热带气旋内中尺度波动的不稳定机理研究进展

在回顾了近年来热带气旋波动动力学研究的基础上,介绍了热带气旋内中尺度波动不稳定机理研究方面的进展,分别对热带气旋三类中尺度特征波动的不稳定,即经典重力惯性波、涡旋Rossby波和具有物理性质不可分的混合波的不稳定进行了物理分析,给出了热带气旋内对称不稳定、横波不稳定、对流对称不稳定、涡旋Rossby波正压不稳定及混合波不稳定的动力解释,进一步说明热带气旋内中尺度扰动发展是与基本气流的动力(水平和垂直切变)及热力状态之间的相互作用密切相关。     

Modelling the pre-failure instabilities of sand

A simple incremental model describing the pre-failure behaviour of granular soils is presented. The model describes both the dry/fully drained and undrained response. It takes into account an initial anisotropy of soil and an initial state defined as either contractive or dilative. A physically sound definition of loading/unloading is assumed, which differs from elasto-plastic approaches. The model is based on extensive empirical data and gives predictions conformable with experimental results. It also describes pre-failure instabilities of granular soils, both dry/fully drained and undrained. The Hill’s criterion was used to examine stability. It was shown that this condition can be formulated either in terms of the effective stresses or by the total stresses. In the extreme cases of either dry/fully drained or undrained conditions, these alternative formulations are equivalent. This is not so in the case of partial drainage of pore water and associated volumetric deformations as well as pore pressure changes. The model describes the pre-failure instabilities well, and additionally allows for analytical derivation of the instability line. It was shown that the second order work, appearing in the Hill’s condition, is equivalent to the entropy source.     

Probabilistic block theory analysis for a rock slope at an open pit mine in USA

A new formulation is given to conduct a probabilistic block theory analysis. A new computer code (PBTAC) is developed to perform both deterministic and probabilistic block theory analysis. The variability of the discontinuity orientation and shear strength is incorporated in the probabilistic block theory analysis. Discontinuity orientation is treated as a bivariate random variable including the correlation that exists between the dip angle and dip direction. PBTAC code was applied to perform both deterministic and probabilistic block theory analyses for a part of an open pit mine in USA. Needed geological and geotechnical data for the analyses were obtained from field and laboratory investigations. The variability of the discontinuity orientations resulted in important differences between the probabilistic and deterministic block theory analyses results. The results confirmed that the design value selected for the maximum safe slope angle (MSSA) for a particular region in the open pit mine based on the deterministic block theory analysis can be on the unsafe side. In summary, the results showed clearly the superiority of probabilistic block theory analysis over the deterministic block theory analysis in obtaining additional important information with respect to designing rock slopes. The calculated values agree very well with the existing almost stable bench face angles reported by the mining company.     

Convective Instability of a Mushy Layer - I: Uniform Permeability

Mushy layers arise and are significant in a number of geophysical contexts, including freezing of sea ice, solidification of magma chambers and inner-core solidification. A mushy layer is a region of solid and liquid in phase equilibrium which commonly forms between the liquid and solid regions of a solidifying system composed of two or more constituents. We consider the convective instability of a plane mushy layer which advances steadily upwards as heat is withdrawn at a uniform rate from the bottom of a eutectic binary alloy. The solid which forms is assumed to be composed entirely of the denser constituent, making the residual liquid within the mush compositionally buoyant and thus prone to convective motion. In this article we focus on the large-scale mush mode of instability, arguing that the 'boundary-layer' mode is not amenable to the standard stability analysis, because convective motions occur on that scale for any non-zero value of the Rayleigh number. We quantify the minimum critical Rayleigh number and determine the structure of the convective modes of motion within the mush and the associated deflections of the mush-melt and mush-solid boundaries. This study of convective perturbations differs from previous analyses in two ways; the inhibition of motion and deformation of the mush-melt interface by the stable stratification of the overlying melt is properly quantified and deformation of the mush-solid interface is permitted and quantified. We find that the mush-melt interface is almost unaffected by convection while significant deformation of the mush-solid interface occurs. We show that each of these effects causes significant (unit-order) changes in the predicted critical Rayleigh number. The marginal modes depend on three dimensionless parameters: a scaled eutectic temperature, τ _e (which characterizes the eutectic temperature relative to the depression of the liquidus), a scaled superheat, τ_∞ (which measures the amount by which the temperature of the incoming melt exceeds the liquidus temperature) and the Stefan number, S (which measures the latent heat of crystallization). To survey parameter space, we focus on seven cases, a standard case having S = τ_∞ = τ _e = 1, and six others in which one of the parameters is either large or small compared with unity: a nearly pure case (τ _e = 100; having little of the light constituent), the large superheat limit (τ_∞→ ∞), a case of large latent heat (S = 100), the near eutectic limit (τ _e → 0), a case of small superheat (τ_∞ = 0.01) and the case of zero latent heat (S = 0). The critical Rayleigh number and the associated wavelength of the convection pattern are determined in each case. The eigenvector for each case is presented in terms of the streamlines and the isolines of the perturbation temperature and solid fraction.     

MHD simulations of rayleigh-taylor instability in young supernova remnants

Radio observations shows that young supernova remnants such as Tycho and Cas A generally exhibit a circular clumpy shell. This shell shows a radial magnetic field whose equipartition strength is 2 to 3 orders of magnitude higher than the interstellar field. A simple compression of the ambient field by the shock can explain neither of these observations. We show that the Rayleigh-Taylor instability which occurs at the ejecta/ISM interface can explain these observations. We have done MHD simulations of the instability in the shell of Type-I supernova remnants for the first time by utilizing moving grid technique. Our simulation shows that Rayleigh-Taylor and Kelvin-Helmholtz instabilities amplify ambient magnetic fields locally and produce the clumpy radio shell. Strong magnetic field lines draped around the Rayleigh-Taylor fingers produce the radial B-vector polarization, whereas thermal bremsstrahlung from the dense fingers themselves produce the clumpy X-ray emission.     

Dynamic Model of Mesoscale Eddies

Oceanic mesoscale eddies which are analogs of well known synoptic eddies (cyclones and anticyclones), are studied on the basis of the turbulence model originated by Dubovikov (Dubovikov, M.S., "Dynamical model of turbulent eddies", Int. J. Mod. Phys. B7, 4631-4645 (1993).) and further developed by Canuto and Dubovikov (Canuto, V.M. and Dubovikov, M.S., "A dynamical model for turbulence: I. General formalism", Phys. Fluids 8, 571-586 (1996a) (CD96a); Canuto, V.M. and Dubovikov, M.S., "A dynamical model for turbulence: II. Sheardriven flows", Phys. Fluids 8, 587-598 (1996b) (CD96b); Canuto, V.M., Dubovikov, M.S., Cheng, Y. and Dienstfrey, A., "A dynamical model for turbulence: III. Numerical results", Phys. Fluids 8, 599-613 (1996c)(CD96c); Canuto, V.M., Dubovikov, M.S. and Dienstfrey, A., "A dynamical model for turbulence: IV. Buoyancy-driven flows", Phys. Fluids 9, 2118-2131 (1997a) (CD97a); Canuto, V.M. and Dubovikov, M.S., "A dynamical model for turbulence: V. The effect of rotation", Phys. Fluids 9, 2132-2140 (1997b) (CD97b); Canuto, V.M., Dubovikov, M.S. and Wielaard, D.J., "A dynamical model for turbulence: VI. Two dimensional turbulence", Phys. Fluids 9, 2141-2147 (1997c) (CD97c); Canuto, V.M. and Dubovikov, M.S., "Physical regimes and dimensional structure of rotating turbulence", Phys. Rev. Lett. 78, 666-669 (1997d) (CD97d); Canuto, V.M., Dubovikov, M.S. and Dienstfrey, A., "Turbulent convection in a spectral model", Phys. Rev. Lett. 78, 662-665 (1997e) (CD97e); Canuto, V.M. and Dubovikov, M.S., "A new approach to turbulence", Int. J. Mod. Phys. 12, 3121-3152 (1997f) (CD97f); Canuto, V.M. and Dubovikov, M.S., "Two scaling regimes for rotating Raleigh-Benard convection", Phys. Rev. Letters 78, 281-284, (1998) (CD98); Canuto, V.M. and Dubovikov, M.S., "A dynamical model for turbulence: VII. The five invariants for shear driven flows", Phys. Fluids 11, 659-664 (1999a) (CD99a); Canuto, V.M., Dubovikov, M.S. and Yu, G., "A dynamical model for turbulence: VIII. IR and UV Reynolds stress spectra for shear driven flows", Phys. Fluids 11, 656-677 (1999b) (CD99b); Canuto, V.M., Dubovikov, M.S. and Yu, G., "A dynamical model for turbulence: IX. The Reynolds stress for shear driven flows", Phys. Fluids 11, 678-694 (1999c) (CD99c).). The CD model derives from general principles and does not resort to any free parameters. Yet, it successfully describes a wide variety of quite different turbulent flows. In the present work we apply CD model to the compressible ocean. The model yields mesoscale eddies generated by the baroclinic instability. The latter, in turn, arises from the nonhorizontal orientation of the surfaces of the constant potential density (isopycnals). The obtained dynamic equations for eddy fields reduce to a vertical eigen value problem, an eigen value real part yielding an eddy radius, while an imaginary part - an eddy drift velocity. The size of the eddy is about 3r_d (where r_d is the Rossby deformation radius). The eddy dynamics has the following distinctive features: (1) the large scale potential energy feeds the eddy potential energy (EPE) at scales ～ r_d , (2) from r_d EPE cascades to the smaller scales down to ～ l ₁ determined from the condition that the spectral Rossby number Ro(q) ≡ qU'(q)f^?1 becomes ～ 1 (q is two-dimensional wave number within an isopycnal surface), (3) at scales ～ l ₁ EPE transforms into eddy kinetic energy (EKE) which cascades backwards to the larger scales up to ～ r_d , where it transforms back into EPE, thereby closing the energy flux circulation in a wavenumber space, (4) dissipation of the eddy energy (EE) occurs at scales ～ l ₁ since at those scales the fluctuating component of the vertical shear is maximal and equals to the Brunt-Vaisala frequency. The latter equality is the well known condition for generating the vertical turbulence which dissipates EE. The model enables to determine all turbulence characteristics, including the horizontal (isopycnal) diffusivity κ _h in terms of the large scale mean fields. From the typical values of the latter follow estimates for the parameters of an eddy which agree well with the observational and simulational data: k_h ～ 10³m²s^?1, EKE K ～ 10³m²s^?1, r_d ～ 3 × 10⁴m, l_I ～ 10. In what concerns the bolus velocity, it contains additional terms (as compared to the model of Gent and McWilliams (Gent, P.R. and McWilliams, J.C., "Isopycnal mixing in ocean circulation models", J. Phys. Oceanogr. 20, 150-155 (1990)) which result from the eddy fields advection by a mean velocity ū. Since the latter varies with depth, it is inevitable to differ from the eddy drift velocity that produces a shearing force eroding the eddy coherent structures and, therefore, contributing negatively to EE production. This is in contrast with the positive contribution from the GM term (which is due to the baroclinic instability). In those regions where the disruptive action is stronger, there is no eddy generation.     

The perfect landscape

The “perfect storm” metaphor describes the improbable coincidence of several different forces or factors to produce an unusual outcome. The perfect landscape is conceptualized as a result of the combined, interacting effects of multiple environmental controls and forcings to produce an outcome that is highly improbable, in the sense of the likelihood of duplication at any other place or time. Geomorphic systems have multiple environmental controls and forcings, and degrees of freedom in responding to them. This allows for many possible landscapes and system states. Further, some controls and forcings are causally contingent. These contingencies are specific to time and place. Dynamical instability in many geomorphic systems creates and enhances some of this contingency by causing the effects of minor initial variations and small disturbances to persist, and grow disproportionately large, over time. The joint probability of any particular set of global controls is low, as the individual probabilities are < 1, and the probability of any set of local, contingent controls is even lower. Thus, the probability of existence of any landscape or earth surface system state at a particular place and time is negligibly small: all landscapes are perfect. Recognition of the perfection of landscapes leads away from a worldview holding that landforms and landscapes are the inevitable outcomes of deterministic laws, such that only one outcome is possible for a given set of laws and initial conditions. A perfect landscape perspective leads toward a worldview that landforms and landscapes are circumstantial, contingent results of deterministic laws operating in a specific environmental context, such that multiple outcomes are possible.     

Sequence of instability processes triggered by heavy rainfall in the northern Italy

Northern Italy is a geomorphologically heterogeneous region: high mountains, wide valleys, gentle hills and a large plain form a very varied landscape and influence the temperate climate of the area. The Alps region has harsh winters and moderately warm summers with abundant rainfall. The Po Plain has harsh winters with long periods of subfreezing temperatures and warm sultry summers, with rainfall more common in winter.Geomorphic instability processes are very common. Almost every year, landslides, mud flows and debris flows in the Alpine areas and flooding in the Po flood plain cause severe damage to structures and infrastructure and often claim human lives. Analyses of major events that have struck northern Italy over the last 35 years have provided numerous useful data for the recognition of various rainfall-triggering processes and their sequence of development in relation to the intensity and duration of rainfall. Findings acquired during and after these events emphasise that the quantity and typology of instability processes triggered by rainfall are related not only to an area's morphological and geological characteristics but also to intense rainfall distribution during meteorological disturbances. Moreover, critical rainfall thresholds can vary from place to place in relation to the climatic and geomorphological conditions of the area. Once the threshold has been exceeded, which is about 10% of the local mean annual rainfall (MAR), the instability processes on the slopes and along the hydrographic networks follow a sequence that can be reconstructed in three different phases.In the first phase, the initial instability processes that can usually be observed are soil slips on steep slopes, mud–debris flows in small basins of less than 20 km² in area, while discharge increases substantially in larger stream basins of up to 500 km². In continuous precipitation, in the second phase, first mud–debris flows can be triggered also in basins larger than 20 km² in area. Tributaries swell the main stream, which is already in a critical condition. The violent flow causes severe problems mainly along valley bottoms of rivers with basins up to 2000 km² in area. First bedrock landslides can occur, reaching a considerable area density, with volumes from a few hundred up to about one to two million cubic meters. In continuous precipitation, in the third phase, basins of more than 2000 km² in area reach their first critical stage. River-bed morphology is extensively modified, with erosional and depositional processes which can locally undermine the stability of structures and infrastructures. Waters overflow levees, flooding villages and towns to various widths and depths and sometimes claiming casualties. Some days after an intense rainfall period, large landslides involving the bedrock can still take place. These processes usually cause the movement of very large rock masses. The total duration of rainfall usually has a greater effect on these landslides than does the number of short periods of very intensive precipitation. This sequence cannot be divided into separate phases when the events occur simultaneously because of the presence of intense rainfall pulses and the generation of very diffuse surface runoff. Such situations usually happen during short-lasting heavy summer rainstorms or in late spring, when snow melt combines with intense rainfall. The three-phase sequence has been identified in three severe events that are analysed in this paper: Valtellina (Lombardy) in 1987, Tanaro Valley (Piedmont) in 1994 and Aosta Valley in 2000; but this sequence has also been observed during other events that occurred in northern Italy: in Piedmont in 1968, 1977, 1978, 1993 and 2000; in Lombardy in 1983 and 1992; in the Aosta Valley in 1993.     

暴雨发生的不稳定条件的试验

本文根据Ｈｏｓｋｉｎｓ所提出的惯性重力波不稳定判据：Ｒｉ＜ｆ／ζａ，结合湿斜压大气的特点，对１９９６年６月２９日０２时发生在我国东部的一次降水过程进行了分析，得出了下列特征：西南低空急流是降水得以产生所需水汽的载体；对流层下部深厚不稳定层结是对流性降水所必须的热力层结条件；该地区对流层下部满足Ｒｉｓｅ＜ｆ／ζａ，６ｈ后该地区惯性重力波不稳定增长。在充足水汽条件下，该地区发生暴雨。