ATM OCN Fall ATM OCN Fall 1999 LECTURE 17 THE THEORY OF WINDS: PART II - FUNDAMENTAL FORCES A. INTRODUCTION –How do winds originate? –What factors influence the winds?

ATM OCN Fall B. EXPLANATIONS of ATMOSPHERIC MOTION F Practical Problems F Historical Concepts F Forces of Motion & Newton's Laws

ATM OCN Fall NEWTON’S EQUATIONS of MOTION F 1st Law (Conservation of Inertia) Object at rest will remain at rest or object moving at constant velocity will continue until acted upon by a net force. F 2nd Law Force = mass x acceleration. F 3rd Law For every action, an equal & opposite reaction exists.

ATM OCN Fall B. EXPLANATIONS of ATMOSPHERIC MOTION (con’t) F Implications of Newtonian Laws F Vectors, Forces and Units –Speed or magnitude of velocity [mph or meters per second, etc.] –Acceleration [ft/sec/sec or meter/sec 2 ] –Force [pounds, or Newtons]

ATM OCN Fall C. DESCRIBING ATMOSPHERIC MOTION F Reasons for Atmospheric Motions: –Buoyancy Effects; –Dynamic Effects. F Complications involved with Atmospheric Motion: –Spherical planet; –Rotating planet & non-inertial frame of reference.

ATM OCN Fall DESCRIBING ATMOSPHERIC MOTION (con’t) F Three-Dimensional Equation of Motion for the Atmosphere –A vector equation; –Entails specification of all forces per unit mass (i.e., equivalent to acceleration); –All forces do not act alone; –Vector sum of individual forces equals net force.

ATM OCN Fall Numerical Weather Prediction

ATM OCN Fall Numerical Weather Prediction

ATM OCN Fall Numerical Weather Prediction

ATM OCN Fall FORCES ASSOCIATED WITH ATMOSPHERIC MOTION F Following forces influence motion of air parcels: –Pressure Gradient Force –Gravitational Force or Gravity –Coriolis Effect or "Force" –Frictional Force or Friction –Centripetal Force or more specifically --

ATM OCN Fall PRESSURE GRADIENT FORCE F Generated by differences in pressure within a fluid element; F Responsible for initiation of all air motion; F A 3-dimensional vector that has:

ATM OCN Fall PRESSURE GRADIENT FORCE (con’t) F Magnitude of pressure gradient force vector depends: –directly upon difference in pressure over a given distance (i.e., slope or grade equals “pressure gradient”). F Direction of pressure gradient force vector is: –from High pressure to Low pressure, –along steepest direction of pressure gradient.

ATM OCN Fall GRAVITATIONAL FORCE or GRAVITY F Produced by mutual physical attraction between massive bodies; F Gravity refers to acceleration; F Acts continuously, regardless of motion; F A vector quantity that has:

ATM OCN Fall GRAVITATIONAL FORCE or GRAVITY (con’t) F Magnitude of gravity vector depends upon: –Mass of earth & object; –Distance between two objects (inverse square relationship). – [NOTE: Issac Newton quantified relationship] –Usually gravity is assumed 32 ft/s 2 = 9.8m/s 2 F Direction of gravity vector is –toward vicinity of earth’s center (i.e., essentially downward).

ATM OCN Fall PRESSURE GRADIENT FORCE (con’t)

ATM OCN Fall PRESSURE GRADIENT FORCE (con’t)

ATM OCN Fall CORIOLIS EFFECT or FORCE F Produced by earth’s rotation; F A “fictitious force” used to explain apparent deflection of moving object on a rotating frame of reference;

ATM OCN Fall CORIOLIS EFFECT or FORCE (con’t)

ATM OCN Fall CORIOLIS EFFECT or FORCE (con’t)

ATM OCN Fall CORIOLIS EFFECT or FORCE F Produced by earth’s rotation; F A “fictitious force” used to explain apparent deflection of moving object on a rotating frame of reference; F Acts only after motion is initiated; F Can only modify direction of motion; F A 3-dimensional vector, but consider only horizontal component described by:

ATM OCN Fall CORIOLIS EFFECT or FORCE (con’t) F Magnitude of horizontal Coriolis force vector depends upon: –Rotation rate of earth (Direct relationship); –Speed of object; (Direct relationship) –Latitude (specifically, sine of latitude).

ATM OCN Fall CORIOLIS EFFECT or FORCE (con’t) F Direction of horizontal component of Coriolis force vector: –Causes a deflection of moving object to right of direction of motion in Northern Hemisphere; but –Deflects moving object to left of intended motion in Southern Hemisphere.

ATM OCN Fall FRICTIONAL FORCE or FRICTION F Produced by “viscosity” (interactions of moving fluid elements with one another or with a boundary surface) due to: –random molecular motions; –large random turbulent motions of fluid associated with either: u thermal turbulence u mechanical turbulence

ATM OCN Fall FRICTIONAL FORCE (con’t) F Acts only after motion is initiated; F Acts to retard motion; F Magnitude of friction force vector depends upon: –Speed of motion of fluid; –Type of surface, e.g., “surface roughness”. F Direction of friction force vector is –opposite motion vector.

ATM OCN Fall CENTRIPETAL FORCE F Produces curved motion; F Opposite the “centrifugal force”; F Acts only after motion is initiated; F In reality, a net force Used to describe imbalance of other forces in curved motion; F Centripetal force vector is described by:

ATM OCN Fall CENTRIPETAL FORCE (con’t.) F Magnitude of centripetal force vector depends upon: –Speed of instantaneous motion (a direct relationship); –Radius of curvature (an inverse relationship). F Direction of centripetal force vector is –inward toward center of curvature.

ATM OCN Fall SUMMARIZING F A 3-D Equation of Motion for Atmosphere (in word form) : Net force = Pressure gradient force + gravitation force + Coriolis force + friction. F Notes: –The above is a vector equation! –Since a unit mass is used, force is equivalent to an acceleration.