Abstract
§3. Relation between Vorticity, Convergence and Horizontal Pressure Field.
In chapter 2, we discussed the fundamental equation of ψ derived from the equations of motion by cross-differentiation. But strictly speaking the above discussion is not satisfactory, because we can not take Q as a known function. In order to treat the problem satisfactorily, we must assumo both ζ and Q as unknown functions. Indeed, ζ and Q are reciprocal in the rotating earth-atmosphere.
In the prescnt chapter, we discuss equations: which are derived from the equations of motion. To elucidate only the dynamics of nacsent cyclones, all terms which are squares and products of velocities and their derivatives are neglected. Assuming that the left hand sides of the above cquations represent those of fundamental state and known functions, we discussed relations between f1, f2 and ζ, Q. The main results are as follows:
(1) If eddy viscosity vanishes and f1 and f2 are timely constant, ζ and Q depend only on f1 and f2 respectively.
(2) If f1 and f2 vanish. ζ and Q osciilate and their amplitudes damp exponentially in our atmosphere.
(3) If f1 and f2 are variable, ζ and Q depend both on f1 and f2. Further, when the variation of f1 and f2 are comparable with one day, the effects of f1 and f2 on ζ and Q are comparable. The effect of viscosity on this point is small compared with that of variablity of f1 and f2 in our atmosphere.
