1. The 3-dimensional vorticity 5 =Vxu is a vector that is equal to the curl of the vector field defining the magnitude and direction of the wind u at every point in space. In a Cartesian coordinate system with u=(u,v,w) corresponding to the components of the wind in the x,y (horizontal) and z (vertical) coordinates, respectively it is defined by the equation i j k a a a dx dy az Vxur (1.1) u V W (1a) Use (1.1) to define the component of vorticity in the direction of the unit vector i which points in the direction of increasing x. (16) By sketching wind vectors associated with (v,w) on an y-z cross-section of a plane with constant x values, (as shown below) give an example of a vector wind field that has a positive i- component. (Use your answer from (1a) as a guide and you should only need to plot 4-8 vectors to give the general idea). Assume that w=0 at z=0 and that z=0 where the y-axis crosses the z- axis. y 1. The 3-dimensional vorticity 5 =Vxu is a vector that is equal to the curl of the vector field defining the magnitude and direction of the wind u at every point in space. In a Cartesian coordinate system with u=(u,v,w) corresponding to the components of the wind in the x,y (horizontal) and z (vertical) coordinates, respectively it is defined by the equation i j k a a a dx dy az Vxur (1.1) u V W (1a) Use (1.1) to define the component of vorticity in the direction of the unit vector i which points in the direction of increasing x. (16) By sketching wind vectors associated with (v,w) on an y-z cross-section of a plane with constant x values, (as shown below) give an example of a vector wind field that has a positive i- component. (Use your answer from (1a) as a guide and you should only need to plot 4-8 vectors to give the general idea). Assume that w=0 at z=0 and that z=0 where the y-axis crosses the z- axis. y