Measured multiple flow states in turbulent thermal convection with aspect ratio 10

This study experimentally demonstrates that turbulent Rayleigh-Benard convection in a large-aspect-ratio cell exhibits multiple self-organized flow states with varying numbers of stacked rolls, where the initial conditions and Prandtl number significantly influence the flow structure, global momentum transport scaling, and heat transfer efficiency.

The Gist

Imagine a giant, shallow swimming pool where the bottom is heated like a hot tub and the top is cooled like an ice rink. In this pool, the water doesn't just sit still; it churns, swirls, and dances in a chaotic pattern known as turbulent convection.

This paper is like a detective story about what happens when you make that pool very long and very narrow (10 times longer than it is deep). The scientists wanted to see how the water moves in this specific shape and whether the flow is predictable or if it can surprise them.

Here is the story of their discovery, broken down into simple concepts:

1. The "Roller Coaster" of Water

Usually, when you heat water from below, it rises in big, messy blobs. But in this long, narrow pool, the water organizes itself into neat, horizontal rolls, like a row of giant, spinning tires stacked side-by-side.

• The Surprise: The scientists expected the water to always settle into one specific pattern (like always having exactly 6 tires). Instead, they found that the water is indecisive.
• The Metaphor: Imagine you have a set of LEGO bricks. If you build a tower, it usually looks the same every time. But in this experiment, if you build the tower, take it apart, and build it again with the exact same instructions, sometimes you get 4 bricks wide, sometimes 5, and sometimes 6. The water "chooses" a different number of rolls every time, even though the temperature and the pool size are identical. This is called multiple flow states.

2. The "Traffic Jam" vs. The "Freeway"

The scientists noticed something interesting about the "traffic" of the water depending on how thick the fluid was (a property called the Prandtl number).

• Thin Fluid (Low Prandtl): The water moves like a busy highway with cars (rolls) driving side-by-side. The traffic is mostly horizontal.
• Thick Fluid (High Prandtl): When they used a thicker fluid (like a mix of water and glycerol), the "rolls" broke down. The water stopped spinning in big circles and started shooting up and down like fountains or plumes.
• The Analogy: It's the difference between a calm river flowing in lanes (rolls) and a chaotic waterfall where water shoots straight up and down (plumes). This change completely altered how fast the water moved and how much heat it carried.

3. The "Shape Shifter"

The researchers found that the size of these rolls matters a lot for how fast the water moves.

• Big Rolls: When there are fewer, larger rolls, the water moves very fast sideways (horizontally) but slowly up and down.
• Small Rolls: When there are many, smaller rolls, the water moves slower sideways but faster up and down.
• Why? Think of it like a crowded hallway. If the hallway is wide (big roll), people can walk side-by-side quickly, but they don't need to rush up or down stairs. If the hallway is narrow (small roll), people have to squeeze past each other, so they move slower sideways but have to move up and down the stairs more frequently to get through.

4. The "Push" Experiment

To prove that the water's behavior depends on how it starts, the scientists gave the water a little "nudge."

• The Setup: They placed tiny heaters on the side walls to create a specific pattern of heat.
• The Result: By forcing the water into a specific shape (like a double-roll), they could trap it there for hours. Even after they turned off the heaters, the water stayed in that "unnatural" shape for a long time.
• The Lesson: The water has "memory" of how it was started. It's like a ball rolling in a valley. Sometimes the ball settles in the deepest part of the valley (the most common 6-roll state). But if you give it a hard shove, it can roll into a smaller, deeper hole nearby (the 2-roll or 3-roll state) and stay there.

5. Why Does This Matter?

You might ask, "Who cares about water in a long box?"

• Real World: This happens in the oceans, the atmosphere, and even inside planets like Jupiter. These systems are huge and long, just like the scientists' box.
• The Takeaway: If the ocean or atmosphere can switch between different "modes" of flow (like switching from 6 rolls to 4), it changes how much heat is moved around the planet. This could affect weather patterns and climate models.
• The Big Picture: The study shows that nature isn't always predictable. Even with the same rules (temperature, gravity), a system can settle into different, stable patterns. Understanding these "multiple states" helps us predict how heat and energy move in our world.

In summary: The scientists discovered that in long, thin containers, turbulent water is a bit of a chameleon. It can organize itself into different numbers of spinning rolls, and which pattern it picks depends on how thick the water is and how it was started. These different patterns act like different gears in a machine, changing how efficiently heat is transported from the bottom to the top.

Technical Summary

1. Problem Statement

Turbulent Rayleigh–Bénard (RB) convection is a fundamental model for understanding thermally driven turbulence in geophysical and astrophysical systems. While the existence of multiple flow states (multistability) has been well-documented in systems with small aspect ratios ($\Gamma \leq 1$), experimental evidence for such phenomena in large aspect ratio ($\Gamma \gg 1$) systems remains scarce.

• The Gap: Previous numerical simulations suggest that large $\Gamma$ systems can support a wide range of horizontally stacked convection rolls depending on initial conditions. However, experimental observations have been limited, often showing fewer rolls than simulations predict, and lacking systematic evidence of how these multiple states influence global transport properties (heat and momentum).
• Objective: To systematically investigate the existence, stability, and transport characteristics of multiple flow states in a turbulent RB convection cell with a large aspect ratio ($\Gamma = 10$) over a wide range of Rayleigh ($Ra$) and Prandtl ($Pr$) numbers.

2. Methodology

• Experimental Setup:
  • Geometry: A rectangular convection cell with dimensions $L=100$ cm (length), $W=3$ cm (width), and $H=10$ cm (height), yielding $\Gamma = 10$ and a lateral aspect ratio $\Gamma_{lateral} = 0.3$.
  • Fluids: Experiments utilized water, glycerol-water mixtures, and silicone oil to vary the Prandtl number ($Pr$) from 4.3 to 67.3.
  • Parameters: Rayleigh numbers ($Ra$) ranged from $5.4 \times 10^7$ to $7.2 \times 10^9$.
  • Measurement: Planar Particle Image Velocimetry (PIV) was used to measure the velocity field in the central vertical plane. Two cameras were stitched to cover the full length of the cell.
  • Duration: Measurements spanned from 2 hours to over 22 hours to capture spontaneous transitions and stable states.
• Control Perturbations: To test the sensitivity of the flow to initial conditions, the authors employed localized sidewall heating (two electric heaters at mid-height) to impose specific flow structures and observe their evolution.

3. Key Contributions

1. First Systematic Experimental Evidence: Provides the first comprehensive experimental confirmation of multiple coexisting flow states in a large aspect ratio ($\Gamma=10$) turbulent RB system.
2. Flow Control & State Selection: Demonstrates that the final turbulent state is not unique but depends on initial conditions and perturbations, revealing "hidden" stable states (e.g., double and triple roll configurations) that are rarely accessed spontaneously.
3. Scaling Laws & Structural Transition: Identifies a distinct structural transition from a roll-dominated regime to a plume-dominated regime at high $Pr$($Pr=67.3$), marked by a change in global momentum transport scaling.
4. Roll Size vs. Transport: Quantifies the relationship between individual roll size and local Reynolds numbers, showing how mass conservation constraints dictate velocity scaling within rolls.

4. Key Results

A. Existence of Multiple Flow States

• Spontaneous Multistability: Under identical control parameters ($Ra, Pr$), the flow spontaneously organizes into different numbers of horizontally stacked rolls.
  • Most Probable State: A 6-roll structure is the most frequently observed.
  • Observed Range: The number of rolls ($n$) varies between 3 and 7.
  • Stability: These states can persist for hours. Rare spontaneous transitions between states (e.g., 4-roll to 5-roll) were observed.
• Controlled Transitions: By applying localized heating, the researchers forced the system into a 2-roll and a 3-roll state, which were previously unobserved in spontaneous runs. This confirms the existence of multiple potential wells in the flow configuration space.
• Discrepancy with Simulations: The number of rolls observed experimentally (3–7) is significantly lower than predicted by 2D numerical simulations (which suggest $\geq 8$). The authors attribute this to 3D effects (lateral confinement $\Gamma_{lateral}=0.3$) and rigid sidewall boundary conditions, which suppress the formation of smaller rolls compared to periodic boundary conditions.

B. Structural Transition at High Prandtl Number

• Low/Medium $Pr$($4.3 \leq Pr \leq 18.3$): The flow is dominated by large-scale, horizontally stacked convection rolls.
• High $Pr$($Pr = 67.3$): A structural transition occurs. The number of "roll-like" structures increases significantly, but the flow is no longer dominated by coherent rolls. Instead, it transitions to a plume-dominated regime characterized by vertically aligned thermal plumes.
• Scaling Change:
  • For $Pr \leq 18.3$: Global Reynolds number scales as $Re \sim Ra^{0.58} Pr^{-0.97}$.
  • For $Pr = 67.3$: The scaling exponent changes to $Re \sim Ra^{0.72}$, indicating a fundamental shift in the momentum transport mechanism.

C. Roll Size and Local Transport

• Velocity Scaling: Within individual rolls, the horizontal Reynolds number ($Re_{u,roll}$) increases with roll size ($\Gamma_{roll}$), while the vertical Reynolds number ($Re_{w,roll}$) decreases.
• Mass Conservation: The ratio follows $Re_{w,roll}/Re_{u,roll} \sim \Gamma_{roll}^{-0.61}$. This is consistent with mass conservation ($uH \sim wL$), where larger rolls require higher horizontal velocities to maintain volume flux balance.
• Global Transport:
  • Heat Transfer ($Nu$): Increases with the number of rolls. A higher number of rolls creates more vertical channels for heat transport.
  • Momentum Transfer: As the number of rolls increases (and individual roll size decreases), the vertical momentum transport strengthens, while horizontal transport weakens.

5. Significance

• Fundamental Physics: The study confirms that multistability is an intrinsic feature of turbulent thermal convection, even in large-scale, high-Reynolds number systems. It challenges the notion that high turbulence leads to a single unique state.
• Geophysical Relevance: The findings offer insights into natural systems (e.g., ocean currents, atmospheric flows, planetary atmospheres) where large aspect ratios and multiple stable flow configurations are common.
• Transport Efficiency: The research establishes a direct link between flow topology (number of rolls) and global transport efficiency. It suggests that the organization of large-scale structures is a critical factor in determining heat and momentum fluxes, which is vital for modeling climate and industrial heat transfer processes.
• Potential Well Framework: The authors propose a "potential well" interpretation where frequently observed states have wide basins of attraction, while rare states (accessed via strong perturbations) correspond to narrow, deep wells. This framework helps explain the hysteresis and path-dependence observed in turbulent flows.

In conclusion, this paper provides a rigorous experimental foundation for understanding the complexity of large-scale turbulent convection, highlighting the critical roles of initial conditions, boundary constraints, and Prandtl number in determining flow topology and transport efficiency.