Introduction to Acoustics

Sound Propagation in the Atmosphere 4.8 Wind and Temperature Gradient Effects on Outdoor Sound 131
4.8 Wind and Temperature Gradient Effects on Outdoor Sound
The atmosphere is constantly in motion as a consequence
of wind shear and uneven heating of the Earth’s
surface (Fig. 4.14).
Any turbulent flow of a fluid across a rough solid
surface generates a boundary layer. Most interest, from
the point of view of community noise prediction, focuses
on the lower part of the meteorological boundary layer
called the surface layer. In the surface layer, turbulent
fluxes vary by less than 10% of their magnitude but
the wind speed and temperature gradients are largest. In
typical daytime conditions the surface layer extends over
50–100 m. Usually, it is thinner at night. Turbulence
may be modeled in terms of a series of moving eddies
or turbules with a distribution of sizes.
In most meteorological conditions, the speed of
sound changes with height above the ground. Usually,
temperature decreases with height (the adiabatic lapse
condition). In the absence of wind, this causes sound
waves to bend, or refract, upwards. Wind speed adds or
subtracts from sound speed. When the source is downwind
of the receiver the sound has to propagate upwind.
As height increases, the wind speed increases and the
amount being subtracted from the speed of sound increases,
leading to a negative gradient in the speed of
sound. Downwind, sound refracts downwards. Wind effects
tend to dominate over temperature effects when
both are present. Temperature inversions, in which air
temperature increases up to the inversion height, cause
sound waves to be refracted downwards below that
height. Under inversion conditions, or downwind, sound
1 km
100 m
0 m
U
θ
Free troposphere
Boundary layer
Surface layer
Ground
Fig. 4.14 Schematic representation of the daytime atmospheric
boundary layer and turbulent eddy structures. The
curve on the left shows the mean wind speed (U) and
the potential temperature profiles (θ = T + γdz, where
γd = 0.098 ◦ C/km is the dry adiabatic lapse rate, T is the
temperature and z is the height)
levels decrease less rapidly than would be expected from
wavefront spreading alone.
In general, the relationship between the speed of
sound profile c(z), temperature profile T(z) and wind
speed profile u(z) in the direction of sound propagation
is given by
�
T(z) + 273.15
c(z) = c(0)
+ u(z) , (4.46)
273.15
where T is in ◦Canduis in m/s.
4.8.1 Inversions and Shadow Zones
If the air temperature first increases up to some height before
resuming its usual decrease with height, then there
is an inversion. Sound from sources beneath the inversion
height will tend to be refracted towards the ground.
This is a favorable condition for sound propagation and
may lead to higher levels than would be the case under
acoustically neutral conditions. This will also be true for
receivers downwind of a source. In terms of rays between
source and receiver it is necessary to take into account
any ground reflections. However, rather than use plane
wave reflection coefficients to describe these ground reflections,
a better approximation is to use spherical wave
reflection coefficients (Sect. 4.6.2).
There are distinct advantages in assuming a linear effective
speed of sound profile in ray tracing and ignoring
the vector wind since this assumption leads to circular
ray paths and relatively tractable analytical solutions.
With this assumption, the effective speed of sound c can
be written,
c(z) = c0(1 + ζz) , (4.47)
where ζ is the normalized sound velocity gradient
[(dc/dz)/c0]andzis the height above ground. If it also
assumed that the source–receiver distance and the effective
speed of sound gradient are sufficiently small that
there is only a single ray bounce, i. e., a single ground
reflection between the source and receiver, it is possible
to use a simple adaptation of the formula (4.22), replacing
the geometrical ray paths defining the direct and
reflected path lengths by curved ones. Consequently, the
sound field is approximated by
p = � exp(−ik0ξ1) + Q exp(−ik0ξ2) � /4πd , (4.48a)
where Q is the appropriate spherical wave reflection
coefficient, d is the horizontal separation between the
source and receiver, and ξ1 and ξ2 are, respectively,
Part A 4.8