Theory of Basin Scale Dynamics of a Stratified Rotating Fluid

The dynamics of a stratified fluid contained in a rotating rectangular box is described in terms of the evolution of the lowest moments of its density and momentum fields. The first moment of the density field also gives the position of the fluids centre-of-mass. The resulting low-order model allows for fast assessment both of adopted parameterisations, as well as of particular values of parameters. In the ideal fluid limit (neglect of viscous and diffusive effects), in the absence of wind, the equations have a Hamiltonian structure that is integrable (non-integrable) in the absence (presence) of differential heating. In a non-rotating convective regime, dynamically rich behaviour and strong dependence on the single (lumped) parameter are established. For small values of this parameter, in a self-similar regime, further reduction to an explicit map is discussed in an Appendix. Introducing rotation in a nearly geostrophic regime leads through a Hopf bifurcation to a limit cycle, and under the influence of wind and salt to multiple equilibria and chaos, respectively.     

Soil erosion assessment and its verification using the Universal Soil Loss Equation and Geographic Information System: a case study at Boun,Korea

This study is aimed at the evaluation of the hazard of soil erosion and its verification at Boun, Korea, using a Geographic Information System (GIS) and remote sensing. Precipitation, topographic, soil, and land use data were collected, processed, and constructed into a spatial database using GIS and remote sensing data. Areas that had suffered soil erosion were analysed and mapped using the Universal Soil Loss Equation (USLE). The factors that influence soil erosion are rainfall erosivitiy (R) from the precipitation database, soil erodibility (K) from the soil database, slope length and steepness (LS) from the topographic database, and crop and management (C) and conservation supporting practices (P) from the land use database. Land use was classified from Landsat Thematic Mapper satellite images. The soil erosion map verified use of the landslide location data. Landslide locations were identified in the Boun area from interpretation of aerial photographs and field surveys.     

海冰动力学数值方法研究进展

在海冰动力学数值模拟和预测研究中,人们将海冰视为连续介质分别建立了欧拉坐标下的有限差分（FD）方法、拉格朗日坐标下的光滑质点流体动力学（SPH）方法、欧拉和拉格朗日坐标相结合的质点网格法（PIC）,近年来又发展了基于非连续介质的颗粒流（GF）方法。对以上几种海冰动力学数值方法的特点和适用性进行了讨论,结果表明：FD、PIC和SPH方法可适用于中长期海冰动力学数值模拟,但SPH方法的计算效率需进一步提高;GF方法在不同尺度下的海冰动力学数值模拟中的计算精度均有很强的适用性,但目前较适用于小尺度下海冰动力学基本特性的数值试验研究,计算时效还不能满足实际海冰数值模拟和预测的要求。为进一步提高海冰动力学模拟的精度和适用性,在不同时空尺度下分别发展与其相适应的数值方法是必要的。     

Nonlinear Time Series Analysis of Volcanic Tremor Events Recorded at Sangay Volcano,Ecuador

The assumption that volcanic tremor may be generated by deterministic nonlinear source processes is now supported by a number of studies at different volcanoes worldwide that clearly demonstrate the low-dimensional nature of the phenomenon. We applied methods based on the theory of nonlinear dynamics to volcanic tremor events recorded at Sangay volcano, Ecuador in order to obtain more information regarding the physics of their source mechanism. The data were acquired during 21–26 April 1998 and were recorded using a sampling interval of 125 samples s^–1 by two broadband seismometers installed near the active vent of the volcano. In a previous study Johnson and Lees (2000) classified the signals into three groups: (1) short duration (<1 min) impulses generated by degassing explosions at the vent; (2) extended degassing chugging events with a duration 2–5 min containing well-defined integer overtones (1–5 Hz) and variable higher frequency content; (3) extended degassing events that contain significant energy above 5 Hz. We selected 12 events from groups 2 and 3 for our analysis that had a duration of at least 90 s and high signal-to-noise ratios. The phase space, which describes the evolution of the behavior of a nonlinear system, was reconstructed using the delay embedding theorem suggested by Takens. The delay time used for the reconstruction was chosen after examining the first zero crossing of the autocorrelation function and the first minimum of the Average Mutual Information (AMI) of the data. In most cases it was found that both methods yielded a delay time of 14–18 samples (0.112–0.144 s) for group 2 and 5 samples (0.04 s) for group 3 events. The sufficient embedding dimension was estimated using the false nearest neighbors method which had a value of 4 for events in group 2 and was in the range 5–7 for events in group 3. Based on these embedding parameters it was possible to calculate the correlation dimension of the resulting attractor, as well as the average divergence rate of nearby orbits given by the largest Lyapunov exponent. Events in group 2 exhibited lower values of both the correlation dimension (1.8–2.6) and largest Lyapunov exponent (0.013–0.022) in comparison with the events in group 3 where the values of these quantities were in the range 2.4–3.5 and 0.029–0.043, respectively. Theoretically, a nonlinear oscillation described by the equation ++g(x)=fcost can generate deterministic signals with characteristics similar to those observed in groups 2 and 3 as the values of the parameters ,,f, are drifting, causing instability of orbits in the phase space.     

Undrained dynamic-loading ring-shear apparatus and its application to landslide dynamics

Landslides are gravitational mass movements of rock, debris or earth. Some move very slowly, thus conforming to the field of statics, but some move rapidly. Study of the initiation and motion of rapid landslides needs to develop Landslide Dynamics involving dynamic loading and dynamic generation/dissipation of excess pore-water pressure. New developments in science can be facilitated by new technological advances. This study aimed to develop a new apparatus that can geotechnically simulate the formation of the shear zone and the following long and rapid shear displacement that occurs in high-velocity landslides. Professor K. Sassa and his colleagues at DPRI (Disaster Prevention Research Institute), Kyoto University, have worked to develop an undrained dynamic-loading ring-shear apparatus for this purpose. A series of different types of apparatus (DPRI-3, 4, 5, 6, 7) have been developed from 1992 to the present. This paper describes the development of this apparatus and its application to the study of earthquake-induced landslides and the latest landslide-triggered debris flow in Japan. Also, tests of the latest version (DPRI-7) with a transparent shear box for direct observation of the shear zone during a rapid shearing are described.     

Numerical simulations of a Mars geodesy network experiment: Effect of orbiter angular momentum desaturation on Mars' rotation estimation

The scientific objectives of a geodetic experiment based on a network of landers, such as NEIGE (NEtlander Ionosphere and Geodesy Experiment) are to improve the current knowledge of Mars' interior and atmosphere dynamics. Such a network science experiment allows monitoring the motions of the Martian rotation axis with a precision of a few centimeters (or milli-arc-seconds (mas)) over annual and sub-annual periods. Thereto, besides radio tracking of a Mars orbiter from the Earth, radio Doppler shifts between this orbiter and several landers at the planet's surface will be performed. From the analysis of these radio Doppler data, it is possible to reconstruct the orbiter motion and Mars' orientation in space. The errors on the orbit determination (position and velocity of the orbiter) have an impact on the geodetic parameters determination from the Doppler shifts and must be removed from the signal in order to achieve a high enough accuracy. In this paper, we perform numerical simulations of the two Doppler signals involved in such an experiment to estimate the impact of the spacecraft angular momentum desaturations on the determination of Mars' orientation variations. The attitude control of the orbiter needs such desaturation maneuvers regularly repeated. They produce velocity variations that must be taken into account when determining the orbit. For our simulations, we use a priori models of the Martian rotation and introduce the spacecraft velocity variations induced by each desaturation event. By a least-squares adjustment of the simulated Doppler signals, we then estimate the orbiter velocity variations and the parameters of the Mars' rotation model. We show that these velocity variations are ill resolved when the spacecraft is not tracked, therefore requiring a near-continuous tracking from the Earth to accurately determine the orbit. In such conditions we show that only 15- of lander-orbiter tracking per week allows recovering Mars' orientation parameters with a precision of a few mas over a period of 1 Martian year.     

Formation of terrestrial planets in a dissipating gas disk with Jupiter and Saturn

We have performed N-body simulations on final accretion stage of terrestrial planets, including the eccentricity and inclination damping effect due to tidal interaction with a gas disk. We investigated the dependence on a depletion time scale of the disk, and the effect of secular perturbations by Jupiter and Saturn. In the final stage, terrestrial planets are formed through coagulation of protoplanets of about the size of Mars. They would collide and grow in a decaying gas disk. Kominami and Ida [Icarus 157 (2002) 43-56] showed that it is plausible that Earth-sized, low-eccentricity planets are formed in a mostly depleted gas disk. In this paper, we investigate the formation of planets in a decaying gas disk with various depletion time scales, assuming disk surface density of gas component decays exponentially with time scale of τ_gas. Fifteen protoplanets with are initially distributed in the terrestrial planet regions. We found that Earth-sized planets with low eccentricities are formed, independent of initial gas surface density, when the condition (τ_cross+τ_growth)/2?τ_gas?τ_cross is satisfied, where τ_cross is the time scale for initial protoplanets to start orbit crossing in a gas-free case and τ_growth is the time scale for Earth-sized planets to accrete during the orbit crossing stage. In the cases satisfying the above condition, the final masses and eccentricities of the largest planets are consistent with those of Earth and Venus. However, four or five protoplanets with the initial mass remain. In the final stage of terrestrial planetary formation, it is likely that Jupiter and Saturn have already been formed. When Jupiter and Saturn are included, their secular perturbations pump up eccentricities of protoplanets and tend to reduce the number of final planets in the terrestrial planet regions. However, we found that the reduction is not significant. The perturbations also shorten τ_cross. If the eccentricities of Jupiter and Saturn are comparable to or larger than present values (∼0.05), τ_cross become too short to satisfy the above condition. As a result, eccentricities of the planets cannot be damped to the observed value of Earth and Venus. Hence, for the formation of terrestrial planets, it is preferable that the secular perturbations from Jupiter and Saturn do not have significant effect upon the evolution. Such situation may be reproduced by Jupiter and Saturn not being fully grown, or their eccentricities being smaller than the present values during the terrestrial planets' formation. However, in such cases, we need some other mechanism to eliminate the problem that numerous Mars-sized planets remain uncollided.     

Escapes and Recurrence in a Simple Hamiltonian System

Many physical systems can be modeled as scattering problems. For example, the motions of stars escaping from a galaxy can be described using a potential with two or more escape routes. Each escape route is crossed by an unstable Lyapunov orbit. The region between the two Lyapunov orbits is where the particle interacts with the system. We study a simple dynamical system with escapes using a suitably selected surface of section. The surface of section is partitioned in different escape regions which are defined by the intersections of the asymptotic manifolds of the Lyapunov orbits with the surface of section. The asymptotic curves of the other unstable periodic orbits form spirals around various escape regions. These manifolds, together with the manifolds of the Lyapunov orbits, govern the transport between different parts of the phase space. We study in detail the form of the asymptotic manifolds of a central unstable periodic orbit, the form of the escape regions and the infinite spirals of the asymptotic manifolds around the escape regions. We compute the escape rate for different values of the energy. In particular, we give the percentage of orbits that escape after a finite number of iterations. In a system with escapes one cannot define a Poincaré recurrence time, because the available phase space is infinite. However, for certain domains inside the lobes of the asymptotic manifolds there is a finite minimum recurrence time. We find the minimum recurrence time as a function of the energy.This revised version was published online in October 2005 with corrections to the Cover Date.     

A Case Study on the Effects of Heterogeneous Soil Moisture on Mesoscale Boundary-Layer Structure in the Southern Great Plains, U.S.A. Part II: Mesoscale Modelling

The importance of soil moisture inputs and improved model physics in the prediction of the daytime boundary-layer structure during the Southern Great Plains Hydrology Experiment 1997 (SGP97) is investigated using the non-hydrostatic fifth-generation Pennsylvania State University/National Center for Atmospheric Research (PSU/NCAR) Mesoscale Model MM5. This is Part II of a two-part study examining the relationship of surface heterogeneity to observed boundary-layer structure. Part I focuses on observations and utilizes a simple model while Part II uses observations and MM5 modelling. Soil moisture inputs tested include a lookup table based on soil type and season, output from an offline land-surface model (LSM) forced by atmospheric observations, and high-resolution ( 800 m) airborne microwave remotely sensed data. Model physics improvements are investigated by comparing an LSM directly coupled with the MM5 to a simpler force-restore method at the surface. The scale of land surface heterogeneities is compared to the scale of their effects on boundary-layer structure.The use of more detailed soil moisture fields allowed the MM5 to better represent the large-scale (hundreds of km) and small-scale (tens of km) horizontal gradients in surface-layer weather and, to a lesser degree, the atmospheric boundary-layer (ABL) height, which was evaluated against observations measured by differential absorption lidar (DIAL). The benefits of coupling an LSM to the MM5 were not readily evident in this summertime case, with the model having particular difficulty simulating the timing of maximum surface fluxes while underestimating the depth of the mixed layer.