Fission of a weakly nonlinear interfacial solitary wave at a step     

Roger Grimshaw  Efim Pelinovsky  Tatiana Talipova 《地球物理与天体物理流体动力学》2013,107(2):179-194

The transformation of a weakly nonlinear interfacial solitary wave in an ideal two-layer flow over a step is studied. In the vicinity of the step the wave transformation is described in the framework of the linear theory of long interfacial waves, and the coefficients of wave reflection and transmission are calculated. A strong transformation arises for propagation into shallower water, but a weak transformation for propagation into deeper water. Far from the step, the wave dynamics is described by the Korteweg-de Vries equation which is fully integrable. In the vicinity of the step, the reflected and transmitted waves have soliton-like shapes, but their parameters do not satisfy the steady-state soliton solutions. Using the inverse scattering technique it is shown that the reflected wave evolves into a single soliton and dispersing radiation if the wave propagates from deep to shallow water, and only dispersing radiation if the wave propagates from shallow to deep water. The dynamics of the transmitted wave is more complicated. In particular, if the coefficient of the nonlinear quadratic term in the Korteweg-de Vries equation is not changed in sign in the region after the step, the transmitted wave evolves into a group of solitons and radiation, a process similar to soliton fission for surface gravity waves at a step. But if the coefficient of the nonlinear term changes sign, the soliton is destroyed completely and transforms into radiation. The effects of cubic nonlinearity are studied in the framework of the extended Korteweg-de Vries (Gardner) equation which is also integrable. The higher-order nonlinear effects influence the amplitudes of the generated solitons if the amplitude of the transformed wave is comparable with the thickness of lower layer, but otherwise the process of soliton fission is qualitatively the same as in the framework of the Korteweg-de Vries equation.  相似文献   

Mode coupling analysis and differential rotation in a flow driven by a precessing cylindrical container     

Thierry Lehner  Waleed Mouhali  Jacques Leorat  Alex Mahalov 《地球物理与天体物理流体动力学》2013,107(4):369-401

We present a theoretical weakly nonlinear analysis of the dynamics of an inviscid flow submitted to both rotation and precession of an unbounded cylindrical container, by considering the coupling of two Kelvin (inertial) waves. The parametric centrifugal instability known for this system is shown to saturate when one expands the Navier–Stokes equation to higher order in the assumed small precession parameter (ratio of precession to rotation frequencies) with the derivation of two coupled Landau equations suitable to describe the dynamics of the modes. It is shown that an azimuthal mean flow with differential rotation is generated by this modes coupling. The time evolution of the associated dynamical system is studied. These theoretical results can be compared with water experiments and also to some numerical simulations where viscosity and finite length effects cannot be neglected.  相似文献   

Pdif波在中国CDSN台站的运动学特征          下载免费PDF全文

许健生  隗永刚  张淑珍 《地震工程学报》2013,35(3):610-617

利用中国数字地震台网(简称CDSN,下同)11个台的宽频带长周期(VLP)数字记录对1990-2012年间的124个极远震记录进行了分析处理,在震中距100.0°～179.0°之间,获取了CDSN11个台站的Pdif波的震相数据,得到了Pdif波在地球核幔界面上衍射的运动学特征和《Pdif波走时表》。所得结果大大拓展了Pdif的记录范围,在144.0°～179.0°之间弥补了《IASPEI1991地震波走时表》的缺失,为更大范围内的Pdif震相分析提供了参考标准,有助于提高中国地震台网的地震分析水平和积累震相分析经验,以及对地球核幔边界物理性质的认识。  相似文献   

On the quest for chaotic attractors in hydrological processes     

《水文科学杂志》2013,58(6):1065-1091

Abstract

In the last two decades, several researchers have claimed to have discovered low-dimensional determinism in hydrological processes, such as rainfall and runoff, using methods of chaotic analysis. However, such results have been criticized by others. In an attempt to offer additional insights into this discussion, it is shown here that, in some cases, merely the careful application of concepts of dynamical systems, without doing any calculation, provides strong indications that hydrological processes cannot be (low-dimensional) deterministic chaoti. Furthermore, it is shown that specific peculiarities of hydrological processes on fine time scales, such as asymmetric, J-shaped distribution functions, intermittency, and high autocorrelations, are synergistic factors that can lead to misleading conclusions regarding the presence of (low-dimensional) deterministic chaos. In addition, the recovery of a hypothetical attractor from a time series is put as a statistical estimation problem whose study allows, among others, quantification of the required sample size; this appears to be so huge that it prohibits any accurate estimation, even with the largest available hydrological records. All these arguments are demonstrated using appropriately synthesized theoretical examples. Finally, in light of the theoretical analyses and arguments, typical real-world hydrometeorological time series, such as relative humidity, rainfall, and runoff, are explored and none of them is found to indicate the presence of chaos.  相似文献   

On the frontal condition for finite amplitude α2Ω-dynamo wave trains in stellar shells     

Andrew P. Bassom  Andrew M. Soward 《地球物理与天体物理流体动力学》2013,107(3-4):285-328

Abstract

In a previous paper, Bassom et al. (Proc. R. Soc. Lond. A, 455, 1443–1481, 1999) (BKS) investigated finite amplitude αΩ-dynamo wave trains in a thin turbulent, differentially rotating convective stellar shell; nonlinearity arose from α-quenching. There asymptotic solutions were developed based upon the small aspect ratio ε of the shell. Specifically, as a consequence of a prescribed latitudinally dependent α-effect and zonal shear flow, the wave trains have smooth amplitude modulation but are terminated abruptly across a front at some high latitude θ_F. Generally, the linear WKB-solution ahead of the front is characterised by the vanishing of the complex group velocity at a nearby point θ_f; this is essentially the Dee–Langer criterion, which determines both the wave frequency and front location.

Recently, Griffiths et al. (Geophys. Astrophys. Fluid Dynam. 94, 85–133, 2001) (GBSK) obtained solutions to the α²Ω-extension of the model by application of the Dee—Langer criterion. Its justification depends on the linear solution in a narrow layer ahead of the front on the short O(θ_f—θ_F) length scale; here conventional WKB-theory, used to describe the solution elsewhere, is inadequate because of mode coalescence. This becomes a highly sensitive issue, when considering the transition from the linear solution, which occurs when the dynamo number D takes its critical value D _c corresponding to the onset of kinematic dynamo action, to the fully nonlinear solutions, for which the Dee—Langer criterion pertains.

In this paper we investigate the nature of the narrow layer for α²Ω-dynamos in the limit of relatively small but finite α-effect Reynolds numbers R _α, explicitly ε^½ ? R ² _α ? 1. Though there is a multiplicity of solutions, our results show that the space occupied by the corresponding wave train is generally maximised by a solution with θ_f—θ_F small; such solutions are preferred as evinced by numerical simulations. This feature justifies the application by GBSK of the Dee—Langer criterion for all D down to the minimum D _min that the condition admits. Significantly, the frontal solutions are subcritical in the sense that |D _min| ≤ |D _c|; equality occurs as the α-effect Reynolds number tends to zero. We demonstrate that the critical linear solution is not connected by any parameter track to the preferred nonlinear solution associated with D _min. By implication, a complicated bifurcation sequence is required to make the connection between the linear and nonlinear states. This feature is in stark contrast to the corresponding results for αΩ-dynamos obtained by BKS valid in the limit R _{2 α} ? ε^½, which, though exhibiting a weak subcriticality, showed that the connection follows a clearly identifiable nonbifurcating track.  相似文献   

Resistive wave breaking in the Earth's outer core     

Steven D. London 《地球物理与天体物理流体动力学》2013,107(5):397-411

The equations for an electrically conducting fluid in cylindrical coordinates are linearized assuming that the inertial terms in the momentum equation can be ignored (small Rossby number), and that the ratio of the Elsasser number and magnetic Reynolds number is one. After these assumptions, the governing equations are linearized about an ambient solution which vanishes at the the equator. Upon assuming large Elsasser and magnetic Reynolds number, the solutions to the linearized equations are approximated by wave trains having very short wave length (relative to the core radius) but which vary slowly (on a scale of the core radius). The period of the waves is much longer than a day but much shorter than the period of the slow hydromagnetic oscillations. These waves are found to be trapped in a region about the equator and away from the axis of rotation. The waves break at a latitudinal wave region boundary, in the sense that the waves become exponentially large in a boundary layer, having as an exponent some positive power of the large azimuthal wave number. This behavior is amplified as the Elsasser number becomes smaller while still remaining relatively large. Waves in more Earth-like parameter regimes are discussed briefly.  相似文献   

A Nonlinear Representation of Model Uncertainty in a Convective-Scale Ensemble Prediction System     

Zhizhen XU  Jing CHEN  Mu MU  Guokun DAI  Yanan MA 《大气科学进展》2022,39(9):1432-1450

How to accurately address model uncertainties with consideration of the rapid nonlinear error growth characteristics in a convection-allowing system is a crucial issue for performing convection-scale ensemble forecasts. In this study, a new nonlinear model perturbation technique for convective-scale ensemble forecasts is developed to consider a nonlinear representation of model errors in the Global and Regional Assimilation and Prediction Enhanced System (GRAPES) Convection-Allowing Ensemble Prediction System (CAEPS). The nonlinear forcing singular vector (NFSV) approach, that is, conditional nonlinear optimal perturbation-forcing (CNOP-F), is applied in this study, to construct a nonlinear model perturbation method for GRAPES-CAEPS. Three experiments are performed: One of them is the CTL experiment, without adding any model perturbation; the other two are NFSV-perturbed experiments, which are perturbed by NFSV with two different groups of constraint radii to test the sensitivity of the perturbation magnitude constraint. Verification results show that the NFSV-perturbed experiments achieve an overall improvement and produce more skillful forecasts compared to the CTL experiment, which indicates that the nonlinear NFSV-perturbed method can be used as an effective model perturbation method for convection-scale ensemble forecasts. Additionally, the NFSV-L experiment with large perturbation constraints generally performs better than the NFSV-S experiment with small perturbation constraints in the verification for upper-air and surface weather variables. But for precipitation verification, the NFSV-S experiment performs better in forecasts for light precipitation, and the NFSV-L experiment performs better in forecasts for heavier precipitation, indicating that for different precipitation events, the perturbation magnitude constraint must be carefully selected. All the findings above lay a foundation for the design of nonlinear model perturbation methods for future CAEPSs.  相似文献   

The Roles of Barotropic Instability and the Beta Effect in the Eyewall Evolution of Tropical Cyclones     

Jie JIANG  Yuqing WANG 《大气科学进展》2022,39(11):1800-1815

Diabatic heating by convection in the eyewall often produces an annular region of high potential vorticity (PV) around the relatively low PV eye in a strong tropical cyclone (TC). Such a PV ring is barotropically unstable and can encourage the exponential growth of PV waves. In this study, such instability and the subsequent nonlinear evolution of three TC-like vortices having PV rings with different degrees of hollowness on an f-plane are first examined using an unforced, inviscid shallow-water-equation model. Results show that the simulated eyewalls evolve similarly to those in the nondivergent barotropic model. It is also found that the polygonal eyewall structure can be decomposed into vortex Rossby waves (VRWs) of different wavenumbers with different amplitudes, allowing for wave-wave interactions to produce complicated behaviors of mesovortices in the TC eyewall. The same set of PV rings has been examined on a beta-plane. Although the beta effect has been rendered unimportant to the eyewall evolution due to the relatively small scale of the inner-core circulation, this study shows that the beta effect may erode the coherent structure of mesovortices in the eyewall of an initially hollow PV-ring vortex. Mesovortices modeled on the beta-plane with a greater beta parameter tend to experience an earlier breakdown and enhanced radial gradients of the basic-state (azimuthally mean) angular velocity, followed by wave-wave, wave-flow interactions, leading to earlier merger and axisymmetrization processes. This result implies that the beta effect could be one of the forcings that shorten the lifetime of quasi-steady mesovortices in the eyewall of real TCs.  相似文献   

瞬时单位线法在浙江省应用的几个问题研究     

傅联森  陈润  周焕 《水文》2012,32(3):43-46,87

纳希瞬时单位线在浙江省地区得到应用,为了使该方法适用于该地区,需要对其中的模型参数和非线性外延控制两个问题进行研究。通过对瞬时单位线法中n和K参数作用的研究分析,结合浙江省地区的实际情况,研究出按照流域面积大小分级取用n值的关系;同时通过对浙江省地区实际水雨情进行计算分析,得出临界雨强控制在30～40mm/h在浙江省地区是合理的。该成果为纳希瞬时单位线在浙江省地区的使用提供了参考依据。  相似文献   

Sedimentological and ichnological signatures of changes in wave,river and tidal influence along a Neogene tropical deltaic shoreline     

LUIS A. BUATOIS  NUBIA SANTIAGO  MEYLIN HERRERA  PIRET PLINK‐BJÖRKLUND  RON STEEL  MARÍA ESPIN  KAOLU PARRA 《Sedimentology》2012,59(5):1568-1612

Analysis of Neogene cores from the Eastern Venezuela Basin along 65 km of a west–east trending shoreline allows characterization of the sedimentological and ichnological signatures of wave, river and tidal processes. The area displays deltas prograding northward from the Guyana Shield. Twenty‐three facies are defined and grouped into four categories (wave‐influenced, river‐influenced, tide‐influenced and basinal). Wave‐dominated deltaic deposits occur mostly in the Tácata Field. The delta plain was characterized by tide‐influenced distributary channels separated by interdistributary bays. Fluvial discharge in the delta front and prodelta was repeatedly interrupted by storm‐wave reworking and suspended sediment fallout. Delta‐front and prodelta deposits contain some ichnotaxa that typically do not occur in brackish water (for example, Chondrites and Phycosiphon). Amalgamated storm deposits are unburrowed or contain vertical Ophiomorpha. Lateral (especially on the updrift side) to the river mouths, waves caused nearly continuous accretion of the associated strandplains. These deposits are the most intensely bioturbated, and are dominated by the estenohaline echinoid‐generated ichnogenus Scolicia. River‐dominated deltaic deposits are present in the Santa Bárbara, Mulata, Carito and El Furrial Fields. Low‐sinuosity rivers characterized the alluvial plain, whereas the subaerial delta plain was occupied by higher‐sinuosity rivers. The subaqueous delta plain includes distributary channels and tide‐influenced interdistributary bays. Further seaward, successions are characterized by terminal distributary‐channel and distributary mouth‐bar deposits, as well as by delta‐front and prodelta deposits showing evidence of sediment gravity‐flow and fluid‐mud emplacement. Delta‐front and prodelta deposits are unbioturbated to sparsely bioturbated, suggesting extreme stress, mostly as a result of high fluvial discharge and generation of sediment gravity flows. Tidal influence is restricted to interdistributary bays, lagoons and some distributary channels. From an ichnological perspective, and in order of decreasing stress levels, four main depositional settings are identified: river‐dominated deltas, tide‐influenced delta plains, wave‐dominated deltas and wave‐dominated strandplain–offshore complexes.  相似文献