Wind-Tunnel Measurements Of Restitution Coefficients And Ejection Number Of Snow Particles In Drifting Snow: Determination Of Splash Functions

Wind-tunnel experiments of drifting snow were carried out andsplash functions were formulated to describe probability distributions of vertical restitution coefficient, horizontal restitution coefficient and ejection number when a natural snow particle collided at a natural snow surface. The following results were obtained:(1) The vertical restitution coefficient was usually larger than unity and decreased sharply with impact angle. At smaller impact angles around 5 degrees the vertical restitution coefficient exceeded a magnitude of ten.(2) The horizontal restitution coefficient, ranging from -1 to 1.5, decreased with impact velocity, but was not clearly dependent on impact angle.(3) The ejection number amounted to five per impact and increasedwith impact velocity.(4) Three splash functions to express the probability distributions of the vertical restitution coefficient, horizontal restitution coefficient and ejection number were formulated, which will be used in future computer simulations of the snow drifting process.     

Electrostatic Force in Blowing Snow

Separation of electrostatic charge during the transport of particles by wind adds a force to the gravitational and fluid forces that determine trajectories of particles moving by saltation. Evaluating this electrostatic force requires the electric field strength very near the saltation surface, and charge-to-mass ratios for the moving particles. Field mill readings 4 cm above the surface in a moderate blizzard showed electric field strength as high as +30 kV m^-1. Another experiment gave charge-to-mass ratios of individual saltation particles in low-level drifting that ranged between +72 C kg^-1 and -208 C kg^-1. From these measurements, we estimated electrostatic forces as large as the gravitational force on some saltating particles. Including forces of this magnitude in the equations of motion significantly alters predicted saltation trajectories from those for uncharged particles. Predictions appear reasonable that for some saltating particles, the electrostatic force prevents new surface impacts. These results should help improve models of energy transfer in the planetary boundary layer during blizzards and sandstorms.     

The Electric Field During Blowing Snow Events

A model is proposed to determine the electric field strength in blowing snow. To test this model, the electric field strength was measured over an 80-day period during the Canadian Arctic Shelf Exchange Study (CASES) in 2004. The electric field strength at 0.5 m correlates well with the difference between 10-m wind speed and a threshold wind speed, although there is a large amount of variation between the electric fields generated during different blowing snow events. Although the model predicts that the electric field should be proportional to particle number density, the correlation is weak. The correlation of wind speed and electric field strength suggests that particles become charged primarily due to friction-induced temperature difference as they impact upon the surface. The strength of the electric field is likely influenced by a large number of other factors that are difficult to measure. However, the model predicts electric field strengths in excess of 25 kV m⁻¹ near the surface, which would have a significant effect on particle motion.     

Laboratory Studies Of Wind Stress Over Surface Waves

Simultaneous laboratory observations of wind speed, wind stress, and surfacewind-wave spectra are made under a variety of wind forcing patterns using cleanwater as well as water containing an artificial surfactant. Under typical experimentalconditions, more than half of the total stress is supported by the wave-induced stressrather than by the surface viscous stress. When the surfactant reduces the shortwind-wave spectra, the wind stress also decreases by as much as 20–30% at agiven wind speed. When the wind forcing is modulated in time, the wind stresstends to be higher under decreasing wind than under increasing wind at a givenwind speed, mainly because the response of short wind-wave spectra to varyingwind forcing is delayed in time. These examples clearly demonstrate that therelationship between the wind speed and the wind stress can be significantlymodified if the surface wave field is not in equilibrium with the wind forcing.Next, we examine whether the wind stress is estimated accurately if the wave-inducedstress by all surface wave components is explicitly evaluated by linear superpositionand is added to the surface viscous stress. It is assumed that the surface viscous stressis uniquely related to the wind speed, and that the wind input rate is determined by thelocal, reduced turbulent stress rather than the total stress. Our wind stress estimatesincluding the wave contributions agree well with observed wind stress values, evenif the surface wave field is away from its equilibrium with the wind in the presenceof surface films and/or under time-transient wind forcing. These observations stronglysuggest that the wind stress is accurately evaluated as a sum of the wave-induced stressand the surface viscous stress. At very high winds, our stress estimates tend to be lowerthan the observations. We suspect that this is because of the enhancement of wind stressover very steep (or breaking) short wind-waves.     

Shear stress partitioning in large patches of roughness in the atmospheric inertial sublayer

Drag partition measurements were made in the atmospheric inertial sublayer for six roughness configurations made up of solid elements in staggered arrays of different roughness densities. The roughness was in the form of a patch within a large open area and in the shape of an equilateral triangle with 60 m long sides. Measurements were obtained of the total shear stress (τ) acting on the surfaces, the surface shear stress on the ground between the elements (τ_S) and the drag force on the elements for each roughness array. The measurements indicated that τ_S quickly reduced near the leading edge of the roughness compared with τ, and a τ_S minimum occurs at a normalized distance (x/h, where h is element height) of (downwind of the roughness leading edge is negative), then recovers to a relatively stable value. The location of the minimum appears to scale with element height and not roughness density. The force on the elements decreases exponentially with normalized downwind distance and this rate of change scales with the roughness density, with the rate of change increasing as roughness density increases. Average τ_S : τ values for the six roughness surfaces scale predictably as a function of roughness density and in accordance with a shear stress partitioning model. The shear stress partitioning model performed very well in predicting the amount of surface shear stress, given knowledge of the stated input parameters for these patches of roughness. As the shear stress partitioning relationship within the roughness appears to come into equilibrium faster for smaller roughness element sizes it would also appear the shear stress partitioning model can be applied with confidence for smaller patches of smaller roughness elements than those used in this experiment.