Direct Lagrangian tracking simulation of droplet growth in vertically-developing turbulent cloud

This study introduces a new vertically-elongated Lagrangian tracking model to demonstrate that turbulent wind fluctuations accelerate warm-cloud droplet growth and precipitation onset by enhancing both autoconversion and accretion processes compared to non-turbulent conditions.

The Gist

Imagine you are trying to understand how rain forms in a cloud. For decades, scientists have been trying to simulate this process on computers, but it's like trying to predict the path of a single leaf falling through a stormy forest while also tracking millions of other leaves.

This paper by Masaya Iwashima and Ryo Onishi introduces a new, super-detailed way to simulate exactly how raindrops grow and fall, specifically looking at how turbulence (the chaotic, swirling wind inside a cloud) changes the game.

Here is the story of their discovery, explained simply:

1. The Old Way vs. The New Way

The Old Way (The "Box" Method):
Previously, scientists simulated clouds using a small, square box with invisible walls. If a raindrop hit a wall, it magically reappeared on the other side. It was like playing a video game in a small room where the walls loop around.

• The Problem: Real clouds aren't small boxes. They are tall towers stretching from the ground to the sky. In a real cloud, the air near the bottom is different from the air near the top. The old "box" method couldn't capture this vertical journey.

The New Way (The "Elevator" Method):
The authors built a new simulation that looks like a tall, narrow elevator shaft stretching from the ground to the top of the cloud.

• The Innovation: They didn't just simulate the air moving up and down; they also injected a "snapshot" of chaotic, swirling wind (turbulence) into this shaft.
• The Tracking: Instead of averaging the air, they tracked individual droplets (like following specific people in a crowd) as they moved, grew, and bumped into each other.

2. The Two Experiments: The Calm Room vs. The Dance Floor

To see what turbulence actually does, they ran two simulations side-by-side:

• The "Calm Room" (LAM-case): Imagine a room with a gentle, steady breeze blowing upward. Droplets float up, grow slowly by collecting water vapor, and eventually fall.
• The "Dance Floor" (TURB-case): Imagine the same room, but now it's a wild dance floor with swirling winds, eddies, and chaotic gusts.

3. What Happened? (The Surprising Results)

The "Bumping" Effect (Autoconversion)

In the calm room, droplets mostly float along with the wind. They rarely bump into each other because they are all moving at similar speeds.
In the Dance Floor, the swirling winds act like a giant mixer. They toss the droplets around, making them crash into each other much faster.

• The Analogy: Think of a crowded hallway. If everyone walks in a straight line, you rarely bump into anyone. But if everyone starts dancing and spinning, you bump into people constantly.
• The Result: In the middle of the cloud, the turbulence caused tiny droplets to smash together and merge into slightly larger ones much earlier than in the calm cloud. This is called autoconversion.

The "Rainmaker" Effect (Accretion)

Once those slightly larger droplets formed in the middle of the cloud, they started to fall.

• In the Calm Room: They fell slowly and gently, picking up a few more tiny droplets along the way.
• In the Dance Floor: Because the turbulence had already made them bigger and faster, they fell like bowling balls through a field of ping-pong balls. They swept up (accreted) huge numbers of smaller droplets as they descended.

4. The Final Outcome: Rain Arrives Sooner and Harder

The most exciting part of the study is what happened when the rain hit the "ground" (the bottom of the simulation):

• Timing: In the turbulent cloud, the first raindrops hit the ground 270 seconds (4.5 minutes) earlier than in the calm cloud.
• Size: The first raindrops in the turbulent cloud were 50% larger than those in the calm cloud.

5. Why Does This Matter?

This study proves that turbulence is a secret accelerator for rain.
Without turbulence, clouds might take much longer to produce rain, or the rain might be much lighter. The chaotic wind doesn't just mix the air; it actively forces droplets to collide, merge, and grow into raindrops much faster.

The Big Picture:
Think of a cloud as a giant factory.

• Without turbulence: The factory is quiet. Workers (droplets) move slowly, and it takes a long time to assemble the final product (rain).
• With turbulence: The factory is a high-speed assembly line with conveyor belts shaking and spinning. The workers are thrown together, they merge quickly, and the final product rolls off the line much faster and in bigger batches.

This new model helps scientists understand why some clouds dump heavy rain quickly while others drizzle for hours, improving our ability to predict weather and climate.

Technical Summary

1. Problem Statement

Cloud microphysics modeling has historically relied on Eulerian methods (bulk or spectral/bin methods) or Lagrangian methods like the Super-Droplet Method (SDM). While Direct Numerical Simulation (DNS) coupled with particle tracking offers a highly accurate, stochastic-free representation of turbulence-particle interactions, previous studies were limited to cubic domains with periodic boundary conditions.

• Limitation: Periodic boxes cannot capture the vertical structure of real atmospheric clouds (e.g., variations in supersaturation, droplet size distribution, and updrafts from ground to cloud top).
• Gap: There was a lack of research combining vertically-elongated domains (to simulate realistic cloud structures) with explicit turbulence to study how turbulence influences the full lifecycle of warm-cloud microphysical processes (activation, condensation, collision-coalescence, and sedimentation).

2. Methodology

The authors developed a new explicit cloud microphysical model based on Direct Numerical Simulation (DNS) coupled with Lagrangian particle tracking.

• Computational Domain:
  • A vertically-elongated quasi-1D domain extending from the ground (0 m) to the cloud top (~2250 m).
  • Horizontal dimensions were set to 5 mm to resolve hydrodynamic interactions while managing computational cost.
  • Turbulence Implementation: A snapshot of Homogeneous Isotropic Turbulence (HIT) was generated in a cubic domain and stacked vertically to fill the elongated domain. Random perturbations were added to particle positions at boundary crossings to prevent artificial "curtain-like" structures caused by periodicity.
• Physical Models:
  • Flow Field: A kinematic model (KiD warm-1) prescribing a time-dependent updraft ($w_{updraft}$) combined with the HIT velocity field.
  • Microphysics:
    • CCN Activation: Stochastic model based on supersaturation.
    • Condensation/Evaporation: Coupled with water vapor fields via a source term.
    • Collision-Coalescence: Calculated geometrically with Stokes flow hydrodynamic interactions. Coalescence efficiency was set to 1; breakup was neglected (Weber number $We \lesssim 1$).
• Simulation Cases:
  • LAM-case: Laminar flow (only prescribed updraft, no turbulence).
  • TURB-case: Turbulent flow (prescribed updraft + HIT fluctuations).
  • Both cases simulated warm-cloud processes over 1800 seconds.

3. Key Contributions

1. Novel Framework: Successfully extended the direct tracking method to a vertically-elongated domain while incorporating explicit turbulence, bridging the gap between fundamental DNS studies and realistic cloud modeling.
2. Explicit Turbulence-Microphysics Coupling: Provided a high-fidelity simulation of how turbulent wind fluctuations interact with droplet motion and growth throughout the entire vertical column of a cloud.
3. Mechanistic Insight: Isolated the specific roles of turbulence in different cloud layers (lower, middle, upper) and at different developmental stages (early updraft vs. later sedimentation).

4. Key Results

The comparison between the LAM (laminar) and TURB (turbulent) cases yielded the following insights:

• Enhanced Collision Rates: Turbulence significantly increased collision frequencies. In the middle layer during the early stage ($t < 600$ s), collision frequencies in the TURB case exceeded $5000 \, m^{-3}s^{-1}$, compared to $<1000 \, m^{-3}s^{-1}$ in the LAM case.
• Promotion of Autoconversion:
  • The average diameter ratio of colliding droplets was lower in the TURB case (1.66) than in the LAM case (1.88), indicating turbulence promoted collisions between similar-sized droplets (autoconversion).
  • Large droplets ($>100 \, \mu m$) appeared much earlier in the middle layer of the TURB case (~400–450 s) compared to the LAM case (>600 s).
• Accelerated Accretion in Lower Layers:
  • After the initial updraft phase ($t > 600$ s), large droplets formed in the middle/upper layers fell into the lower layers.
  • In the TURB case, these large droplets actively collected smaller droplets (accretion) in the lower layer, causing a sharp increase in average diameter around 800 s, a phenomenon not observed in the LAM case.
• Precipitation Onset and Drop Size:
  • Timing: Precipitation onset at the ground occurred ~270 seconds earlier in the TURB case.
  • Size: The first raindrops reaching the ground were 1.5 times larger in the TURB case compared to the LAM case.
• Impact on Condensation Growth:
  • Analysis of constituent particles revealed that turbulence indirectly enhanced condensation growth. By promoting early collisions, turbulence reduced the total number of droplets (due to coalescence) while the total condensed water mass remained constant. This resulted in a larger average volume per droplet ($V_{TURB} \approx 1.37 V_{LAM}$), altering the condensation growth history.

5. Significance

This study demonstrates that turbulence is a critical accelerator of warm-rain formation processes, acting through two distinct mechanisms:

1. Direct Mechanism: Enhancing collision-coalescence (autoconversion) in the middle cloud layer during the updraft phase.
2. Indirect Mechanism: Modifying the droplet size distribution (DSD) early in the cloud's life, which subsequently alters condensation growth rates and accelerates the accretion process in lower layers.

The findings challenge the limitations of periodic box DNS, showing that realistic vertical structures are necessary to accurately capture the timing and magnitude of precipitation onset. The results suggest that turbulence not only speeds up the formation of rain but also increases the size of the initial raindrops, which has significant implications for weather prediction models and climate simulations that often parameterize these microphysical processes.