有关边界层问题中一类奇异积分方程新的存在性结果

对边界层理论新结果中出现的一类奇异积分方程w（t）=∫1 t（1-s）（λ＋λs＋s）/w（s）ds＋（1-t）∫t 0s/w（s）ds,t∈（0,1）进行讨论，并得出了上述方程在λ∈（-1/2,0）上正解存在性的新结果。     

混合对流方程的凸解的某些性质

为了研究产生于流体力学边界层理论的混合对流方程解的性质,通过研究与混合对流方程等价的奇异积分方程正解的存在性和单调性,获得了混合对流方程凸解的存在性和凸解模的上下界,并将这些性质应用于估计混合对流方程中剪应力函数模的上下界．     

Huxley方程的定性分析

运用微分方程定性理论,对Huxley方程进行定性分析,得到了方程在有限奇点的稳定性及极限环不存在性的结论,并借助Maple软件做出相图．     

RESPONSE OF THE OCEAN UPPER MIXED LAYER TO ATMOSPHERIC FORCING

Using a one-dimension Turbulence Kinetic Energy(TKE)mixed layer model based on a simple eddyKinetic energy parameterization of the ocean upper mixed layer,some numerical examinations are intro- duced in this paper.These examination results show that the TKE ocean mixed layer model can respondwell to the effect of atmospheric forcing on the ocean upper mixed layer.The joint effect of wind stressand heat exchange on the ocean upper layer has nonlinear characteristics.The adjustment time of the re-sponse of the ocean upper mixed layer to the atmospheric forcing is about 12 hours in this model.     

Wave breaking on turbulent energy budget in the ocean surface mixed layer

As an important physical process at the air-sea interface, wave movement and breaking have a significant effect on the ocean surface mixed layer （OSML）. When breaking waves occur at the ocean surface, turbulent kinetic energy （TKE） is input downwards, and a sublayer is formed near the surface and turbulence vertical mixing is intensively enhanced. A one-dimensional ocean model including the Mellor-Yamada level 2.5 turbulence closure equations was employed in our research on variations in turbulent energy budget within OSML. The influence of wave breaking could be introduced into the model by modifying an existing surface boundary condition of the TKE equation and specifying its input. The vertical diffusion and dissipation of TKE were effectively enhanced in the sublayer when wave breaking was considered. Turbulent energy dissipated in the sublayer was about 92.0% of the total depth-integrated dissipated TKE, which is twice higher than that of non-wave breaking. The shear production of TKE decreased by 3.5% because the mean flow fields tended to be uniform due to wave-enhanced turbulent mixing. As a result, a new local equilibrium between diffusion and dissipation of TKE was reached in the wave-enhanced layer. Below the sublayer, the local equilibrium between shear production and dissipation of TKE agreed with the conclusion drawn from the classical law-of-the-wall （Craig and Banner, 1994）.     

Characteristics of intraseasonal variations in the mixed layer of “warm pool” areas

Observational data obtained during the TOGA-COARE IOP in the “warm pool” area of the Western Tropical Pacific were used to analyze some characteristics of the intraseasonal variations in the mixed layer. The influence of westerly burst and rainfall on SST, salinity and mixed layer depth are discussed. There are two pairs of counteracting processes in the “warm pool” mixed layer: (1) The increase of mixed layer depth caused by local westerly bursts and the decrease of mixed layer depth caused by larger scale easterly relaxation; (2) the vertical mixing by local wind and the strong stratification due to rainfall in the mixed layer. Some possible mechanisms through the interactions between the intraseasonal time scale variations of the oceanic mixed layer and atmospheric low frequency oscillations are revealed. Supported by National Natural Science Foundation of China (49276250) and LASG of Beijing.     

基于单齿侵入理论的牙轮钻头钻速方程

考虑井底水平地应力、钻井流体压力及地层孔隙压力,基于单齿侵入理论推导单齿侵入井底岩石的侵深公式,建立纯滚动锥形齿、楔形齿和滚动、剪切复合运动锥形齿等牙轮钻头的钻速方程.通过实验分析刃尖角、井底液柱压力对单齿侵入深度的影响,以及转速、轴向载荷对微钻头、牙轮钻头机械钻速的影响.结果表明:随着牙齿刃尖角的增大,锥形齿和楔形齿的侵深呈指数递减趋势;随着井底液柱压力的增大,牙齿侵入深度呈指数递减趋势,其中锥形齿降低速率大.在软到中硬地层中,牙齿侵入深度大,冲击侵入、回转剪切复合破岩方式的破岩效率高;在硬度地层中,牙齿侵入深度小,纯滚动冲击侵入破岩效率高.为分析实钻时牙轮钻头的机械钻速提供计算方法.     

Analytical solution of boundary integral equations for 2-D steady linear wave problems

Based on the Fourier transform, the analytical solution of boundary integral equations formulated for the complex velocity of a 2-D steady linear surface flow is derived. It has been found that before the radiation condition is imposed, free waves appear both far upstream and downstream. In order to cancel the free waves in far upstream regions, the eigenso-lution of a specific eigenvalue, which satisfies the homogeneous boundary integral equation, is found and superposed to the analytical solution. An example, a submerged vortex, is used to demonstrate the derived analytical solution. Furthermore, an analytical approach to imposing the radiation condition in the numerical solution of boundary integral equations for 2-D steady linear wave problems is proposed.     

Blasius方程中临界值的分析估计

证明了流体力学边界层理论中著名的Blasius方程的一个新性质,它在二维平板流的研究中具有重要的作用,由此建立它的积分形式,并给出方程中的临界值βc的分析估计。     

Blasius方程中临界值的分析估计

证明了流体力学边界层理论中著名的Blasius方程的一个新性质,它在二维平板流的研究中具有重要的作用,由此建立它的积分形式,并给出方程中的临界值βc的分析估计。