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Unformatted text preview: Atmospheric Dynamics Leila M. V. Carvalho Dept. Geography, UCSB Review: Kinematic of the horizontal flow Streamlines: lines parallel to the horizontal velocity V at a particular level and at a particular instant in time http://weather.unisys.com/surface/sfc_con_stream.html Natural Coordinates: Y X n n s s n and s are natural coordinates (perpendicular and parallel to the flow Definitions Sheared with no curvature, no diffluence, stretching or divergence Rotation with cyclonic curvature (NH) and cyclonic shear , no diffluence or stretching (and divergence Radial flow with velocity directly proportional to radius. Diffluence, stretching, divergence and NO CURVATURE Hyperbolic flow: difluence and straching, no divergence (terms cancel). Shear and curvature cancel (vorticity free) What is going on here? Y X n n s s Forces in the Atmosphere Equation of motion: ( First and second Laws of Newton ) Real forces (independent on the rotating system): gravity, pressure gradient force and frictional force Apparent forces due to rotation: apparent centrifugal force (affects gravity) and Coriolis (correction for horizontal movements). Apparent forces: Centrifugal force: Where RA is vector perpendicular to axis of rotation and is angular velocity of earth Combine with gravity to define "effective" gravity Coriolis force: Coriolis force takes care of rotational effects caused by motion relative to surface At rest over the Earth surface will have cetrifugal acceleration= 2R. Suppose it moves eastward with speed u : the centrifugal force would increase to: Centrifugal force= R R u 2 + R Coriolis force: 2 2 2 2 2 R R u R uR R R R u + + = + Expanding the equation we have now: Centrifugal force due to rotation of the Earth (independent of the relative Deflecting forces that act outward along the vector R Synoptic scale motions u<< R: Last term can be neglected in a first approximation Coriolis Force Coriolis force can be divided into vertical and meridional components : R R uR 2 cos 2 u sin 2 u A relative motion along the eastwest coordinate will produce an acceleration in the northsouth direction given by: sin 2 u dt dv Co  = And vertical acceleration given by: cos 2 u dt dw Co = To the right of the movement in the NH Suppose now that a particle initially at rest on the Earth is set in motion equatoward by impulsive forces R As it moves equatorward it will conserve its angular momentum in the absence of torques: a relative westward velocity must develop R + R If we expand the right hand side and neglect second order differentials (and assume that << R R and solve for , : u we get o a...
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 Fall '09
 leila
 Geography

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