A review of: “Problems of Solar and Stellar Oscillations. Iau Colloquium No. 66. Edited by D. O. Gough. D. Reidel Publishing Company, 493 pp. Df1195.00/U.S. $84.50 (ISBN 90-277-1554-8). 1983.”     

Irene M. Moroz 《地球物理与天体物理流体动力学》2013,107(3-4):313-314

Abstract

The model equations describing two-dimensional thermohaline convection of a Boussinesq fluid in a rotating horizontal layer are known to support multiple instabilities, depending on the values of certain control parameters (Arneodo et al., 1985). Most of these multiple instabilities have already been studied for double or triple diffusive convection, where behaviours ranging from simple steady to irregular motions have been found. Here we consider the one remaining bifurcation mentioned by Arneodo et al. (1985): the interaction between a steady and an oscillatory convection roll when the linear spectrum for a single wavenumber comprises one zero and one pair of purely imaginary eigenvalues. The method of centre manifolds and normal forms is used to derive evolution equations for the amplitudes of the convection rolls close to bifurcation and the behaviours associated with the equations is discussed.  相似文献   

Thermal convection of an internally heated infinite prandtl number fluid in a spherical shell     

Alexander P. Anufriev 《地球物理与天体物理流体动力学》2013,107(1):65-83

  相似文献   

Instability of flows near the onset of convection in a rotating layer with stress-free horizontal boundaries     

Olga Podvigina 《地球物理与天体物理流体动力学》2013,107(3):299-326

We investigate instability of convective flows of simple structure (rolls, standing and travelling waves) in a rotating layer with stress-free horizontal boundaries near the onset of convection. We show that the flows are always unstable to perturbations, which are linear combinations of large-scale modes and short-scale modes, whose wave numbers are close to those of the perturbed flows. Depending on asymptotic relations of small parameters α (the difference between the wave number of perturbed flows and the critical wave number for the onset of convection) and ε (ε² being the overcriticality and the perturbed flow amplitude being O(ε)), either small-angle or Eckhaus instability is prevailing. In the case of small-angle instability for rolls the largest growth rate scales as ε^8/5, in agreement with results of Cox and Matthews (Cox, S.M. and Matthews, P.C., Instability of rotating convection. J. Fluid. Mech., 2000, 403, 153–172) obtained for rolls with k = k _c . For waves, the largest growth rate is of the order ε^4/3. In the case of Eckhaus instability the growth rate is of the order of α².  相似文献   

Convection in rotating annular channels heated from below. Part 1. Linear stability and weakly nonlinear mean flows     

Xinhao Liao†  Yingli Chang 《地球物理与天体物理流体动力学》2013,107(6):445-465

Convection in a Boussinesq fluid in an annular channel rotating about a vertical axis with lateral rigid sidewalls, stress-free top and bottom, uniformly heated from below is investigated. The sidewalls are assumed to be either perfectly insulating or conducting. Three different types of convection are identified when the channel is rotating sufficiently fast: (i) global oscillatory convection preferred for small Prandtl numbers in channels with intermediate or large aspect ratios (width to height ratio), (ii) wall-localized oscillatory convection representing the most unstable mode for moderate or large Prandtl numbers in channels with intermediate or large aspect ratios and (iii) global stationary convection preferred in channels with sufficiently small aspect ratios regardless of the size of the Prandtl number. The corresponding weakly nonlinear problem describing differential rotation and meridional circulation is also examined, showing that geostrophic, multiple-peaked (two prograde and two retrograde) differential rotation can be maintained by the Reynolds stresses in wall-localized convective eddies in a rapidly rotating channel.  相似文献   

航道对多方向波传播影响   总被引：2，自引：0，他引：2  

陈汉宝  刘海源 《海洋工程》2005,23(4):27-32

应用Boussinesq方程对不同入射角、不同方向集中度的波浪与航道的相互作用进行模拟,得到了航道的折射影响规律以及不同入射角、不同方向集中度的波浪对航道作用的差别.结果对试验研究及工程实践有指导意义.  相似文献   

Velocity predictions for shoaling and breaking waves with a Boussinesq-type model     

Franoise Ozanne  Andrew J. Chadwick  David A. Huntley  David J. Simmonds  John Lawrence 《Coastal Engineering》2000,41(4)

In this paper, the performance of a 1-D Boussinesq model is evaluated against laboratory data for its ability to predict surf zone velocity moments. Wave evolution over a plane beach and a complex bathymetry both extending into the surf-zone is examined for six cases. For the plane beach, these comprise two cases, a spilling and a plunging cnoidal wave. For the complex bathymetry, these comprise four cases of longer and short wavelengths (spilling and plunging breakers), with regular and irregular periodicity. The model evaluation places emphasis on parameters of the wave field that could be used for the prediction of sediment transport; orbital velocity, undertow, velocity skewness, kurtosis and asymmetry. It is found that, despite an overestimation of the depth-averaged horizontal velocity in the regular waves cases, the predicted higher order velocity moments and undertow are in good agreement with the laboratory data. A bispectral analysis demonstrates that the nonlinear transfers of energy amongst the low order harmonics are well reproduced, but energy exchanges with the higher harmonics are less well predicted. As a result, the model handles velocity moments better in the shorter wave tests than in the long wave cases where triad interactions are stronger. Of the four parameters describing wave breaking, the model behaviour is most sensitive to the critical wave front slope φ_B, especially with regard to velocity skewness and kurtosis predictions. It is also found that increasing the thickness of the surface roller for the case of plunging breakers improves the model's performance.  相似文献   

地形与流对水平无旋浅水波的影响   总被引：1，自引：0，他引：1  

孙明光  高虎山 《海洋工程》2000,18(2):62-67

本文在水平无旋及Boussinesq假设之下,导出了水面变化与水平速度场耦合方程组,以及相应的压力与垂向速度解析表示式。通过数值方法求得水面变化及某一特定水深的水平速度分布之后,压力分布及其余水深的速度分布即可由简单计算得到。由色散关系式可知,不同水深的长波色散关系在O(ε)近似之下是等同的。粘性的存在会使波高随时间的增加而衰减,但粘性与底斜率的耦合又可能使波高增长,形成不稳定;计算及分析说明,当同向流增大时,波速增大,波长增大,波高会增加;而水深减少,使波速减少,波长缩短,振幅增加。  相似文献   

不规则波Boussinesq型方程的造波,消波和反射   总被引：5，自引：1，他引：4  

朱良生  洪广文 《海洋工程》2000,18(4):43-48

对前人提出的造波、消波和反射边方法分析表明,其方法是极浅水波近似,不适用于任意水深的水域,本文就任意水深变化Ｂｏｕｓｓｉｎｅｓｑ型方程,提出了不规则波新的造波原理、方法和消波边界及部分反射边界波动方程,试验表明,本文提出的造波、消波和反射方程有效而可靠的。  相似文献   

Modelling of water table variation in response to time-varying recharge from multiple basins using the linearised Boussinesq equation     

S. N. Rai  A. Manglik 《Journal of Hydrology》1999,220(3-4):141-148

A mathematical model is presented to describe the variations of the water table in an unconfined aquifer due to time-varying recharge applied from four rectangular basins. The model is developed by solving the linearised Boussinesq equation using the extended finite Fourier cosine transform. The time-varying recharge rate is approximated by a number of piecewise linear elements of different lengths and slopes depending on the nature of the variation in recharge rate. Application of this model for the prediction of water table fluctuations and in the sensitivity analysis of various controlling parameters on the aquifer response is demonstrated in an example.  相似文献   

一种近岸区波浪破碎模型   总被引：7，自引：0，他引：7  

李绍武  王尚毅  柴山知也 《海洋学报》1999,21(1):103-110

从波浪破碎的能量关系入手,以紊流能量方程为基础,考虑破碎区内单个波在不同破碎阶段所提供的紊动能量强度的变化过程,提出了一种波浪破碎模式.通过将这一模型引入Boussinesq方程中,初步建立了一种近岸区波浪变形数学模型,并用波浪水槽实验资料对模型模拟波高和平均水位的情况进行了初步验证,得到了良好的结果.  相似文献