PHSC 3033: Meteorology Air Forces

PHSC 3033: Meteorology Air Forces

Pressure Gradient P/ d = Pressure Gradient (Change in Pressure/Distance) Horizontal Pressure Gradient Force (PGF): Force due to pressure differences, and the cause of air movement (winds) on the surface of the Earth.

Horizontal Pressure Gradient Force (PGF) Air moves from High pressure to Low pressure. The force provided by the pressure difference is the pressure gradient force. Force is directed perpendicular to the isobars from Highs to Lows.

Isobars Isobars = Contours of Constant Pressure Topographical Analogy: Just as close topographic lines indicate steep terrain, close isobars mean steep pressure gradient, large pressure force and therefore strong winds. SURFACE MAP

Standard Isobaric Levels Each isobaric level picks out a general altitude to study. These are constant altitude charts, similar to the surface map.

Bernoulli s Principle Pressure is lower for faster steady flow than for slower Higher v, Lower P Airplane Wings Lower v, Higher P

Bernoulli s Equation Recall that WORK = change in both Potential Energy and Kinetic Energy. W = Force * Distance = P A x = P V Finally, P 2, v 2, x 2, h 2, A 2 h 2 Initially, P 1, v 1, x 1, h 1, A 1

KE = 1/2 m (v 2 -v 1 ) 2 PE = mg (h 2 -h 1 ) Bernoulli s Equation Finally, P 2, v 2, x 2, h 2, A 2 h 2 Initially, P 1, v 1, x 1, h 1, A 1

KE = 1/2 m (v 2 -v 1 ) 2 PE = mg (h 2 -h 1 ) Bernoulli s Equation W = KE + PE Leads to the equation of continuity... P + 1/2 ρ v 2 + ρ g h = constant The sum of pressure, kinetic energy per volume and potential energy per volume have the same value along all points in a streamline.

Wind Speed Vectors Vectors are arrows representing wind direction and speed.

Coriolis

Coriolis FORCE A. Force: due to a rotating frame of reference. B. Objects moving in a straight line with respect to the stars, will experience an apparent deflection to the RIGHT in the N.Hemisphere and an apparent deflection to the LEFT in the S. Hemisphere. C. The Coriolis force is strongest at the poles and zero at the equator. D. The Coriolis force is proportional to the speed. E. The "force" affects the direction NOT the speed. But since velocity is a vector, with both direction and speed, the velocity change is the same as acceleration and the Coriolis force is the culprit.

Coriolis Force Equation Relative to a carousel, someone walking on a carousel moves in a straight line with respect to the fixtures. Relative to others and equipment on the ground, the person moves in an arc as if affected by a force. The Coriolis Force F c = 2Ω v sin φ v = wind speed Ω = angular velocity φ = latitude (Earth rotation, 360 degrees/24 hours) (sin 0 = 0.0 equator, sin 90 = 1.0 poles)

F c = 2Ω v sin φ Coriolis Deflection Increase of the Coriolis Force with wind speed.

Density and Pressure The warmer air column is less dense. At the same height, the pressure is higher in the warmer air column.

Latitude Pressure Gradient At the same altitude, the pressure is higher on average in the warmer latitudes.

Temperature PGF versus Altitude

Global Circulation In the absence of rotation, air would tend to flow from the equator toward the poles. Hot, less dense air rising at the equator, becomes denser as it cools and descends at the poles, traveling back to tropical areas to heat up again.

Pressure Gradient Force Air flows from high pressure to low pressure, so on average, from the equators to the poles.

Geostrophic Flow PGF = Coriolis 1/ρ* P/ d = 2 Ω v sin φ The wind velocity is v = (1/ρ 2 Ω sin φ)* P/ d This is known as the geostrophic wind equation.

Geostrophic flow Remember that the coriolis force depends upon velocity. As air is accelerated by the PGF its speed increases and the coriolis deflection grows. Equilibrium is reached when the PGF and coriolis effect are equal.

Geostrophic flow With the inclusion of the Coriolis Force, air flows parallel to isobars of constant pressure.

Westerlies At mid latitudes, air moving from S. to N. in the northern hemisphere flows from west to east.

Bernoulli Winds

Friction retards wind speed near the surface due to topography, lowering the coriolis force. Therefore, wind direction is altered from parallel to isobars. Friction Effect

Cyclonic Flow

Low Pressure Cyclonic Winds

High Pressure Cyclonic Winds

Isobar Surface Map

Table 7.2: Summary of the properties of forces acting on air in the Earth s atmosphere Force Direction in which force acts Strength depends on Effect on air Balances Vertical Pressure Gradient Force Upward, from higher to lower pressure Magnitude of the vertical pressure gradient Accelerates air vertically toward lower pressure Hydrostatic balance when equal and opposite to gravitational force Horizontal Pressure gradient force Horizontally, from higher to lower pressure Magnitude of the horizontal pressure gradient Accelerates air horizontally Geostrophic balance when equal and opposite to Coriolis force Coriolis Force Frictional force To the right (left) of the wind direction in the Northern (Southern) Hemisphere Opposite the direction of the flow Wind speed and latitude The roughness of the underlying surface Affects wind direction, but no effect on wind speed Reduces air velocity, important primarily in boundary layer Geostrophic balance when equal and opposite to horizontal pressure gradient force Gravitational force Toward the center of the earth Essentially constant in the troposphere Accelerates air downward Hydrostatic balance when equal and opposite to vertical pressure gradient force.