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本文详细研究了正压准地转模式的谱这一经典而未完全解决的问题,取基流为平直的(y),得到离散谱即为通常的标准模;而实数域为连续谱,相应谱函数有界,但其微商无界而可积。文中指出,任意扰动可分解为两部份之和:与离散谱对应的部份φ′d(x,y,t)和与连续谱对应的部份φ′c(x,y,t)。利用离散谱的广义“加权正交性”可以方便地求出φ′d。证明当t→∞时,φ′c连同其能量E′c和y方向的尺度l_c趋向于零。文中还提出用有限差分法计算谱和谱函数,这方法保持原问题的整体性质以及不稳定判据。当格点数为有限时,虽然连续谱被歪曲为计算离散谱,但在相当长时段内φ′c的演变特性仍可得到正确反映,且当格距趋于零时,在内计算谱点越来越密,而趋于连续分布。
In this paper, the problem of classical quasi-geostrophic spectrum is studied in detail. The base flow is straight (y), and the discrete spectrum is the normal standard mode. The real number domain is continuous, The corresponding spectral function is bounded, but its derivative is unbounded and integrable. It is pointed out that arbitrary perturbation can be decomposed into two parts: φ’d (x, y, t) corresponding to discrete spectrum and φ’c (x, y, t) corresponding to continuous spectrum. Using the generalized “weighted orthogonality” of discrete spectrum, φ’d can be easily found. It is proved that when t → ∞, φ’c tends to zero along with its energy E’c and y-scale l_c. The paper also proposes to use the finite difference method to calculate the spectral and spectral functions, which preserves the overall nature of the original problem and the instability criterion. When the number of grid points is finite, although the continuum is distorted to calculate the discrete spectrum, the evolution characteristics of φ’c can still be correctly reflected for a long period of time, and when the grid spacing tends to zero, The more dense, and tend to be continuous distribution.