01.Kinematicsofthehorizontalwindfield.pptVIP

* Kinematics of the horizontal wind field (Kinematics: from the Greek word for ‘motion’, a description of the motion of a particular field without regard to how it came about or how it will evolve) y N W S E x V v u To derive a mathematical expression for the key kinematic properties of the wind field we will use the coordinate system on the right. y x0, y0 x, y We will use Taylor Expansion to estimate the wind field at an arbitrary point x,y from the wind at a nearby point x0, y0 Peform a 2D Taylor expansion: For simplicity, lets assume that x0, y0 is the origin 0,0 And that we can obtain an adequate estimate of u,v by retaining only the first derivatives. We are assuming that over the small distance the u and v field vary linearly. Then… Let’s take a simple step and write each derivative term as (for example) : Now we will write two nonsense equations From before: (1) (2) (3) (4) Now we add (1) and (3). We also separately add (2) and (4). Then we rearrange the terms and get………… Divergence Relative Vorticity Stretching Deformation Translation Shearing Deformation Any wind field that varies linearly can be characterized by these five distinct properties. Non-linear wind fields can be closely characterized by these properties. x y Translation The effect of translation on a fluid element: Change in location, no change in area, orientation, shape x y Divergence (d 0) Convergence (d 0) The effect of convergence on a fluid element: Change in area, no change in orientation, shape, location x y Positive (cyclonic) vorticity (? 0). Negative (anticyclonic) vorticity (? 0) The effect of negative vorticity on a fluid element: Change in orientation, no change in area, shape, location x y E-W Stretching Deformation (D1 0). N-S Stretching Deformation (D1 0). The effect of stretching deformation on a fluid element: Change in shape, no change in area, orientation, location x y SW-NE Shearing Deformation (D1 0). NW-SE Shearing Deformation (D1 0). The