Dr. Michael L. Larsen – Research Overview

Accounting for Deviations from Perfect Spatialn Randomness in Coagulation and Collisional Growth

 

Basic Background

 

It is common knowledge that the water vapor present in the atmosphere sometimes ends up forming into preciptation that falls to the ground.  Although your middle school teachers probably emphasized the water cycle as a whole, the process between “water vapor evaporates from the water surface” to “rain falls from the sky” is usually left a bit hazy.  Generally , you have some idea that clouds are involved, but often that’s about it for understanding the process.

 

Well, atmospheric scientists have a little better grasp on the problem than that – though we still don’t completely understand everything that’s going on.

 

After water evaporates from the water’s surface, we now have some water vapor immediately above the water’s surface.  We have winds in the atmosphere and water molecules don’t have a whole lot of inertia, so wherever the winds above the surface of the water go, the airborne water molecules tend to get swept along with it.  A lot of this water stays near the surface of the earth, but some makes its way a little higher up in the atmosphere.  Why?  Well, the air layer near the surface of the earth tends to be a little warmer than the layer above it, thus causing buoyancy (hot air rises) and bringing the water vapor with it.

 

Now, the reason that the amount of water vapor evaporated into the atmosphere was that amount and not less or more was governed by the equilibrium thermodynamics over the water’s surface.  The details are, for my purposes here, not that important but the main point is that as the air (with the water vapor coming along for the ride) rises in the atmosphere, its temperature decreases changing the equilibrium and eventually “saturating” the air.

 

Once the air is saturated or supersaturated, the water vapor has a tendency to leave the vapor phase and condense back on a solid.  This vapor is now up in the atmosphere – the only solids it finds are dust/dirt/smog – collectively, we call these things aerosol particles in the business.  Some aerosol particles are hydrophobic and won’t be good sources for the water to condense on.  Many, however, form good cites for water drops to form.  When the water vapor condenses on the aerosol particle, we get a cloud droplet.

 

Now, water can continue to condense on water droplets as well as dry particulates.  This is what we call condensational growth and is part of the process of getting precipitation.  The theory governing this process is fairly well understood, but beyond the scope of this discussion.  (For the interested, see Kohler theory in an atmospheric microphysics textbook or talk to Dr. Larsen directly).

 

Condensational growth will only get you so far.  The bigger the drop gets, the more vaper it takes to make it bigger yet.  (Volume is proportional to the cube of the diameter, so it takes a lot of water vapor to get to a large enough water drop to form into rain.  At some point (in the neighborhood of a few tens of microns in diameter), a larger fraction of the droplet growth is due to the collision/coalescence process than through condensational growth.

 

The collision/coalescence process sounds fancy, but it is just the process of smaller droplets smashing into each other to form a larger drop.  This happens naturally in clouds and is the main way of turning a cloud drop into a raindrop.  After going through many collisions, eventually some cloud droplets becomes large enough that the gravitational force is larger than the updrafts keeping the cloud in the air.  Then we get rain.

 

DISCLAIMER – Don’t view the above as an exhaustive introduction.  There is GROSS simplification involved, and in some places I even lied to you a little.  This is just to give you a slightly more complete version than you typically get in middle school water cycle explanations.

 

 

 

So what’s the Problem?

 

You know how I keep mentioning that airborne particulates are not perfectly random?  Well, that happens here, too.  The theoretical relationship that calculates the rate of small droplets colliding into each other to form larger droplets assumes the drops are perfectly randomly distributed in space.  If you follow the above link to perfectly random and look at the picture, it isn’t hard to convince yourself that those two systems will evolved differently as particles collide into each other.

 

This has analogues to pair-production in biological applications; if particle clump, then the average particle will undergo more collisions per unit time than in a perfectly random distribution.  That means the rate of particle growth may be underestimated using the current theoretical treatment.

 

This is good, because we observe rain forming out of a cloud faster than we think it should be possible.  The fact that our theoretical predictions are based on false assumptions regarding particle distributions may be part of the reason for our confusion.

 

 

 

What is Dr. Larsen doing to try and Solve the Problem?

 

If we are able to quantify how much cloud particles depart from perfect spatial randomness, then that helps us quantify the amount of error we currently have in assuming the collisions occur in a perfectly random environment.  In principle, we may even be able to geometrically simulate the process with a computational tool called “direct numerical simulation” or DNS, but first we have to know the statistical description of the droplets as they are at some point in time in the cloud.  Dr. Larsen is working on this and associated problems with the generation of precipitation.

 

 

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