How are snowflakes formed?They are formed by the continuous growth and aggregation of ice crystals in the clouds. The shapes of snowflakes are very diverse, and the common ones are hexagons, stars, and so on. The shape of snowflakes depends on the temperature and humidity conditions in which they grow, as well as the changes they undergo as they fall through the air. The shape of snowflakes affects the speed at which they fall, aka the terminal velocity, which is determined by the balance between gravity and air resistance.
However, snowflakes do not maintain terminal velocity all the time as they fall, but are affected by atmospheric turbulence. Turbulence is an irregular flow phenomenon that causes random fluctuations in velocity and pressure in a fluid. Turbulence can deviate the trajectory of snowflakes, sometimes speeding them up, sometimes slowing them down, and sometimes even keeping them in the air. These phenomena all affect the time and distance at which snowflakes fall, as well as how they interact with other substances in the atmosphere.
So, how do we describe and quantify the acceleration of snowflakes in turbulent currents?This is a very complex problem because snowflakes vary in shape and size, and the strength and structure of turbulence can also vary with height and time. To solve this problem, we need to conduct experimental observations and theoretical analysis. Recently, such work was done by using a novel experimental setup to measure the statistical properties of the vertical velocity and acceleration of snowflakes in atmospheric boundary layer turbulence.
The experimental setup consists of a tower with a height of 10 meters, a high-speed camera, a laser emitter and a laser receiver. The laser emitter and receiver are mounted at the top and bottom of the tower, respectively, to form a vertical laser plane. The high-speed camera is mounted on one side of the tower at an angle to the laser plane. As snowflakes pass through the laser plane, they reflect the laser light and are captured by a high-speed camera. By analyzing the images of high-speed cameras, information on the position, velocity, and acceleration of snowflakes can be obtained. At the same time, instruments were installed on the tower to measure parameters such as temperature, humidity, pressure and wind speed in the atmosphere, as well as the characteristic scale and intensity of turbulence.
The advantage of this experimental setup is that the movement of snowflakes can be measured with high precision in a natural atmospheric environment without any assumptions or classification of the shape and size of snowflakes. The disadvantage of this experimental setup is that it can only measure the vertical motion of the snowflake, not the horizontal direction, nor the rotation and deformation of the snowflake.
The results of this article are based on two experiments conducted near Salt Lake City, Utah, in December 2019 and January 2020, which measured the movement of about 100,000 snowflakes. The data covers different atmospheric conditions, including different temperatures, humidity, wind speeds, and turbulence intensity, as well as different snowflake shapes and sizes. To analyze these data, the authors used two dimensionless parameters, the Reynolds number and the Stokes number.
The Reynolds number is used to describe the strength and structure of turbulent flows, which are determined by the characteristic velocity, characteristic length, and kinematic viscosity of the fluid. The Stokes number is used to describe the inertial effect of a snowflake, which is determined by the terminal velocity of the snowflake, the density of the snowflake, the density of the fluid, and the characteristic time of the turbulence.
They found that despite the complexity of the snowflake's structure and the fact that the turbulence is not uniform, the acceleration distribution of the snowflake can be uniquely determined by the Stokes number. That is, as long as we know the inertia and turbulence characteristics of snowflakes, we can ** the probability distribution of their acceleration.
The authors also found that the root-mean-square acceleration of a snowflake is approximately proportional to the Stokes number, which means that the greater the inertia, the greater the fluctuation in acceleration. If the acceleration is normalized by root mean square acceleration, then the distribution of acceleration is approximately exponential, and the coefficient of the exponent is -3 2, which is independent of neither the Reynolds number nor the Stokes number. This result is very different from the acceleration distribution of fluid particles in turbulent flows, which generally obeys a Gaussian distribution.
Surprisingly, the authors found that if a pseudo-acceleration is calculated using the fluctuation of the terminal velocity of a snowflake in still air, then the distribution of this pseudo-acceleration is also exponential, and the coefficient of the exponent is also -3 2. This equivalence suggests that there is a potential link between how turbulence determines the trajectory of snowflakes, and how microphysics determines the shape and size of snowflakes.