A high order Godunov scheme with constrained transport and adaptive mesh refinement for astrophysical and geophysical MHD

We propose to extend the well-known MUSCL-Hancock scheme for Euler equations to the induction equation modeling the magnetic field evolution in kinematic dynamo problems. The scheme is based on an integral form of the underlying conservation law which, in our formulation, results in a “finite-surface” scheme for the induction equation. This naturally leads to the well-known “constrained transport” method, with additional continuity requirement on the magnetic field representation. The second ingredient in the MUSCL scheme is the predictor step that ensures second order accuracy both in space and time. We explore specific constraints that the mathematical properties of the induction equations place on this predictor step, showing that three possible variants can be considered. We show that the most aggressive formulations reach the same level of accuracy than the other ones, at a lower computational cost. More interestingly, these schemes are compatible with the Adaptive Mesh Refinement (AMR) framework. It has been implemented in the AMR code RAMSES. It offers a novel and efficient implementation of a second order scheme for the induction equation. The scheme is then adaptated to solve for the full MHD equations using the same methodology. Through a series of test problems, we illustrate the performances of this new code using two different MHD Riemann solvers (Lax–Friedrich and Roe) and the need of the Adaptive Mesh Refinement capabilities in some cases. Finally, we show its versatility by applying it to the ABC dynamo problem and to the collapse of a magnetized cloud core.     

Evolution of scouring process downstream of grade‐control structures under steady and unsteady flows

For many incised channels, one of the most common strategies is to install some hard structures, such as grade‐control structures (GCSs), in the riverbed to resist further incision. In this study, a series of experiments, including both steady and unsteady flow conditions, were conducted to investigate the scouring process downstream of a GCS. Three distinct phases, including the initial, developing and equilibrium phases, during the evolution of scour holes were identified. In addition, a semi‐empirical method was proposed to predict the equilibrium scour‐hole profile for the scour countermeasure design. In general, the comparisons between the experimental and simulated results are reasonably consistent. As the studies on temporal variation of the scour depth at GCSs caused by floods are limited, the effect of flood hydrograph shapes on the scour downstream of GCSs without upstream sediment supply was also investigated experimentally in this study. Based on the dimensional analysis and the concept of superposition, a methodology is proposed to simulate the time evolution of the maximum scour depth downstream of a GCS for steady flows. Moreover, the proposed scheme predicts reasonably well the temporal variations of the maximum scour depth for unsteady flows with both single and multiple peak. Copyright © 2012 John Wiley & Sons, Ltd.     

Seesaw Pattern of Rainfall Anomalies between the Tropical Western North Pacific and Central Southern China during Late Summer

It is well known that suppressed convection in the tropical western North Pacific(WNP) induces an anticyclonic anomaly,and this anticyclonic anomaly results in more rainfall along the East Asian rain band through more water vapor transport during summer, as well as early and middle summer. However, the present results indicate that during late summer(from mid-August to the beginning of September), the anomalous anticyclone leads to more rainfall over central southern China(CSC), a region quite different from preceding periods. The uniqueness of late summer is found to be related to the dramatic change in climatological monsoon flows: southerlies over southern China during early and middle summer but easterlies during late summer. Therefore, the anomalous anticyclone, which shows a southerly anomaly over southern China, enhances monsoonal southerlies and induces more rainfall along the rain band during early and middle summer. During late summer,however, the anomalous anticyclone reflects a complicated change in monsoon flows: it changes the path, rather than the intensity, of monsoon flows. Specifically, during late summers of suppressed convection in the tropical WNP, southerlies dominate from the South China Sea to southern China, and during late summers of enhanced convection, northeasterlies dominate from the East China Sea to southern China, causing more and less rainfall in CSC, respectively.     

An experimental study of sapped drainage network development

In a basin developed on a stream table, effluent subsurface flow supported a channel network that evolved by a combination of headward growth, lateral widening and divide decay. The area occupied by the developing network increased with time. Circularity was used to characterize network evolution which occurred in three phases (initiation, extension and abstraction). Basin sediment discharge declined exponentially with time. Pronounced quasi-cyclic variability was superimposed upon this general trend. Some of the variability was directly linked to changes in the amount of sediment supplied to the channel. The variation of mean network sediment yield (mean sediment discharge scaled by network area) with time adequately described the general decline in sediment discharge as the network evolved.     

Single-Column Model Intercomparison for a Stably Stratified Atmospheric Boundary Layer

The parameterization of the stably stratified atmospheric boundary layer is a difficult issue, having a significant impact on medium-range weather forecasts and climate integrations. To pursue this further, a moderately stratified Arctic case is simulated by nineteen single-column turbulence schemes. Statistics from a large-eddy simulation intercomparison made for the same case by eleven different models are used as a guiding reference. The single-column parameterizations include research and operational schemes from major forecast and climate research centres. Results from first-order schemes, a large number of turbulence kinetic energy closures, and other models were used. There is a large spread in the results; in general, the operational schemes mix over a deeper layer than the research schemes, and the turbulence kinetic energy and other higher-order closures give results closer to the statistics obtained from the large-eddy simulations. The sensitivities of the schemes to the parameters of their turbulence closures are partially explored.     

Long internal waves in shear flows: topographic resonance and wave-induced global instability

Issues pertaining to a mechanism whereby long internal waves in shallow seas may give rise to enhanced rates of resuspension of sedimentary material are addressed. The proposed mechanism is intimately related to the creation of conditions in the bottom boundary layer which are favorable for flow separation and spontaneous onset of global instability. It is shown that long waves generated by topographic resonance and propagating upstream against the oncoming current, especially a sheared current, have a strong tendency to release a coherent, pulsating dynamics in their footprint. The passage-through-resonance problem for a sheared, stratified flow is considered, conditions for topographic resonance in the flow model are defined, and preliminary results for the unsteady dynamics in the boundary layer under the footprint of a long wave packet are presented.     

Laboratory experiments on along-slope flows in homogeneous and stratified rotating fluids

Laboratory experiments have been carried out for the flow along isobaths of simulated shelf-continental slope geometry. Cases of both homogeneous and linearly stratified fluids are considered and the background flows are sufficiently strong to have the flow near the bottom boundary range from transitional to fully turbulent. The background motions are impulsively started and flows with a coast on the right (spin-down) and on the left (spin-up) are considered. The homogeneous spin-down and spin-up processes are smooth in the sense that no vortical structures were found to be of the order of the slope width or larger. Flows reach equilibrium more quickly for spin-down cases, and this is attributed to secondary flows forced by the basin geometry. All of the stratified experiments exhibited large-scale instabilities as evidenced by the generation of slope and basin scale eddy structures and a much slower decay than their homogeneous counterparts.     

The development of an intervening opportunities model with spatial dominance effects

In this paper an intervening opportunities model with spatial dominance is developed. The usual assumption in spatial theory is that decision makers are influenced not just by the size of a destination or distance but by these two factors in combination, that is, spatial dominance. Decision-makers will have more knowledge about, and clearly perceive destinations that exert the greatest amount of spatial dominance on their origins, just as they would primate cities. Thus destinations are ranked in terms of the spatial dominance calculated for each destination. Empirical verification of the model utilizes state-to-state migration flow data for the US. Calibration results compare favourably with the traditional intervening opportunities model and the production constrained gravity model. Received: 7 October 1999/Accepted: 15 June 2000     

机载合成孔径雷达图像频谱分析技术地质应用评价

频谱分析是空间滤波的一种。本文使用光学傅里叶变换分析SAR图像的空间频率特征。从取得的功率谱与功率谱角分布数据中可以:(1)确定与雷达后向散射方向有关面的走向最大(最小)方位角;(2)分析频谱曲线两个峰的夹角及其地学意义;(3)推算其水系密度;(4)研究样区地形基本特征。 这些资料有助于研究线性构造区域展布特征,岩类识别和地貌分类等。     

Roughness effect on the correction factor of surface velocity for rill flows

Flow velocity is one of the most important hydrodynamic variables for both channelized (rill and gullies) and interrill erosive phenomena. The dye tracer technique to measure surface flow velocity V_s is based on the measurement of the travel time of a tracer needed to cover a known distance. The measured V_s must be corrected to obtain the mean flow velocity V using a factor α_v = V/V_s which is generally empirically deduced. The V_s measurement can be influenced by the method applied to time the travel of the dye-tracer and α_v can vary in different flow conditions. Experiments were performed by a fixed bed small flume simulating a rill channel for two roughness conditions (sieved soil, gravel). The comparison between a chronometer-based (CB) and video-based (VB) technique to measure V_s was carried out. For each slope-discharge combination, 20 measurements of V_s, characterized by a sample mean V_m, were carried out. For both techniques, the frequency distributions of V_s/V_m resulted independent of slope and discharge. For a given technique, all measurements resulted normally distributed, with a mean equal to one, and featured by a low variability. Therefore, V_m was considered representative of surface flow velocity. Regardless of roughness, the V_m values obtained by the two techniques were very close and characterized by a good measurement precision. The developed analysis on α_v highlighted that it is not correlated with Reynolds number for turbulent flow regime. Moreover, α_v is correlated neither with the Froude number nor with channel slope. However, the analysis of the empirical frequency distributions of the correction factor demonstrated a slope effect. For each technique (CB, VB)-roughness (soil, gravel) combination, a constant correction factor was statistically representative even if resulted in less accurate V estimations compared to those yielded by the slope-specific correction factor.