Page 48 - Spring 2015

sound Propagation in the Atmospheric boundary layer
A positive vertical gradient in ceff leads to downward refrac- tion of sound, whereas a negative vertical gradient leads to upward refraction. Temperature gradients and wind shear both contribute to gradients in ceff. Depending on the atmo- spheric state and propagation direction, they may combine to strengthen or diminish overall refraction. Negative gradi- ents may be caused by a temperature lapse condition, mean- ing that the temperature, and hence the sound speed, de- creases with height. It may also be caused by a negative wind shear, meaning that the wind speed decreases with height as usually occurs for propagation in the upwind direction. A positive vertical gradient may be caused either by a ground- based temperature inversion, meaning that the temperature decreases with height, or by a positive wind shear, which usually occurs in the downwind direction.
Temperature stratification is related to the static stability of the atmosphere. When the temperature gradient equals –0.0098°C/m in air that is unsaturated by water vapor, the air column is said to be neutrally stratified. This value is re- ferred to as the dry adiabatic lapse rate. If the temperature gradient is less (more negative) than the adiabatic lapse rate, the air column is buoyantly unstable in the sense that an air parcel, when displaced adiabatically from its original posi- tion, will tend to accelerate in the direction of displacement. When the temperature gradient is greater than the adiabatic lapse rate, the air column is buoyantly stable in that a dis- placed parcel will tend to oscillate about its original position.
If the wind speed is very high, stratification in the ASL is generally close to neutral due to the strong turbulent mixing induced by the wind shear. At lower wind speeds, stratifica- tion of the ASL will depend on radiative transfer between the ground and atmosphere. On a clear day, as the ground is heated by the sun, heat is conducted to the overlying air and unstable stratification develops. Conversely, on a clear night, cooling of the ground leads to stable stratification. A thick stratus cloud layer encourages near-neutral stratifica- tion. Hence we have the following four fundamental sound propagation “regimens” (and transitions in-between):
1. High wind (day or night): Temperature stratification is near neutral. Refraction depends primarily on wind shear and hence on the propagation direction.
2. Low wind, clear, daytime: Stratification is unstable and upward refraction prevails. Buoyancy instabilities cre- ate strong turbulence.
3. Low wind, cloudy (day or night): Weak refraction, gen- erally upward, prevails in all directions. Turbulence tends to be weak.
Figure 2. Characteristic effective sound speed profiles for 4 limiting cases of the ASL. The profiles are arbitrarily offset along the horizon- tal axis so as to improve visibility.
4. Low wind, clear, nighttime: Ground-based temperature inversions often form, which lead to the prevalence of strong downward refraction. Turbulence is suppressed by the stable stratification but may occur intermittently.
Characteristic effective sound speed profiles for these four cases are illustrated in Figure 2.
The Monin-Obukhov similarity theory (MOST) has been widely adopted in the atmospheric sciences (e.g., Wyngaard, 2010) for modeling mean profiles and turbulence statistics in the ASL and increasingly for sound propagation studies (e.g., Wilson, 2003). The basic scaling parameters of MOST are the friction velocity (u*; which relates to the wind shear), the sensible heat flux from the surface to the overlying air (QH), the height from the surface (z), and the Boussinesq buoyancy parameter (β = g/Ts; where g is the gravitational acceleration and Ts is the temperature at the surface). MOST involves normalizing dimensional quantities by these scales. However, MOST cannot be used when turbulent mixing is suppressed, as happens in strong inversion conditions. MOST should also not be applied above the ASL where the wind direction rotates with height due to Coriolis forces.
Figure 3 shows Crank-Nicholson parabolic equation (CNPE; West et al., 1992) calculations of transmission loss (TL; which is defined as the difference, in dB, between the calcu- lated sound pressure field and the field that would be pro- duced by the same source at a distance of 1 m in free space) for wind and temperature profiles approximating the four conditions described above, namely u* = 0.6 m/s and QH = 0 W/m2 (high-wind, neutral conditions), u* = 0.1 m/s and QH = 200 W/m2 (low-wind, clear daytime conditions), u* = 0.0 m/s and QH = 0 W/m2 (low-wind, cloudy conditions), and u* = 0.08 m/s and QH = 0 -10 W/m2 (low-wind, clear night- time conditions). In all cases, the source height is 5 m and its frequency is 250 Hz and the ground impedance (normalized by the characteristic impedance of air) is set to 8.77 + 8.39i,
46 | Acoustics Today | Spring 2015