SHW Ch. 6 - Forces/Force Balances
Pressure Gradient Force (PGF): the force applied to a small parcel of air due to pressure differences created by a difference in air density (more molecules), air temperature (more energy per molecular collision), or both; Figures 6.1 & 6.2
PGF is always perpendicular to the isobars, with a direction from high pressure toward low pressure; Figure 6.4
Pressure Gradient: the rate at which pressure changes with distance
the most extreme horizontal pressure gradients on earth occur in tornadoes and in the eyewalls of hurricanes, and in rare cases, in extratropical cyclones; Figures 6.3 & 6.4
Gravitational Force (g): any two elements of mass are attracted to each other by gravity, with the magnitude of the force being proportional to the mass of each object and inversely proportional to the square of the distance between the two objects: (m1*m2) / d2
the earth is much more massive than any air parcel and the distance between the center of the earth and a parcel at the top of the troposphere versus the bottom of the troposphere is so small, that for weather applications, the magnitude of the gravitational force (g) acting on any air parcel is considered to be constant throughout the troposphere: 9.8 m / sec2
the direction of the gravitational force is always downward toward the center of the Earth
Frictional Force (F): when faster moving air molecules collide with slower moving air molecules; this creates turbulence
the direction of the frictional force always acts in a direction opposite to the motion of the air, and therefore, always acts to reduce the speed of the flow
Mechanical Turbulence: occurs when air encounters "roughness" due to such things as trees, buildings and terrain; these objects deflect the wind in all directions, mixing air down from aloft and up from the surface; Figure 6.5
Thermal Turbulence: occurs when the air near the surface is heated sufficiently during the day that it becomes unstable and rises to higher altitudes; Figure 6.5
convection carries slower-moving air to altitudes where the winds are stronger; the mixing tends to reduce the air flow at the higher altitude
Thermal turbulence may also transport fast-moving air downward from higher altitudes, producing gusty surface winds; very common in Spring
Shear-induced Turbulence: occurs when wind speeds change rapidly with distance, typically with height; when the wind shear becomes large, tumbling motions mix layers of faster and slower moving air, smoothing the vertical wind profile
(SHW Ch. 6 - Forces/Force Balances Continued)
Frictional drag is strongest near the Earth's surface and decreases rapidly with height
Boundary Layer (BL) also known as the "Friction Layer": where friction is an important force
depends on the underlying surface roughness (hills, buildings, trees, etc.)
on a clear, calm night, the BL over a lake may extend only a few hundred meters upward, but may extend a few thousand meters upward over a city on a hot, windy afternoon
Coriolis "Force" (CF): an apparent "force" associated with the rotation of the Earth (first described mathematically in 1835 by Gustav Gaspard de Coriolis); Fig. 6.6
angular momentum: the product of an object's mass (M), its rotational velocity (V) and its radius from the axis about which it is rotating (R): M * V * R
through "conservation of angular momentum" an air parcel must speed up as it moves from the equator northward toward either pole; on the rotating Earth:
at the equator, an air parcel at rest is moving 1670 km/hr (1018 mph)!
at 30° N or S Latitude, an air parcel at rest is moving 1446 km/hr (882 mph)
at 60° N or S Latitude, an air parcel at rest is moving 835 km/hr (508 mph)
at the north and south poles, there is no rotational speed
if an air parcel is pushed northward it will pick up speed ("V"), as "R" decreases, causing the parcel to move faster than the Earth below, creating an apparent "deflection" to the east (to the right of its initial motion); Figure 6.7
the Coriolis "Force" does the following:
objects will deviate to the right of their direction of motion in the Northern Hemisphere (and to the left in the Southern Hemisphere)
affects the direction an object will move across the Earth's surface, but has no effect on its speed
is strongest for fast-moving objects and zero for stationary objects
is zero at the equator and a maximum at the poles
Force Balances: air motions are driven by pressure differences that develop due to the uneven solar heating that occurs across the Earth's surface, in addition to the disruption of airflow over the world's mountain ranges
the imbalances between the forces affecting atmospheric motion cause the storm systems of the world to develop, in an attempt to regain "balance"
Horizontal Motions above the BL: Acceleration = horizontal PGF + CF
Horizontal Motions within the BL: Acceleration = horizontal PGF + CF + F
Vertical Motions: Acceleration = vertical PFG + Gravity
(SHW Ch. 6 - Forces/Force Balances Continued)
Hydrostatic Balance: whenever the upward pressure gradient force is exactly balanced by gravity; Figure 6.8
except in thunderstorms, the atmosphere is essentially in hydrostatic balance everywhere on Earth
Geostrophic Balance: a balance between the PGF and CF; Figure 6.9
the atmosphere is nearly, but rarely, in exact geostrophic balance; Figure 6.10
The Jetstream:
a narrow band of strong winds the encircles the Earth in the mid-latitudes
is typically 300 to 500 km (200 to 300 miles) wide
can extend from the tropopause at 250 mb down to about 500 mb
typically follows a wavelike pattern; Figure 6.11
its maximum speed usually occurs just below the tropopause
there can be as many as three jetstreams (subtropical, polar and arctic) present or as few as one, at any one longitude between the equator and the pole
regions of exceptionally strong winds, within the jetstream, are called jetstreaks
Geostrophic Balance and the Jetstream: Figure 6.12
for illustration, the surface pressure is assumed to be the same everywhere
with this assumption, the same number of molecules reside in any column above a unit area in the cold air and in the warm air
in a 1 km layer above the surface, there must be more molecules in the cold air (smaller thickness) than in the warm air (greater thickness)
at the 1 km height, the pressure must be lower in the cold air than in the warm air
this causes a downward slope from the warm air to the cold air
pressure surfaces slope more steeply at higher altitudes than those at lower altitudes
the steeper the slope, the stronger the horizontal PGF and the stronger the geostrophic wind; this is the reason that winds increase with height in the troposphere
the pole-equator temperature gradients imply that the PGF will have a component directed poleward toward the cold air in both hemispheres
considering geostrophic balance, this further implies that the upper tropospheric winds will generally have a west to east component in both hemispheres
temperature gradients are typically not uniform; sharp temperature gradients exist within the narrow regions of fronts
with a concentrated temperature gradient along the leading edge of the cold air, a locally strong pressure gradient is induced over the front, such that the jetstream must reside over the cold air dome; Figure 6.13