Mixing by offshore wind infrastructure: Resolving the density stratified wakes past vertical cylinders

Using structure-resolved direct numerical simulations, this study identifies two distinct wake regimes—weakly stratified and strongly stratified—revealing that deep-water offshore wind sites trigger large-scale internal waves that facilitate far-field energy propagation and explain previously enigmatic field observations.

The Gist

The Big Idea: The "Ocean Blender" Problem

Imagine you are building a massive wind farm in the middle of the ocean. To get the best wind, you have to move further out into deep water. But deep water isn't just a uniform soup; it’s often stratified.

Think of stratified water like a giant, multi-layered cake. The top layer might be warm and light, while the bottom layer is cold and heavy. Because they have different densities, they don't like to mix. They stay separated, like oil and vinegar in a salad dressing.

This "layering" is actually a huge deal for the planet. These layers act like a barrier, controlling how much carbon the ocean absorbs and how nutrients move around to feed sea life.

The question the scientists asked is: When we stick massive steel poles (wind turbine foundations) into this "ocean cake," do they act like a giant spoon that stirs the layers together? And if they do, how much "stirring" are we actually doing?

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The Two "Stirring" Styles

The researchers used supercomputers to simulate water flowing past these poles. They discovered that the ocean doesn't just stir in one way; it switches between two completely different "modes" depending on how strong the layers are.

1. The "Whirlpool" Mode (Weak Stratification)

• The Analogy: Imagine stirring a cup of coffee with a spoon. You create a narrow, energetic little whirlpool right in the middle.
• What happens: If the layers are weak (like a thin layer of cream in coffee), the pole creates a tight, violent wake of turbulence. It’s very energetic, but it stays mostly in a narrow "lane" behind the pole. It mixes the water, but it doesn't "break" the layers very effectively over long distances.

2. The "Wave Machine" Mode (Strong Stratification)

• The Analogy: Imagine a heavy ship moving through a calm, layered lake. Instead of just a little splash, the ship creates massive, rolling waves that travel far away from the boat.
• What happens: If the layers are very strong (like a thick layer of heavy syrup under light water), the pole does something weird. It creates a "recirculation cell"—a little loop of water that sits right on the boundary between the layers. This loop acts like a pump, triggering stationary internal waves.
• The Twist: These waves aren't just moving water; they are moving energy. They carry energy away from the turbine and far into the distance, much further than the actual "messy" turbulence.

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Why Does This Matter? (The "Energy Budget")

The scientists wanted to track the "money" (energy) of the ocean.

1. The Income: The wind and tides push the water, hitting the pole and creating "drag" (energy loss).
2. The Spending: That energy goes into making turbulence (swirls) and waves.
3. The Result: Eventually, that energy is "spent" on mixing—actually blending the warm and cold layers together.

They found that in the "Wave Machine" mode, the ocean is actually quite efficient at this. Even though the "messy" part of the wake might look small, the waves it creates are doing a lot of the heavy lifting in moving energy around.

The Bottom Line

If we want to build massive wind farms without accidentally "over-stirring" the ocean and messing up its delicate biological and chemical balance, we can't just use old, simple models.

We have to realize that deep-water wind farms aren't just obstacles; they are wave-makers. As we move into deeper, more layered waters, we need to account for these "internal waves" that can carry the effects of our turbines much further than we ever expected.

Technical Summary

Technical Summary: Mixing by Offshore Wind Infrastructure

Title: Mixing by offshore wind infrastructure: Resolving the density stratified wakes past vertical cylinders
Authors: Charlie J. Lloyd & Robert M. Dorrell (Loughborough University)
Date: February 12, 2026

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1. Problem Statement

As offshore wind development moves into deeper waters, infrastructure is increasingly situated in seasonally stratified environments. Density stratification acts as a critical barrier to vertical transport, influencing tidal energy dissipation, biological productivity, and the global carbon budget. While it is known that offshore wind structures introduce anthropogenic turbulence that enhances water column mixing, current understanding is limited by two factors:

• Field-scale simulations rely on sweeping assumptions regarding fine-scale stratified turbulence.
• Field observations are sparse, inconsistent, and often struggle to distinguish between structure-induced mixing and natural environmental variability.

There is a critical need for high-fidelity numerical data to bridge the gap between idealized simulations and real-world observations, specifically to improve the parameterization of infrastructure wakes in regional-scale oceanographic models.

2. Methodology

The study employs Direct Numerical Simulations (DNS) and high-resolution Large Eddy Simulations (LES) to provide the first fully structure-resolved analysis of two-layer stratified flow past a vertical cylinder.

• Numerical Framework: The authors use the overlapping Schwarz-Spectral-Element-Method (SSEM) implemented in NEK5000. This allows for high-resolution hexahedral meshes in the cylinder wake while maintaining computational efficiency in the far-field.
• Governing Equations: The Boussinesq momentum and continuity equations are solved alongside a scalar transport equation for temperature.
• Dimensionless Parameters: The dynamics are governed by the cylinder Reynolds number ($Re_d$), the cylinder Richardson number ($Ri_d$, representing stratification strength), and the Prandtl number ($Pr$).
• Simulation Matrix: Six cases were analyzed, varying $Re_d$ (500 and 2000) and $Ri_d$ (0.05, 0.5, and 2.0).
• Energy Budget Analysis: The authors implement a volume-integrated approach to track energy pathways between Mean Kinetic Energy (KE), Mean Potential Energy (PE), Turbulent Kinetic Energy (TKE), and Scaled Buoyancy Variance (SBV).

3. Key Contributions

• Identification of Two Wake Regimes: The paper establishes a mechanistic distinction between "weakly stratified" and "strongly stratified" wakes.
• Discovery of Stationary Internal Waves: The study identifies a novel mechanism where strong vertical motions in the wake generate large-scale stationary internal waves.
• Mechanistic Energy Framework: It provides the first framework connecting water-column mixing to reversible and irreversible energy exchanges across mean, turbulent, and potential energy reservoirs.
• Benchmark Database: The resulting high-fidelity data serves as a critical benchmark for validating low-fidelity (RANS/LES) oceanographic models.

4. Results

A. Wake Regimes

1. Weakly Stratified Regime ($Ri_d \leq 0.5$): Characterized by a narrow, highly energetic wake dominated by horizontal shear. Mixing occurs primarily in the far-wake as turbulent fluctuations gradually become more isotropic, allowing for vertical temperature transport.
2. Strongly Stratified Regime ($Ri_d = 2.0$): Characterized by the emergence of a thermocline-spanning recirculation cell attached to the cylinder. This cell induces strong vertical shearing, which triggers the formation of large-scale stationary internal waves.

B. Energy Dynamics

• Internal Waves: These waves account for up to 10% of the total energy budget and provide a new mechanism for far-field energy propagation.
• Mixing Efficiency ($\Gamma_{tot}$): The total efficiency (the fraction of power lost to drag that results in irreversible mixing) varies from approximately 2% at low $Ri_d$ to 8.5% at high $Ri_d$.
• Turbulence Production: In the strongly stratified regime, turbulence production shifts from being dominated by spanwise shear to being driven by vertical shear ($P_z$) within the thermocline.

C. Drag and Detectability

• Stronger stratification reduces the drag coefficient and its fluctuations due to the suppression of the Karman Vortex (KV) street by the recirculation cell.
• This regime change explains why field observations often fail to detect energetic wakes in highly stratified waters: the energy is redistributed into wide-spread, steady internal waves rather than localized, high-intensity turbulent eddies.

5. Significance

This work has profound implications for the future of offshore renewable energy:

• Model Accuracy: It provides the physical constraints necessary to improve the parameterization of sub-grid-scale infrastructure wakes in regional ocean models.
• Environmental Impact Assessment: By identifying the "strongly stratified" regime, the study warns that future deep-water wind farms may impact the ocean differently than current shallow-water sites, specifically through long-range energy propagation via internal waves.
• Design and Array Planning: Understanding the interaction between stationary waves and the thermocline is vital for predicting wake-wake interactions in large-scale offshore wind arrays.