Effects of mean flow skew on turbulent shear layers. Part II. Experimental investigation

This experimental study demonstrates that while mean-flow skew significantly reduces the magnitude of mean and turbulent quantities in planar mixing layers by up to 40%, it exerts only a secondary influence on their fundamental dynamics, preserving key characteristics such as similarity scaling and Townsend's structure parameter.

The Gist

Imagine two rivers flowing side-by-side. In a standard, "planar" scenario, they flow parallel to each other, but one moves much faster than the other. Where they meet, the friction between the fast water and the slow water creates a chaotic, swirling zone called a mixing layer. This is like the white foam you see where a fast-moving stream hits a slow-moving pool. Scientists have studied this flat, parallel interaction for decades because it's the simplest way to understand how fluids mix and how turbulence (chaos) grows.

However, in the real world, things are rarely perfectly flat. Rivers might bend, airplane wings might twist, or air might flow over a curved surface. In these cases, the two streams don't just move at different speeds; they also flow at different angles. This creates a "skewed" mixing layer, where the two streams are trying to merge while also sliding past each other sideways.

This paper is an experimental investigation into exactly what happens when you force these two streams to meet at an angle.

The Experiment: Building a "Twisted" River

The researchers built a wind tunnel to create this scenario.

• The Setup: They used a flat board (a splitter plate) to separate a fast stream of air from a slow stream.
• The Twist: To make the streams meet at an angle, they installed a row of small, curved fins (called "turning vanes") right at the edge of the board where the two streams meet.
• The Action: These vanes acted like a gentle hand, pushing the fast air one way and the slow air the other way, forcing them to collide at a 20-degree angle relative to each other.

They then used sensitive probes (like tiny, high-speed anemometers) to measure the wind speed and turbulence as the air flowed downstream, comparing this "twisted" flow to a standard, flat flow where the vanes were straight.

What They Found: The "Twist" Changes the Numbers, Not the Rules

The researchers discovered that while the "twist" changed the specific numbers, it didn't break the fundamental laws of how the mixing layer behaves.

1. The "Slowing Down" Effect
When the streams were twisted, everything got a bit weaker. The average speed of the wind, the intensity of the turbulence, and the forces pushing the air around were all lower than in the flat case.

• Analogy: Imagine two people running side-by-side. If they are running in a straight line, they generate a lot of wind. If they suddenly try to run in a zig-zag pattern while staying close, they have to spend energy turning, so they end up moving slightly slower and generating less wind overall. The skewed mixing layer was about 40% "weaker" in terms of raw energy and speed compared to the flat one.

2. The Shape Stays the Same
Despite being weaker, the shape of the flow didn't change.

• The Growth: The mixing layer still grew wider at a steady, predictable rate as it moved downstream, just like the flat version.
• The Profile: If you took a snapshot of the wind speed across the layer, it still looked like a smooth "S" curve (mathematically, an error function).
• The Chaos: The turbulence still looked like a bell curve (Gaussian), meaning the chaotic swirls were distributed in the same familiar pattern.

3. The "Efficiency" Surprise
This is the most interesting finding. In other types of twisted flows (like air flowing over a twisted airplane wing), twisting the flow usually makes it much less efficient at moving momentum around. It's like a car engine that sputters and loses power when you turn the steering wheel hard.

• The Result: However, in this mixing layer, the "efficiency" of the turbulence remained unchanged. Even though the flow was twisted, the turbulence was just as good at mixing the air and moving energy as it was in the flat case.
• Analogy: Imagine a group of dancers. If they are dancing in a straight line, they move efficiently. If you tell them to dance in a circle (skew), usually they get clumsy and lose energy. But in this specific experiment, the dancers (the air molecules) adapted perfectly; they changed their formation to the circle but kept their dance moves just as efficient as before.

Why This Matters

Before this study, scientists knew that twisting a flow could change things, but they didn't have a clean, controlled way to study it. Previous experiments were messy, often relying on complex setups that made it hard to tell if the results were due to the twist or just the weirdness of the machine.

This paper provides a clean, reliable "recipe" for creating these twisted flows in a wind tunnel. It proves that while twisting the flow changes the quantity of energy (making it weaker), it doesn't change the quality of the physics (the fundamental way the turbulence organizes itself).

In short: The paper shows that you can twist a turbulent mixing layer, and it will get a bit "tired" (slower and less energetic), but it will still dance to the same tune. The fundamental rules of how these fluids mix remain robust, even when the geometry gets complicated.

Technical Summary

Problem Statement
Planar turbulent mixing layers, formed by two parallel streams of differing velocities, are well-understood canonical flows. However, many practical shear flows—such as those in geophysical contexts, delta wings, and propulsion systems—are inherently three-dimensional (3D), where the mean velocity vectors of adjoining streams differ in both magnitude and orientation. While the effects of mean-flow skew on wall-bounded turbulent boundary layers (TBLs) are documented (notably a reduction in the efficiency of turbulent momentum transport), the structure and dynamics of skewed free-shear mixing layers remain comparatively unexplored. Existing experimental literature on skewed mixing layers is scarce and often inconsistent, partly due to the difficulty of generating controlled 3D flow configurations that isolate intrinsic mean-flow effects from facility-dependent influences. Furthermore, previous numerical studies often rely on idealized initial conditions that may conflate the effects of imposed skew with those of prescribed perturbations.

Methodology
The authors developed and validated a controlled experimental methodology to generate and characterize skewed turbulent mixing layers within the Warhaft Wind and Turbulence Tunnel (WWTT) at Cornell University.

• Flow Generation: Two parallel turbulent streams with different mean velocities ($U_H = 10.5$ m/s and $U_L = 4$ m/s, ratio $r=0.38$) were generated using a passive square-mesh grid partially covered with a wire cloth. A splitter plate separated the streams.
• Imposing Skew: To introduce mean-flow three-dimensionality, turning vanes with a NACA 0012 profile were mounted on both sides of the splitter plate near its trailing edge. By setting the vanes to $\pm 10^\circ$, an effective relative skew angle of $20^\circ$ was imposed between the streams.
• Measurement: The downstream evolution of the flow was investigated using cross-wire (X-wire) thermal anemometry. Measurements were taken in the $xy$-plane at 15 downstream locations ($0.02 \le x/h \le 6$) and in the $xz$-plane at selected locations.
• Data Analysis: The study focused on an "intermediate field" region ($0.5 \le x/h \lesssim 2$) where the influence of the splitter-plate wake and side-wall confinement was minimized, yet the imposed mean-flow skew remained dynamically significant. Statistical convergence was rigorously verified using bootstrap resampling and ensemble consistency checks.
• Companion LES: The experimental results were compared with a companion Large Eddy Simulation (LES) study conducted at the University of Maryland, which used an idealized temporally evolving framework to provide consistency checks on robust flow features.

Key Contributions and Results
The study systematically quantifies how mean-flow skew modifies turbulent mixing layer dynamics, revealing both quantitative deviations and qualitative invariances:

1. Mean Flow Characteristics:

   • The skewed mixing layer exhibits systematic reductions in mean streamwise velocity and velocity gradients compared to the planar case, with deviations reaching approximately 40% in the near field.
   • Despite these reductions, the mean velocity profiles collapse under similarity scaling (error-function form) for both configurations.
   • The mixing-layer thickness (vorticity and momentum thickness) retains approximately linear downstream growth. However, the velocity thickness ($\delta_U$) in the skewed case grows more slowly than in the planar case.
   • The imposed skew generates a persistent mean spanwise velocity and introduces streamwise-oriented mean vorticity, distinct from the spanwise vorticity dominant in planar layers.

2. Turbulent Statistics:

   • Reynolds Stresses: The skewed configuration shows systematic reductions in primary Reynolds shear stress ($u'v'$) and normal stresses ($u'^2, v'^2, w'^2$) relative to the planar case, with reductions up to 65% for shear stress and ~30% for normal stresses.
   • Secondary Shear Stress: Unlike the planar case where secondary shear stress ($u'w'$) decays downstream, the skewed case exhibits a monotonic downstream increase in the ratio of secondary to primary shear stress. This is attributed to the persistent streamwise mean vorticity generated by the imposed directional shear.
   • Turbulent Kinetic Energy (TKE): The peak TKE in the skewed layer is consistently lower (by ~20%) than in the planar layer.
   • Self-Preservation: The flow does not reach a fully self-preserving turbulent state within the measured region ($x/h < 2$); turbulence statistics continue to evolve downstream, consistent with the extended transient regime required for mixing layers.

3. Townsend's Structure Parameter ($a_1$):

   • A critical finding is that Townsend's structure parameter ($a_1$), which quantifies the efficiency of turbulent momentum transport relative to TKE, remains approximately invariant between the planar and skewed configurations ($a_1 \approx 0.10\text{--}0.11$).
   • This contrasts sharply with 3D turbulent boundary layers, where comparable mean-flow skewing reduces $a_1$ by approximately 30%.

Significance and Claims
The paper claims to establish a controlled experimental framework and an empirical benchmark for future investigations of three-dimensional free-shear turbulence. The primary conclusion is that while mean-flow skew modifies turbulent mixing layers quantitatively (reducing mean and turbulent magnitudes and altering secondary stress evolution), it exerts only a secondary influence on their underlying dynamics. The fundamental characteristics—such as the self-similar mean velocity profile, linear thickness growth, Gaussian Reynolds stress profiles, and the efficiency of momentum transport ($a_1$)—remain largely unchanged.

The authors explicitly state that the study does not claim to have resolved the physical origin of the quantitative differences (whether due to reduced mean shear or the spanwise velocity component itself) and notes that the flow remains in a transient regime. The work is presented as a foundational step to isolate intrinsic 3D effects, providing a reliable dataset for validating future theoretical and numerical models of non-planar free-shear turbulence.