7.4 Pressure gradient force and Coriolis effect

Pressure gradient force and Coriolis effect are key players in atmospheric motion. They shape wind patterns, from local breezes to global circulation. Understanding these forces helps us grasp why winds blow and how weather systems form and move.

These forces don't act alone. They interact, creating complex wind patterns like trade winds and jet streams. By learning how they work together, we can better predict weather and understand the atmosphere's behavior on various scales.

Pressure gradient force and atmospheric motion

Fundamentals of pressure gradient force

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• Pressure gradient force (PGF) drives atmospheric motion resulting from pressure differences between locations
• PGF magnitude directly proportional to pressure difference and inversely proportional to distance between measurement points
• Acts from high to low pressure areas perpendicular to isobars on weather maps
• Determines initial speed and direction of air movement later modified by other forces
• Primary driver of horizontal and vertical air motions contributing to wind patterns and weather systems (thunderstorms, hurricanes)

Characteristics and effects of PGF

• In absence of other forces air would flow directly from high to low pressure (rarely occurs due to Earth's rotation and friction)
• PGF strength varies with pressure difference ($\Delta P$) and distance ($\Delta x$) according to the formula: $PGF = -\frac{1}{\rho} \frac{\Delta P}{\Delta x}$
• Influences both large-scale (global circulation patterns) and small-scale (local breezes) atmospheric phenomena
• Interacts with other forces like Coriolis effect and friction to create complex wind patterns (trade winds, jet streams)
• Vertical component of PGF balances gravity creating hydrostatic equilibrium in the atmosphere

Coriolis effect and wind direction

Mechanics of the Coriolis effect

• Apparent deflection of moving objects relative to Earth's rotating surface
• Affects path of air masses ocean currents and projectiles moving over long distances
• Deflects air to the right in Northern Hemisphere and left in Southern Hemisphere
• Magnitude dependent on latitude strongest at poles zero at equator
• Coriolis force proportional to speed of moving air mass and sine of latitude: $f = 2\Omega \sin(\phi)$ (where $\Omega$ is Earth's angular velocity and $\phi$ is latitude)

Impact on atmospheric circulation

• Responsible for cyclonic rotation in low-pressure systems (counterclockwise in Northern Hemisphere clockwise in Southern Hemisphere)
• Creates anticyclonic rotation in high-pressure systems (clockwise in Northern Hemisphere counterclockwise in Southern Hemisphere)
• Crucial for accurate weather prediction and analysis of global wind patterns (Hadley cells Ferrel cells)
• Influences formation and movement of large-scale weather systems (hurricanes mid-latitude cyclones)
• Contributes to the development of planetary waves (Rossby waves) in upper-level wind patterns

Applying pressure gradient and Coriolis effect

Geostrophic wind and balance

• Interaction between pressure gradient force and Coriolis effect results in geostrophic wind
• Geostrophic wind flows parallel to isobars above friction layer
• Geostrophic balance occurs when PGF and Coriolis force are equal and opposite resulting in steady-state wind flow
• Strength of geostrophic winds directly related to spacing of isobars (tightly packed isobars indicate stronger winds)
• Geostrophic wind speed calculated using the formula: $v_g = \frac{1}{f\rho} \frac{\Delta P}{\Delta n}$ (where $f$ is Coriolis parameter $\rho$ is air density and $\frac{\Delta P}{\Delta n}$ is pressure gradient)

Interpreting wind patterns

• In Northern Hemisphere winds circulate counterclockwise around low-pressure systems and clockwise around high-pressure systems
• Opposite circulation patterns occur in Southern Hemisphere
• Gradient wind flow accounts for curvature of isobars incorporating centripetal acceleration in addition to PGF and Coriolis effect
• Analyzing wind patterns requires examination of isobar spacing orientation and curvature on weather maps
• Consider latitude and hemisphere when interpreting wind direction and speed
• Thermal wind concept explains vertical wind shear in relation to horizontal temperature gradients

Wind flow balance: Pressure vs Friction vs Coriolis

Surface wind modifications

• Near Earth's surface friction disrupts geostrophic balance causing winds to cross isobars at an angle towards low pressure
• Angle at which surface winds cross isobars varies with surface roughness (10° over smooth surfaces like oceans 45° over rough terrain like mountains)
• Friction reduces wind speed in boundary layer decreasing Coriolis effect leading to new force balance
• Depth of friction layer varies with surface conditions and atmospheric stability (generally extends from surface to about 1 km in height)
• Surface drag coefficient influences magnitude of frictional force affecting wind speed and direction near ground

Vertical wind profile and Ekman spiral

• Above friction layer winds approach geostrophic balance as friction becomes negligible
• Ekman spiral describes change in wind direction and speed with height due to balance of PGF Coriolis effect and decreasing friction
• Wind veers (turns clockwise) with height in Northern Hemisphere backs (turns counterclockwise) in Southern Hemisphere
• Net transport of air in Ekman layer is 90° to the right of surface wind in Northern Hemisphere (left in Southern Hemisphere)
• Understanding interplay between forces crucial for predicting local wind patterns (sea breezes mountain-valley breezes) and behavior of weather systems in lower troposphere