Turbulence in vegetated flows: Volume-average analysis and modelling aspects

Two approaches for the modelling of turbulence in vegetated flows have been developed in the past. The “microscopic” approach which is straightforward but limited to simple cases and the “macroscopic” approach which is based on Volume Average Theory (VAT). In this study, aspects of Volume-Average (VA) analysis and modelling are investigated for turbulent vegetated flow using computed three-dimensional results from the solution of the Reynolds-Averaged Navier-Stokes (RANS) equations around a representative vegetal element. In particular (a) the VA transport equations for k and ε, based on VAT, are properly derived, (b) the Boussinesq hypothesis for the VA quantities, employed in 〈k〉-〈ε〉 turbulence models is tested, and (c) the values of the coefficients used in such turbulence models are assessed in comparison with those used in the classical turbulence models.     

A probable mechanism of the water level subsidence in wells as a precursor of an earthquake event

Case histories of water level subsidence in bore-holes as a precursor of earthquakes are given here. Based on the examples, a testable quantitative theory for causative mechanism of the precursor—“draining-injecting water model with variable discharge” is proposed (abbreviated to DIW model). Through analysing the constitution law of which the deformation changes in the porous, water-saturated media under the effect of exterior stress, as first step of all, the authors suggested first a simple “drainage-natural restoration model” (abbreviated to DNR model), calculated and gave a group of theoretical precursor curve by using DNR model, compared the theoretical precursor curves of DNR model with the observational curves, found out the differences of the two curves, studied the causative physical factors that caused the differences then, revised the DNR model, and finally, the theory on “draining-injecting water model with variable discharge” in the paper was obtained. The authors deduced general equation of the two dimensions “draining-injecting water linear source drawdown field” in the paper, suggested and developed the concept on “domain”. DIW model can also give a possible explanation for both regularity and complexity of this precursor. DIW theory can quantitatively divide the seismogenic process of the foci on the short-term and impending process into several phases, and by inversing the discharge functionq(τ) curve, the time values by which the phases are divided were obtained. They will be helpful to predicting the occurrence time of earthquake and judging the DD and IPE model of the seismogenesis. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,15, 194–201, 1993.     

Magnetospheric substorm: Loss of the magnetoplasma equilibrium as a nonlinear dynamical bifurcation

The fast onset of a substorm—a substorm “explosion”—is usually associated with the moment of stability loss of the magnetoplasma equilibrium in the geomagnetic tail. The origination of such a process either from the near-Earth part of the plasma sheet or from its remote part, which is highly stretched into the tail, is now being studied theoretically and verified experimentally (at the present time, in the THEMIS project). In the first case, the resulting disturbance must have the form of a ballooning mode; in the second case, of tearing perturbation. However, in both cases, this stability loss, i.e., a quick breakdown in the balance, replacing the slow quasi-static evolution of configuration, can only occur as a nonlinear process. Taking into account the specific properties of the configuration and possible disturbances in it, we indicate why such a process cannot be the previously proposed “substorm detonation.” It is shown that a suitable mathematical model is a nonlinear dynamical bifurcation occurring on a small time scale, with a delay relative to the moment of passing the marginally stable state.     

Stratified flow in pyroclastic surges

Stratified flow theory is applied to pyroclatic surges in an effort to gain insight into transport dynamics during explosive eruptions. Particle transport is assumed to be by turbulent suspension, and calculations contained herein show that this is likely for many cases including the 18 May 1980 blast at mount St. Helens. The discussion centers on the Rouse number (Pn), which represents a ratio of particle settling velocity to scale of turbulence; the Brunt-Väisälä frequency (N), which is the maximum possible frequency of internal waves; the Froude number (Fr), representing the ratio of inertial forces to gravitational forces; and the Richardson number (Ri), a ratio of buoyant restoring forces to turbulent mixing forces. The velocity or flow power dependence of bed-form wavelength in surge deposits is related to a velocity dependence of wavelength of internal waves in the turbulent surge. This produces a decrease in dune wavelength with increasing distance from vent. Migration direction of bed forms is related toFr as it is defined for a continuously stratified flow. Proximal to distal facies variations in surge deposits reflect increasingPn andRi as the flows move away from their sources. This produces the progression from sandwave to massive to planar facies with increasing distance from vent. Where the long axis of topography is at low angles to the flow direction, massive facies in topographic lows may from concurrently with sandwave facies on highs, due to the higher particle concentration in the lows. Where long axis of topography is at high angles to flow direction, denser lower parts of the surge may be dammed or blocked. Blocked material tends to form massive flows that may move down slope independent of the overriding surge. A model incorporating turbulent transport, stratified flow, and time evolution of pyroclastic surges is proposed for deposits which have been attributed to both pyroclastic flow and pyroclastic surge transport by various workers. During the initial high energy (waxing) phase of the eruptive event,Pn is sufficiently low that only coarse, but poorly sorted, material is deposited to form relatively coarse bottom layers. As the event wanes, remaining finer material is deposited through a thin bed load to produce overlying bedded and cross-bedded veneer deposits. Throughout most of the event, blocking occurs to produce relatively thick and massive deposits in valley bottoms.     

Induced polarization: Simulation and inversion of nonlinear mineral electrodics

Graph-theoretic representations are used to model nonlinear electrodics, while forward and inverse simulations are based on reaction rate theory. The electrodic responses are presented as distorted elliptical Lissajous shapes obtained from dynamic impedance over a full cycle. Simulations show that asymmetry in reaction energy barrier causes slight asymmetry in the shape of the response ellipse and hardly affects the phase angle of the complex electrode impedance. The charge transfer resistance and the diffusion constraints tend to have opposite effects. The former causes reduction in the phase angle, tending to make the impedance purely resistive. Both of these mechanisms show saturation effects. Charge transfer resistance at its limit forces a thin S-type symmetry on the Lissajous patterns, while with diffusion control the size of the Lissajous patterns begins to reduce after saturation. The fixed layer causes substantial increase in the phase angle and tends to “enlarge” the Lissajous patterns. It is responsible for the hysteresis-like shapes of the Lissajous patterns when superimposed on strong charge transfer resistance. This study shows that it is quite possible to deduce the mechanisms that control the electrodic processes by inverting electrodic parameters from “observed” distorted, nonelliptical Lissajous patterns characteristic of nonlinear electrodics. The results and qualities of the inversion technique are discussed.     

Dynamic evolution patterns of the degree of ground resistivity anisotropy and the seismogenic process

Following a new train of thinking, this paper has explored first the potential information in the ground resistivity data observed by the existing geoelectric observation system, investigated and proposed a new dimensionless geoelectric precursor factor, the degree of ground resistivity anisotropy, S, and studied the characteristics of dynamic evolution pattern of S during the seismogenic process. The results show that, during the seismogenic process, the degree of ground resistivity anisotropy (S) displays a process of 'normal' →'abnormal strengthening (amplitude, range)' →abnormal weakening' → 'earthquake occurrence'→ 'normal'. The earthquake would occur at the time when the S value has entered the late stage of strengthening and turns to weaken and in the gradient belt on the margin of S anomaly region. The dynamic evolution pattern of S reflects the changes of the tectonic stress field during the seismogenic process. Therefore, it would be possible to trace the process of earthquake generation and occurrence from the dynamic evolution pattern of S so as to service earthquake prediction.     

On the seismic regime network method

In this paper, based on the previous study of practical use of seismic regime windows and seismic regime belts, the problem of establishing a “seismic regime network” consisting of “windows” and “belts” is further posed and discussed according to the observed fact that many “windows” and “belts” make responses to one earthquake. For the convenience of usage, the “seismic regime network” is divided into two classes, the first class and the second one. The former can be used in tendency prediction for long-term seismic activity in a large area, the latter used in short-term prediction in a small area. In this paper, after briefly discussing the physical significance of “seismic regime network”, it is pointed out that this simple and easily used method can be used to observe and extract seismic precursory information from a large area before a great earthquake, thus it can provide a reliable basis for the analysis and judgement of seismic regime tendency in time and space. No doult, this method is of certain practical significance. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,13, 161–169, 1991. The English version of this paper is improved by Prof. Shaoxie Xu.     

Two notes on the modern theory of inverse problems in geophysics

On the basis of comparison of the approaches to the solution of inverse problems in information theory and geophysics, it is shown that results, obtained in information theory, are suitable to supplement the theory of geophysical inverse problems. The conditions of the existence and uniqueness of the solutions of inverse problems in their practical discrete statement are specified. The terms of ɛ-entropy H _ɛ and informational capacity C _ɛ, characterizing “volumes” of unknown and observed data, are introduced. It is shown, that the instability of the solution of the inverse problem decreases with increase in H _ɛ, (increase in the “complexity” of studied section), if the relation H _ɛ ≤ C _ɛ is maintained.     

The effects of large and small-scale topography upon internal waves and implications for tidally induced mixing in sill regions

A free surface non-hydrostatic model in a cross-sectional form, namely, two-dimensional, in the vertical is used to examine the role of larger-scale topography, namely, sill width, and smaller scale topography, namely, ripples on the sill upon internal wave generation and mixing in sill regions. The present work is set in the context of earlier work and the wider literature in order to emphasise the problems of simulating mixing in hydrographic models. Highlights from previous calculations and references to the literature for detail, together with new results presented here with smooth and “ripple” topography, are used to show that an idealised cross-sectional model can reproduce the dominant features found in observations at the Loch Etive sill. Calculations show that on both the short and long time scales, the presence of small-scale “ripple” topography influence the mixing and associated Richardson number distribution in the sill region. Subsequent calculations in which the position and form of the small-scale sill topography is varied show for the first time that it is the small-scale topography near the sill crest that is particularly important in enhancing mid-water mixing on the lee side of the sill. Both short-term and longer-term calculations with a reduced sill width and associated time series show that as the sill width is reduced, the non-linear response of the system increases. In addition, Richardson number plots show that the region of critical Richardson number, and hence enhanced mixing, increases with time and a reduction in sill width. Calculations in which buoyancy frequency N varies through the vertical show that buoyancy frequency close to the top of the sill is primarily controlling mixing rather than its mean value. Hence, a Froude number based on sill depth and local N is the critical parameter rather than one based on total depth and mean N.     

An algorithmic approach to the total least-squares problem with linear and quadratic constraints

Proper incorporation of linear and quadratic constraints is critical in estimating parameters from a system of equations. These constraints may be used to avoid a trivial solution, to mitigate biases, to guarantee the stability of the estimation, to impose a certain “natural” structure on the system involved, and to incorporate prior knowledge about the system. The Total Least-Squares (TLS) approach as applied to the Errors-In-Variables (EIV) model is the proper method to treat problems where all the data are affected by random errors. A set of efficient algorithms has been developed previously to solve the TLS problem, and a few procedures have been proposed to treat TLS problems with linear constraints and TLS problems with a quadratic constraint. In this contribution, a new algorithm is presented to solve TLS problems with both linear and quadratic constraints. The new algorithm is developed using the Euler-Lagrange theorem while following an optimization process that minimizes a target function. Two numerical examples are employed to demonstrate the use of the new approach in a geodetic setting.     

Linear combinations of order statistics to estimate the quantiles of generalized pareto and extreme values distributions

 Ad hoc techniques for estimating the quantiles of the Generalized Pareto (GP) and the Generalized Extreme Values (GEV) distributions are introduced. The estimators proposed are based on new estimators of the position and the scale parameters recently introduced in the Literature. They provide valuable estimates of the quantiles of interest both when the shape parameter is known and when it is unknown (this latter case being of great relevance in practical applications). In addition, weakly-consistent estimators are introduced, whose calculation does not require the knowledge of any parameter. The procedures are tested on simulated data, and comparisons with other techniques are shown. The research was partially supported by Contract n. ENV4-CT97-0529 within the project “FRAMEWORK” of the European Community – D.G. XII. Grants by “Progetto Giovani Ricercatori” are also acknowledged.     

The 20-second regional magnitude <Emphasis Type="Italic">M</Emphasis><Subscript><Emphasis Type="Italic">S</Emphasis></Subscript>(20R) for the Russian Far East

A new modified magnitude scale M _S (20R) is elaborated. It permits us to extend the teleseismic magnitude scale M _S (20) to the regional epicenter distances. The data set used in this study contains digital records at 12 seismic stations of 392 earthquakes that occured in the northwest Pacific Ocean in the period of 1993–2008. The new scale is based on amplitudes of surface waves of a narrow range of the periods (16–25 s) close to the period of 20 s, for distances of 80–3000 km. The digital Butterworth filter is used for processing. On the basis of the found regional features concerning distance dependence for seismic wave attenuation, all the stations of the region have been subdivided into two groups, namely, “continental” and “island-arc.” For each group of stations, its own calibration function is proposed. Individual station corrections are used to compensate for the local features.     

Complete process of rock failure and the complete course of seismogeny

Conclusion Based on the analysis about the law of deformation rate, the concepts of the deformation rate of precursor, and its stress drop, and the stress drop of instability are discussed. According to the obtained deformationu ₀ corresponding to the maximum stress, the unstable pointu ₁ and the stable pointu ₂ of equilibrium, the complete process of rock failure can be divided into four stages quantitatively, corresponding to “the steady stage I”, “the precursor stage II”, “the unstable stage III” and “the later stage IV” of rock failure respectively, which can be used to simulate the complete course of earthquake. This kind of similarity between the complete process of rock failure and the complete course of earthquake suggests clearly the direction to reveal the law being of universal significance for the simulation of the earthquake in the laboratory experiments. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,13, 517–521, 1991.     

Transport and deposition of pyroclastic material from the ∼1000 A.D. caldera-forming eruption of Volcán Ceboruco, Nayarit, Mexico

The complex eruption sequence from the ∼1000 A.D. caldera-forming eruption of Volcán Ceboruco, known as the Jala Pumice, offers an exceptional opportunity to examine how pyroclastic material is transported and deposited from pyroclastic density currents over variable topography. Three main pyroclastic surge deposits (S1, S2, and S3) and two pyroclastic flow deposits (Marquesado and North-Flank PFDs) were emplaced during this eruption. Pyroclastic surge deposits are massive, planar, or cross-bedded, poor-to-well sorted, and display fluctuations in thickness, median diameter, sorting, and lithology as a function of distance, topography, and flow dynamics. Marquesado pyroclastic flow deposits reveal lateral variations from massive, poorly sorted deposits located within 5 km of Ceboruco to planar bedded, moderately well sorted deposits located >15 km away over the nearly horizontal topography to the south of Ceboruco. North-Flank pyroclastic flow deposits also reveal lateral variations from massive, poorly sorted deposits located within 4 km of Ceboruco to planar bedded, moderately well sorted deposits located 8 km away atop an escarpment that steeply rises 230 m from the northern valley floor. Field observations, granulometric analyses, component analyses, and crystal sedimentation calculations along flow-parallel sampling transects all suggest that both surges and flows were density stratified currents, where deposition occurred from a basal region of higher particle concentration that was supplied from an overlying dilute layer that transports particles in suspension. This supports the idea of a transition between “flow” and “surge” end members with variations in particle concentration. Topography greatly affects the transport and depositional capacity of the pyroclastic density currents as a result of “blocking”, either by topographic obstacles or by abrupt breaks at the base of volcano slopes, whereas the origin of Jala Pumice surge deposits (phreatomagmatic versus magmatic) appears to have little impact on their flow dynamics. Editorial responsibility: A.W. Woods This revised version was published in February 2005 with corrections to the title. An erratum to this article is available at .     

Lava trees and tree molds (“cannon stones”) of Mt. Etna

Unique volcanic structures, known in the literature as “lava trees” and “tree molds”, have formed at several sites on Mt. Etna volcano (northeastern Sicily, Italy). They form when a fluid lava flow runs over a tree, wraps around it and, while the wood burns off, solidifies forming a hollow cast of the tree. The inhabitants of the Etna area call these formations “pietre cannone” (“cannon stones”) because of their cylindrical shape. The first documentation of lava trees is from Hawaii, but the first eye-witnessed accounts of their formation are, to our knowledge, from Etna’s 1865 eruption. Although many of the literature examples of lava trees and tree molds formed in pahoehoe, many of those reported in this work formed in a’a. The sites where we have found the lava tree molds are located within the territory of the Etna Regional Park; most occur next to walking trails and have a high potential for geotourism.     

The middle-long term prediction of the February 3, 1996 Lijiang earthquake (MS=7) by the "criterion of activity in quiescence"

IntroductionIn the book Future CataS~ologr published in 1992, we proposed a viewpoiflt on using the"criterion of activity in quiescence" to predict big eathquake (MsZ7) (GUO, et al, 1992), and predicted in the book that in futore several years or in ten years a big earthquake (Ms27) will be possible to occur in the Zhongdian and nearby in Yunnan Province. In the 1994 nation-wide earthquake tendency consultation meeting we pointed out, once more, in the Zhongdian region of Yunnan Province…     

Morphological development of the retention basin “Hartheim”: A case study

Flow in rivers and on floodplains is complex as it is affected by several interconnected factors such as topography, sediment transport and vegetation characteristics. The resulting processes are explained by the measure “Hartheim” planned for retention purposes at the Upper Rhine river. On the basis of existing formulas and instruments it is demonstrated that a good estimation of the development of the measure is possible. The proposed procedure is a useful tool for estimating morphological developments of restored river sections.     

The wave-induced boundary layer under long internal waves

The boundary layer formed under the footprint of an internal solitary wave is studied by numerical simulation for waves of depression in a two-layer model of the density stratification. The inviscid outer flow, in the perspective of boundary-layer theory, is based on an exact solution for the long wave-phase speed, yielding a family of fully nonlinear solitary wave solutions of the extended Korteweg–de Vries equation. The wave-induced boundary layer corresponding to this outer flow is then studied by means of simulation employing the Reynolds-averaged Navier–Stokes (RANS) formulation coupled with a turbulence closure model validated for wall-bounded flows. Boundary-layer characteristics are computed for an extensive range of environmental conditions and wave amplitudes. Boundary-layer transition, identified by monitoring the eddy viscosity, is correlated in terms of a boundary-layer Reynolds number. The frictional drag is evaluated for laminar, transitional, and turbulent cases, and correlations are presented for the friction coefficient plus relevant measures of the boundary-layer thickness.     

Randomization test and its application

In this paper, one of the distribution-free tests — randomization test, is briefly described. It doesn’t need any distribution assumption and its related parameter estimation and is applicable to random and nonrandom sample. Then it is used to the test of migration of strong earthquakes on the Xianshuihe Fault Belt and “immunity” of large earthquakes in the large northern reigon of China. The test results show that there is 98.7% confidence degree for the migration of strong earthqueks on the Xianshuihe Fault Belt and “immunity” of earthqueks withM _S⩾8 toM _S⩾7 is significant in the large northern region of China. The obtained test results and the test method itself have certain application in the practice. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,15, 484–489, 1993.     

Study on the pattern and mode of vertical crustal deformation during the seismogenic process of intraplate strong earthquakes

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