[Paper Review] Condensation of cloud microdroplets in homogeneous isotropic turbulence

Alessandra S. Lanotte, Agnese Seminara+1 more|ArXiv.org|Oct 17, 2007

Particle Dynamics in Fluid Flows48 references3 citations

TL;DR

This study investigates how homogeneous isotropic turbulence broadens cloud droplet size spectra via condensation, using direct numerical simulations (DNS) at increasing Reynolds numbers. It finds that turbulence-induced supersaturation fluctuations enhance droplet growth variability, leading to significant spectral broadening that scales with Reynolds number and is consistent with dimensional scaling laws, offering a general mechanism for overcoming the condensation bottleneck in warm clouds.

ABSTRACT

The growth by condensation of small water droplets in a three-dimensional homogeneous isotropic turbulent flow is considered. Within a simple model of advection and condensation, the dynamics and growth of millions of droplets are integrated. A droplet-size spectra broadening is obtained and it is shown to increase with the Reynolds number of turbulence, by means of two series of direct numerical simulations at increasing resolution. This is a key point towards a proper evaluation of the effects of turbulence for condensation in warm clouds, where the Reynolds numbers typically achieve huge values. The obtained droplet-size spectra broadening as a function of the Reynolds number is shown to be consistent with dimensional arguments. A generalization of this expectation to Reynolds numbers not accessible by DNS is proposed, yielding upper and lower bounds to the actual size-spectra broadening. A further DNS matching the large scales of the system suggests consistency of the picture drawn, while additional effort is needed to evaluate the impact of this effect for condensation in more realistic cloud conditions.

Motivation & Objective

• To understand how turbulence influences droplet size spectrum broadening during condensation in warm clouds.
• To quantify the role of turbulent fluctuations in supersaturation as a mechanism for breaking the uniform growth bottleneck in cloud microphysics.
• To establish a Reynolds number dependence of droplet size spectrum broadening using direct numerical simulations (DNS).
• To provide bounds on spectral broadening for Reynolds numbers beyond current DNS capabilities.
• To validate the simulation framework by matching large-scale turbulence features and assessing droplet feedback on vapor fields.

Proposed method

• Conducting direct numerical simulations (DNS) of three-dimensional homogeneous isotropic turbulence with millions of Lagrangian droplets.
• Modeling droplet growth via condensation using a simplified thermodynamic model with supersaturation field fluctuations driven by turbulence.
• Using a renormalization technique to account for the feedback of a full droplet population on vapor content, scaling the absorption timescale by the ratio of total to simulated droplet counts.
• Employing a grid cell size matching the diffusive scale (η ≈ 25 cm) to ensure droplets in the same cell experience similar supersaturation.
• Performing multiple simulations with varying droplet concentrations per grid cell (0.4 to 6 droplets/cell) to test convergence and reliability of the renormalization method.
• Analyzing droplet size spectra broadening via standard deviation of droplet radii and comparing results across Reynolds numbers and droplet concentrations.

Experimental results

Research questions

• RQ1 How does turbulence-induced supersaturation fluctuation affect the broadening of cloud droplet size spectra during condensation?
• RQ2 What is the dependence of droplet size spectrum broadening on the Reynolds number of the turbulent flow?
• RQ3 Can the observed broadening be explained by dimensional scaling arguments, and how do they compare to DNS results?
• RQ4 How reliable is the renormalization method used to simulate the feedback of a full droplet population on the vapor field in limited-resolution simulations?
• RQ5 To what extent do the simulation results remain consistent when matching large-scale turbulence features and varying droplet concentration per grid cell?

Key findings

• Spectral broadening of cloud droplet size distributions increases with Reynolds number, as demonstrated by direct numerical simulations at progressively higher resolutions.
• The observed broadening scales with Reynolds number in a manner consistent with dimensional scaling arguments, supporting the physical plausibility of the results.
• The renormalization method for droplet feedback on vapor content converges as droplet concentration per grid cell increases beyond one, with standard deviation and spectral broadening stabilizing at higher densities.
• Simulations with 1 and 3 droplets per grid cell (≈17 and 50 million total droplets) yield consistent spectral broadening, with error bars estimated from this convergence.
• The results suggest that turbulence can act as a general mechanism for broadening droplet spectra, potentially resolving the long-standing condensation bottleneck in warm cloud development.
• Extrapolation beyond DNS-accessible Reynolds numbers yields upper and lower bounds on spectral broadening, enabling estimation of the effect in realistic warm cloud conditions.