最简化的两变量草原生态动力学模式

本文建立了一个简化的草原生态动力学模式,它由单位面积上单一草种的草生物量和土壤湿度这两个变量组成,能够描述它们的相互作用,而其他因子,诸如土壤物理、化学特性、降水量、灌溉量、光照、温度以及消耗率(放牧和鼠、虫害等),则以参数形式出现在这组常微分方程中。定性分析表明:在已知的常定的(即无季节变化的)情况下,草生物量由稳定的平衡态所决定;对于只与土墒有弱相互作用的草种,草量连续依赖于隆水量;而对于与土墒有强相互作用的草种,则存在着临界降水量,大于临界值时有丰富草量,小于临界值时为荒漠。模式中还可给出在降水量一定情况下草原能承受的最大消耗率(放牧率),小于此值者草原可以恢复,大于此值则草原退化为荒漠。     

正压准地转模式的谱和扰动的演变

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。     

非均匀基流上扰动的演变

本文用WKBJ方法统一处理了叠加在非均匀气流上的小扰动随时间的演变问题,得到了二维正压大气中重力-惯性波(快波)和涡旋波(慢波)具有不同的演变规律.前者发展时伴随着波长变短,衰减时波长变长;涡旋波与此正相反.由此可推知:在实际大气中只有短波长的快波比较显著,波长较长的快波不明显,从而不易观测到.还可解释:一个移动性的高空槽脊发展时它加宽,而衰减时总以收缩(波长变短)北退(强度减小)的形式出现.上述两种波的不同演变特性,主要由气流的不均匀性和波动的类别所决定.对于科氏参数为零的情况也对.科氏力的影响只是给波包以附加的弥散,给能量变化过程以次要的影响,并使慢波满足地转风关系.     

Maximum Simplified Dynamic Model of Grass Field Ecosystem With Two Variables

Based on general consideration and analysis, a maximum simplified dynamic model of grass field ecosystem with a single species is developed. The model consists of two variables: grass biomass of grass field per unit area and soil wetness, and is suitable for describing their mutual interaction. Other factors such as physical-chemical characteristics of soil, precipitation, irrigation, sunlight, temperature and consumers, are taken into account as parameters in the dynamical system. Qualitative analysis of the model shows that grass biomass of a possible ecological regime is determined by the stable equilibrium state of the dynamical system. For the grass species interacting weakly with soil wetness the grass biomass continuously depends on the precipitation. While, for a species interacting strongly with soil wetness, grass biomass is abundant if precipitation is larger than some critical value; otherwise, it becomes a desertification regime with very little or even zero grass biomass. The model also sh     

THE SPECTRA OF BAROTROPIC QUASIGEOSTROPHIC MODEL AND THE EVOLUTION OF DISTURBANCES

The spectra of linearized barotropic quasigeostrophic model is one of classical but not yet completelysolved problems in dynamic meteorology. This paper is devoted to a detailed investigation of this problem.It is obtained that in the case of zonal basic flow μ(y), there exist two types of spectra, the discrete andcontinuous. Each discrete spectrum (eigenvalue) gives an eigenfunction (normal mode); and the real num-bers in the interval [μ_(min), μ_(max)] are the continuous spectra; every point c ? [μ_(min), μ_(max)] gives a spectralfunction which is bounded and whose derivative is unbounded but integrable. Every disturbance can berepresented as a linear combination of two parts, ψ'(x, y, t) and ψ'(x, y, t), the former is expressed bythe discrete spectra, and the latter by the continuum. ψ'_d can be easily derived from the initial conditionby the use of the generalized "weighted orthogonality" of normal modes. It is also proved that ψ'_c as wellas its energy E'_c and mean y-direction scale l_c a