Influence of the earth rotation on the interfacial wave solutions and wave-induced tangential stress in a two-layer fluid system

Interfacial waves and wave-induced tangential stress are studied for geostrophic small amplitude waves of two-layer fluid with a top free surface and a flat bottom. The solutions were deduced from the general form of linear fluid dynamic equations of two-layer fluid under the f-plane approximation, and wave-induced tangential stress were estimated based on the solutions obtained. As expected; the solutions derived from the present work include as special cases those obtained by Sun et al. (2004. Science in China, Set. D, 47(12): 1147-1154) for geostrophic small amplitude surface wave solutions and wave-induced tangential stress if tire density of the upper layer is much smaller than that of the lower layer. The results show that the interface and the surface will oscillate synchronously, and the influence of the earth's rotation both on the surface wave solutions and the interfacial wave solutions should be considered.

Higher-order Boussinesq-type equations for interfacial waves in a two-fluid system

Interfacial waves propagating along the interface between a three-dimensional two-fluid system with a rigid upper boundary and an uneven bottom are considered. There is a light fluid layer overlying a heavier one in the system, and a small density difference exists between the two layers. A set of higher-order Boussinesq-type equations in terms of the depth-averaged velocities accounting for stronger nonlinearity are derived. When the small parameter measuring frequency dispersion keeping up to lower-order and full nonlinearity are considered, the equations include the Choi and Camassa's results (1999). The enhanced equations in terms of the depth-averaged velocities are obtained by applying the enhancement technique introduced by Madsen et al. (1991) and Schaffer and Madsen (1995a). It is noted that the equations derived from the present study include, as special cases, those obtained by Madsen and Schaffer (1998). By comparison with the dispersion relation of the linear Stokes waves, we found that the dispersion relation is more improved than Choi and Camassa's (1999) results, and the applicable scope of water depth is deeper.

Rossby waves with linear topography in barotropic fluids

Rossby waves are the most important waves in the atmosphere and ocean, and are parts of a large-scale system in fluid. The theory and observation show that, they satisfy quasi-geostrophic and quasi-static equilibrium approximations. In this paper, solitary Rossby waves induced by linear topography in barotropic fluids with a shear flow are studied. In order to simplify the problem, the topography is taken as a linear function of latitude variable y, then employing a weakly nonlinear method and a perturbation method, a KdV (Korteweg-de Vries) equation describing evolution of the amplitude of solitary Rossby waves induced by linear topography is derived. The results show that the variation of linear topography can induce the solitary Rossby waves in barotropic fluids with a shear flow, and extend the classical geophysical theory of fluid dynamics.

A kind of extended Korteweg-de Vries equation and solitary wave solutions for interfacial waves in a two-fluid system

This paper considers interfacial waves propagating along the interface between a two-dimensional two-fluid with a flat bottom and a rigid upper boundary. There is a light fluid layer overlying a heavier one in the system, and a small density difference exists between the two layers. It just focuses on the weakly non-linear small amplitude waves by introducing two small independent parameters: the nonlinearity ratio epsilon, represented by the ratio of amplitude to depth, and the dispersion ratio mu, represented by the square of the ratio of depth to wave length, which quantify the relative importance of nonlinearity and dispersion. It derives an extended KdV equation of the interfacial waves using the method adopted by Dullin et al in the study of the surface waves when considering the order up to O(mu(2)). As expected, the equation derived from the present work includes, as special cases, those obtained by Dullin et al for surface waves when the surface tension is neglected. The equation derived using an alternative method here is the same as the equation presented by Choi and Camassa. Also it solves the equation by borrowing the method presented by Marchant used for surface waves, and obtains its asymptotic solitary wave solutions when the weakly nonlinear and weakly dispersive terms are balanced in the extended KdV equation.

滑坡泥石流信息遥感获取与空间预测

On the issue of geological hazard evaluation（GHE）, taking remote sensing and GIS systems as experimental environment, assisting with some programming development, this thesis combines multi-knowledges of geo-hazard mechanism, statistic learning, remote sensing (RS), high-spectral recognition, spatial analysis, digital photogrammetry as well as mineralogy, and selects geo-hazard samples from Hong Kong and Three Parallel River region as experimental data, to study two kinds of core questions of GHE, geo-hazard information acquiring and evaluation model. In the aspect of landslide information acquiring by RS, three detailed topics are presented, image enhance for visual interpretation, automatic recognition of landslide as well as quantitative mineral mapping. As to the evaluation model, the latest and powerful data mining method, support vector machine (SVM), is introduced to GHE field, and a serious of comparing experiments are carried out to verify its feasibility and efficiency. Furthermore, this paper proposes a method to forecast the distribution of landslides if rainfall in future is known baseing on historical rainfall and corresponding landslide susceptibility map. The details are as following: (a) Remote sensing image enhancing methods for geo-hazard visual interpretation. The effect of visual interpretation is determined by RS data and image enhancing method, for which the most effective and regular technique is image merge between high-spatial image and multi-spectral image, but there are few researches concerning the merging methods of geo-hazard recognition. By the comparing experimental of six mainstream merging methods and combination of different remote sensing data source, this thesis presents merits of each method ,and qualitatively analyzes the effect of spatial resolution, spectral resolution and time phase on merging image. (b) Automatic recognition of shallow landslide by RS image. The inventory of landslide is the base of landslide forecast and landslide study. If persistent collecting of landslide events, updating the geo-hazard inventory in time, and promoting prediction model incessantly, the accuracy of forecast would be boosted step by step. RS technique is a feasible method to obtain landslide information, which is determined by the feature of geo-hazard distribution. An automatic hierarchical approach is proposed to identify shallow landslides in vegetable region by the combination of multi-spectral RS imagery and DEM derivatives, and the experiment is also drilled to inspect its efficiency. (c) Hazard-causing factors obtaining. Accurate environmental factors are the key to analyze and predict the risk of regional geological hazard. As to predict huge debris flow, the main challenge is still to determine the startup material and its volume in debris flow source region. Exerting the merits of various RS technique, this thesis presents the methods to obtain two important hazard-causing factors, DEM and alteration mineral, and through spatial analysis, finds the relationship between hydrothermal clay alteration minerals and geo-hazards in the arid-hot valleys of Three Parallel Rivers region. (d) Applying support vector machine (SVM) to landslide susceptibility mapping. Introduce the latest and powerful statistical learning theory, SVM, to RGHE. SVM that proved an efficient statistic learning method can deal with two-class and one-class samples, with feature avoiding produce ‘pseudo’ samples. 55 years historical samples in a natural terrain of Hong Kong are used to assess this method, whose susceptibility maps obtained by one-class SVM and two-class SVM are compared to that obtained by logistic regression method. It can conclude that two-class SVM possesses better prediction efficiency than logistic regression and one-class SVM. However, one-class SVM, only requires failed cases, has an advantage over the other two methods as only "failed" case information is usually available in landslide susceptibility mapping. (e) Predicting the distribution of rainfall-induced landslides by time-series analysis. Rainfall is the most dominating factor to bring in landslides. More than 90% losing and casualty by landslides is introduced by rainfall, so predicting landslide sites under certain rainfall is an important geological evaluating issue. With full considering the contribution of stable factors (landslide susceptibility map) and dynamic factors (rainfall), the time-series linear regression analysis between rainfall and landslide risk mapis presented, and experiments based on true samples prove that this method is perfect in natural region of Hong Kong. The following 4 practicable or original findings are obtained: 1) The RS ways to enhance geo-hazards image, automatic recognize shallow landslides, obtain DEM and mineral are studied, and the detailed operating steps are given through examples. The conclusion is practical strongly. 2) The explorative researching about relationship between geo-hazards and alteration mineral in arid-hot valley of Jinshajiang river is presented. Based on standard USGS mineral spectrum, the distribution of hydrothermal alteration mineral is mapped by SAM method. Through statistic analysis between debris flows and hazard-causing factors, the strong correlation between debris flows and clay minerals is found and validated. 3) Applying SVM theory (especially one-class SVM theory) to the landslide susceptibility mapping and system evaluation for its performance is also carried out, which proves that advantages of SVM in this field. 4) Establishing time-serial prediction method for rainfall induced landslide distribution. In a natural study area, the distribution of landslides induced by a storm is predicted successfully under a real maximum 24h rainfall based on the regression between 4 historical storms and corresponding landslides.