2. Checking the necessary criteria for instability... Below are three Northern Hemisphere zonal wind fields that vary only in the north- south (y) direction; there is no variation with height, no variation with longitude, and no meridional component of the wind (v = 0 everywhere). Assume that the Coriolis parameter fis constant everywhere with a value of fo. Y I II. III. The zonal wind profiles for the sheared flows (cases | and II) and the point jet (case III) are given by the equations: U=A(1-y*) forcasel U=Asin(y) forcasell U=A(-|y) forcaselll A is amplitude, a positive constant. For each of the three cases, answer the following: (a) Calculate the relative vorticity from the wind profiles given. (b) Calculate the meridional gradients of vorticity. (] Qualitatively identify any regions or points at which Rossby waves can exist and state the direction they will propagate relative to the background flows above. (d) Explain whether each case has the potential for interacting Rossby waves to lead to an unstable amplification? (Do this by assessing whether the two necessary conditions for an instability to occur are met. If not, the flow is guaranteed to be stable.) (&) Now consider what might happen to your answers to parts (b), (c), and (d) when the planetary vorticity fis not constant, but instead varies meridionally at a rate df/dy = & Does the addition of the varying planetary vorticity have a stabilizing, destabilizing, or no effect on each case? (By adding a background vorticity gradient 5 to the one you calculated in part (b), how might your answers to parts (c) and (d) be revised, pending the particular magnitude of A and of course]