USD 8750 respectively.
10. Is the market size provided in terms of value or volume?
The market size is provided in terms of value, measured in Million and volume, measured in Thousand.
11. Are there any specific market keywords associated with the report?
Yes, the market keyword associated with the report is "Europe Wind Power Industry," which aids in identifying and referencing the specific market segment covered.
12. How do I determine which pricing option suits my needs best?
The pricing options vary based on user requirements and access needs. Individual users may opt for single-user licenses, while businesses requiring broader access may choose multi-user or enterprise licenses for cost-effective access to the report.
13. Are there any additional resources or data provided in the Europe Wind Power Industry report?
While the report offers comprehensive insights, it's advisable to review the specific contents or supplementary materials provided to ascertain if additional resources or data are available.
14. How can I stay updated on further developments or reports in the Europe Wind Power Industry?
To stay informed about further developments, trends, and reports in the Europe Wind Power Industry, consider subscribing to industry newsletters, following relevant companies and organizations, or regularly checking reputable industry news sources and publications.
Methodology
Step 1 - Identification of Relevant Samples Size from Population Database



Step 2 - Approaches for Defining Global Market Size (Value, Volume* & Price*)

Note*: In applicable scenarios
Step 3 - Data Sources
Primary Research
- Web Analytics
- Survey Reports
- Research Institute
- Latest Research Reports
- Opinion Leaders
Secondary Research
- Annual Reports
- White Paper
- Latest Press Release
- Industry Association
- Paid Database
- Investor Presentations

Step 4 - Data Triangulation
Involves using different sources of information in order to increase the validity of a study
These sources are likely to be stakeholders in a program - participants, other researchers, program staff, other community members, and so on.
Then we put all data in single framework & apply various statistical tools to find out the dynamic on the market.
During the analysis stage, feedback from the stakeholder groups would be compared to determine areas of agreement as well as areas of divergence