Nonlinear Processes in Geophysics on the Problem of Optimal Approximation of the Four-wave Kinetic Integral
Nonlinear Processes in Geophysics on the Problem of Optimal Approximation of the Four-wave Kinetic Integral
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地球物理非线性过程中四波运动积分的最优逼近问题
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通讯作者：
L. Farina
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作者：
V. G. Polnikov;L. Farina
讨论了Hasselmann非线性动力学积分的解析和数值近似的优化问题。考虑到动力学积分的一般表达式，给出了获得最佳逼近的原则。从这一点考虑，最广为接受的近似，如离散相互作用近似（DIA）（ZPA），具有相同的根源。它们之间的唯一区别是，本质上，相互作用波的4波配置的选择。为了评价2-D非线性能量传递的任何近似的质量，构造了相对误差的数学度量，并假设了近似效率的含义。利用这些特点，它表明DIA具有更好的精度和效率比ZPA。根据最佳逼近的一般思想，并通过使用所介绍的措施，提出了更有效和更快的版本DIA。
The problem of optimization of analytical and numerical approximations of Hasselmann's nonlinear kinetic integral is discussed in general form. Considering the general expression for the kinetic integral, a principle to obtain the optimal approximation is formulated. From this consideration it follows that the most well-accepted approximations , such as Discrete Interaction Approximation (DIA) (ZPA), have the same roots. The only difference among them is, essentially, the choice of the 4-wave configuration for the interacting waves. To evaluate a quality of any approximation for the 2-D nonlinear energy transfer, a mathematical measure of relative error is constructed and the meaning of approximation efficiency is postulated. By the use of these features it is shown that DIA has better accuracy and efficiency than ZPA. Following to the general idea of optimal approximation and by using the measures introduced, more efficient and faster versions of DIA are proposed.