In atmospheric sciences (
meteorology,
climatology and related fields), the
pressure gradient (typically of
air, more generally of any
fluid) is a physical quantity that describes in which direction and at what rate the
pressure changes the most rapidly around a particular location. The pressure gradient is a dimensional quantity expressed in
units of pressure per unit length. The
SI unit is
pascal per
metre (Pa/m).
Mathematical description
Assuming that the pressure
p is an
intensive quantity, i.e., a single-valued,
continuous and
differentiable function of three-dimensional space (often called a
scalar field), i.e., that
where
x,
y and
z are the
coordinates of the location of interest, then the pressure gradient is the
vector quantity defined as
\nabla p = \begin{pmatrix}
{\frac{\partial p}{\partial x}},
{\frac{\partial p}{\partial y}},
{\frac{\partial p}{\partial z}}
\end{pmatrix}
Physical interpretation
Strictly speaking, the concept of pressure gradient is a
local characterization of the air (more generally of the fluid under investigation). The pressure gradient is defined only at those spatial scales at which pressure (more generally
fluid dynamics) itself is defined.
Within
planetary
atmospheres (including the
Earth's), the pressure gradient is a vector pointing roughly downwards, because the pressure changes most rapidly vertically, increasing downwards. The value of the strength (or
norm) of the pressure gradient in the
troposphere is typically of the order 9 Pa/m (or 90 hPa/km).
The pressure gradient often has a small but critical horizontal component, which is largely responsible for the
wind circulation. The
horizontal pressure gradient is a 2-dimensional vector resulting from the projection of the pressure gradient onto a local horizontal plane.
Near the
Earth's surface, this horizontal pressure gradient is typically pointing towards high pressure
air masses (
anticyclones), its particular orientation at any one time and place depends strongly on the weather situation. At mid-
latitudes, the typical horizontal pressure gradient may take on values of the order of 10
-2 Pa/m (or 10 Pa/km), although rather higher values occur within
meteorological fronts.
Weather and climate relevance
Differences in air pressure between different locations are critical in weather forecasting and climate. As indicated above, the pressure gradient constitutes one of the main forces acting on the air to make it move as wind. Note that the
pressure gradient force points from high towards low pressure zones, it is thus oriented in the opposite direction from the pressure gradient itself.
Sound waves and
shock waves are events that can induce very large pressure gradients, but these are often transitory disturbances.
Day to day experiences and health issues
Our
ears detect and interpret sound waves; as such they are delicate, sensitive organs to measure pressure gradients. Excessive pressure gradients can hurt or damage the
auditory system. By contrast, pressure alone does not have quite the same effect: divers can reach significant depths under water (and thus experience very large pressures) without damage, provided appropriate and necessary precautions are taken.
See also
