. Collected reprints, Essa Institute for Oceanography. Oceanography 752 MONTHLY WEATHER REVIEW Vol. 95, No. 11 so that the effect of operating with d/dt is just the effect of multiplying by if3. An operator formed as a "function" J (d/dt) has, on the operand Ee'^'+*), the effect of multi- plying by /(?/?), for the operand Ee'^'+v the operator d/dt "takes on the value" i/3. In general, the operands will not be of the form £V!*; however, at any time t for which the operand is not zero, there is an exponential function which fits most closely to the operand. If t
. Collected reprints, Essa Institute for Oceanography. Oceanography 752 MONTHLY WEATHER REVIEW Vol. 95, No. 11 so that the effect of operating with d/dt is just the effect of multiplying by if3. An operator formed as a "function" J (d/dt) has, on the operand Ee'^'+*), the effect of multi- plying by /(?/?), for the operand Ee'^'+v the operator d/dt "takes on the value" i/3. In general, the operands will not be of the form £V!*; however, at any time t for which the operand is not zero, there is an exponential function which fits most closely to the operand. If the values of E, /3, of the approximating exponential do not rapidly change with time, tl u it i> reasonable to approximate d/dt with the value i|8. The values of E, /3, depend on the operands and the time t for which the "evaluation of d/dt" is performed and are different for the operands M and R. If /3 is real, so that the opera nd is neither increasing or decreasing in value, the values of G and H will be finite and bounded. Figures 19 a-b give the real and imaginary parts of G and H against a2, with a2 = iD2(j-\-fi)/v (, replacing d/dt by i/3). These figures indicate that a linear approxima- tion to G and H may be acceptable, provider ji is not large. We first examine our experimental computations to determine for which values of /3 the actual oper- ands approximate exponentials. (If M=E W+*\ then dM/dl=ipM, so 0=(l/iM)dM/dt where Mis i egarded as a complex valued function of time and space.) Empirically it was noticed that the transport field usually consists of a train of vortices along the storm's path; in general, these vortices do not travel or increase in strength with any great rapidity, suggesting that for the trans] ort operand M, the value of /3 remains small, and a linear approxima- tion may be acceptable. The storm model used in this study is a previously determined analytic function, and moves with a uniform rectilinear motion. For this case, t
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