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1.
The Lagrangian complex-space singularities of the steady Eulerian flow with stream function sin x 1 cos x 2 are studied by numerical and analytical methods. The Lagrangian singular manifold is analytic. Its minimum distance from the real domain decreases logarithmically at short times and exponentially at large times.  相似文献   

2.

The spectrum of internal gravity waves in the atmosphere and oceans is sufficiently intense that nonlinear interactions must occur, if these waves are analyzed in Eulerian coordinates as is usually done. As it happens, however, if these waves are analyzed in Lagrangian coordinates the most important nonlinearity can be entirely avoided: it is an Eulerian mathematical construct only, not a physical process. The mathematical basis for this assertion is developed here, and some of its consequences are discussed. Among the latter is a questioning of the validity of standard Eulerian eikonal methods of calculating ray paths and related functions in a multiwave environment, discussed in an appendix.  相似文献   

3.
The Eulerian residual transport velocity and the first-order Lagrangian residual velocity for weakly nonlinear systems have been used extensively in the past to depict inter-tidal mass transport. However, these could not explain the observed net surface sediment transport pattern in Jiaozhou Bay (JZB), located on the western Yellow Sea. JZB is characterized by strong tidal motion, complex topography and an irregular coastline, which are features of typical nonlinear systems. The Lagrangian residual velocity, which is applicable to general nonlinear systems, was simulated with the water parcel tracking method. The results indicate that the composition of the Lagrangian residual velocity at different tidal phases coincides well with the observed net surface sediment transport pattern. The strong dependence of water flushing time on the initial tidal phase can also be explained by the significant intra-tidal variation of the Lagrangian residual velocity. To investigate the hydrodynamic mechanism governing the nonlinearity of the M 2 tidal system, a set of nonlinearity indexes were defined and analysed. In the surface layer, horizontal advection is the main contributor to the strong nonlinearity near the bay mouth, while in the bottom layer, the strong nonlinearity near the bay mouth may result from the vertical viscosity and horizontal advection.  相似文献   

4.
Liu  Guangliang  Liu  Zhe  Gao  Huiwang  Gao  Zengxiang  Feng  Shizuo 《Ocean Dynamics》2012,62(10):1443-1456

The Eulerian residual transport velocity and the first-order Lagrangian residual velocity for weakly nonlinear systems have been used extensively in the past to depict inter-tidal mass transport. However, these could not explain the observed net surface sediment transport pattern in Jiaozhou Bay (JZB), located on the western Yellow Sea. JZB is characterized by strong tidal motion, complex topography and an irregular coastline, which are features of typical nonlinear systems. The Lagrangian residual velocity, which is applicable to general nonlinear systems, was simulated with the water parcel tracking method. The results indicate that the composition of the Lagrangian residual velocity at different tidal phases coincides well with the observed net surface sediment transport pattern. The strong dependence of water flushing time on the initial tidal phase can also be explained by the significant intra-tidal variation of the Lagrangian residual velocity. To investigate the hydrodynamic mechanism governing the nonlinearity of the M 2 tidal system, a set of nonlinearity indexes were defined and analysed. In the surface layer, horizontal advection is the main contributor to the strong nonlinearity near the bay mouth, while in the bottom layer, the strong nonlinearity near the bay mouth may result from the vertical viscosity and horizontal advection.

  相似文献   

5.
With a depth-averaged numerical model, the tidally induced Lagrangian residual current in a model bay was studied. To correctly reflect the long-term mass transport, it is appropriate to use the Lagrangian residual velocity (LRV) rather than the Eulerian residual velocity (ERV) or the Eulerian residual transport velocity (ETV) to describe the residual current. The parameter κ, which is defined as the ratio of the typical tidal amplitude at the open boundary to the mean water depth, is considered to be the indicator of the nonlinear effect in the system. It is found that the feasibility of making the mass transport velocity (MTV) approximate the LRV is strongly dependent on κ. The error between the MTV and the LRV tends to increase with a growing κ. An additional error will come from the various initial tidal phases due to the Lagrangian drift velocity (LDV) when κ is no longer small. According to the residual vorticity equation based on the MTV, the Coriolis effect is found to influence the residual vorticity mainly through the curl of the tidal stress. A significant difference in the flow pattern indicates that the LRV is sensitive to the bottom friction in different forms.  相似文献   

6.
Both Eulerian and Lagrangian reactive transport simulations in natural media require selection of a parameter that controls the “promiscuity” of the reacting particles. In Eulerian models, measurement of this parameter may be difficult because its value will generally differ between natural (diffusion-limited) systems and batch experiments, even though both are modeled by reaction terms of the same form. And in Lagrangian models, there previously has been no a priori way to compute this parameter. In both cases, then, selection is typically done by calibration, or ad hoc. This paper addresses the parameter selection problem for Fickian transport by deriving, from first principles and D (the diffusion constant) the reaction-rate-controlling parameters for particle tracking (PT) codes and for the diffusion–reaction equation (DRE). Using continuous time random walk analysis, exact reaction probabilities are derived for pairs of potentially reactive particles based on D and their probability of reaction provided that they collocate. Simultaneously, a second PT scheme directly employing collocation probabilities is derived. One-to-one correspondence between each of D, the reaction radius specified for a PT scheme, and the DRE decay constant are then developed. These results serve to ground reactive transport simulations in their underlying thermodynamics, and are confirmed by simulations.  相似文献   

7.
This article is offered to honor Professor George F. Pinder. Its technical contents were motivated by an Eulerian–Lagrangian method that was recently proposed by him and his collaborators. Two one-node-collocation algorithms, which may be used to advance that method are presented. Although they are here discussed for 1-D problems only, one of them has already been generalized to problems in several space variables. Thus, this paper essentially generalizes the above mentioned Eulerian–Lagrangian method of Pinder et al. to problems in several dimensions. Also, the results presented in this paper have a wider interest in water resources studies because they apply to advection diffusive transport processes in general. The methodology used to develop the new algorithms is a unified theory of domain decomposition methods (DDM), recently introduced by the authors and which owes much to George F. Pinder. The results reported in the present paper illustrate, by the way, its application and power.  相似文献   

8.
The upscaling of dispersivity in solute transport in heterogeneous aquifers is addressed with a numerical stochastic formulation. This work represents progress toward converting theory into scalable numerical models that can be compared to laboratory experiments. Traditional global assumptions of low variance, ergodicity, single correlation scale, stationarity, and the like are avoided through the use of a flexible Lagrangian numerical, not analytical, framework, which allows assumptions to be local. A method of calculating grid-block upscaled dispersivities is presented. Computational results are obtained for a heterogeneous tank experiment, with reasonable behavior.  相似文献   

9.
The responses to tidal and/or wind forces of Lagrangian trajectories and Eulerian residual velocity in the southwestern Yellow Sea are investigated using a high-resolution circulation model. The simulated tidal harmonic constants agree well with observations and existing studies. The numerical experiment reproduces the long-range southeastward Eulerian residual current over the sloping bottom around the Yangtze Bank also shown in previous studies. However, the modeled drifters deployed at the northeastern flank of the Yangtze Bank in the simulation move northeastward, crossing over this strong southeastward Eulerian residual current rather than following it. Additional sensitivity experiments reveal that the influence of the Eulerian tidal residual currents on Lagrangian trajectories is relatively weaker than that of the wind driven currents. This result is consistent with the northeastward movement of ARGOS surface drifters actually released in the southwestern Yellow Sea. Further experiments suggest that the quadratic nature of the bottom friction is the crucial factor, in the southwestern Yellow Sea, for the weaker influence of the Eulerian tidal residual currents on the Lagrangian trajectories. This study demonstrates that the Lagrangian trajectories do not follow the Eulerian residual velocity fields in the shallow coastal regions of the southwestern Yellow Sea.  相似文献   

10.
Abstract

Geostrophic flow in the theory of a shallow rotating fluid is exactly analogous to the drift approximation in a strongly magnetized electrostatic plasma. This analogy is developed and exhibited in detailed to derive equations for the slow nearly geostrophic motion. The key ingredient in the theory is the isolation, to whatever order in Rossby number desired, of the fast motion near the inertial frequency. One of the remaining degrees of freedom represents a new approximate constant of the motion for nearly geostrophic flow. This is the analogue of the familiar magnetic moment adiabatic invariant in the plasma problem.

The procedure is a Rossby number expansion of the Hamiltonian for the fluid expressed in Lagrangian, rather than Eulerian variables. The fundamental Poisson brackets of the theory are not expanded so desirable properties such as energy conservation are maintained throughout.  相似文献   

11.
《Advances in water resources》2005,28(11):1230-1239
Taylor’s hypothesis (TH) for rainfall fields states that the spatial correlation of rainfall intensity at two points at the same instant of time can be equated with the temporal correlation at two instants of time at some fixed location. The validity of TH is tested in a set of 12 storms developed in Rondonia, southwestern Amazonia, Brazil, during the January–February 1999 Wet Season Atmospheric Meso-scale Campaign. The time Eulerian and Lagrangian Autocorrelation Functions (ACF) are estimated, as well as the time-averaged space ACF, using radar rainfall rates of storms spanning between 3.2 and 23 h, measured at 7–10-min time resolution, over a circle of 100 km radius, at 2 km spatial resolution. TH does not hold in 9 out of the 12 studied storms, due to their erratic trajectories and very low values of zonal wind velocity at 700 hPa, independently from underlying atmospheric stability conditions. TH was shown to hold for 3 storms, up to a cutoff time scale of 10–15 min, which is closely related to observed features of the life cycle of convective cells in the region. Such cutoff time scale in Amazonian storms is much shorter than the 40 min identified in mid-latitude convective storms, due to much higher values of CAPE and smaller values of storm speed in Amazonian storms as compared to mid-latitude ones, which in turn contribute to a faster destruction of the rainfall field isotropy. Storms satisfying TH undergo smooth linear trajectories over space, and exhibit the highest negative values of maximum, mean and minimum zonal wind velocity at 700 hPa, within narrow ranges of atmospheric stability conditions. Non-dimensional parameters involving CAPE (maximum, mean and minimum) and CINE (mean) are identified during the storms life cycle, for which TH holds: CAPE mean/CINE mean = [30–35], CAPE max/CINE mean = [32–40], and CAPE min/CINE mean = [22–28]. These findings are independent upon the timing of storms within the diurnal cycle. Also, the estimated Eulerian time ACF’s decay faster than the time-averaged space and the Lagrangian time ACF’s, irrespectively of TH validity. The Eulerian ACF’s exhibit shorter e-folding times, reflecting smaller correlations over short time scales, but also shorter scale of fluctuation, reflecting less persistence in time than over space. No significant associations (linear, exponential or power law) were found between estimated e-folding times and scale of fluctuation, with all estimates of CAPE and CINE. Secondary correlation maxima appear between 50 and 70 min in the Lagrangian time ACF’s for storms satisfying TH. No differences were found in the behavior of each of the three ACF’s for storms developed during either the Easterly or Westerly zonal wind regimes which characterize the development of meso-scale convective systems over the region. These results have important implications for modelling and downscaling rainfall fields over tropical land areas.  相似文献   

12.
1　ＩＮＴＲＯＤＵＣＴＩＯＮ　Ｓｅｄｉｍｅｎｔａｔｉｏｎｉｓａｈｙｄｒａｕｌｉｃｐｒｏｃｅｓｓｏｒａｗａｔｅｒｔｒｅａｔｍｅｎｔｐｒｏｃｅｓｓｔｏｓｅｐａｒａｔｅｓｏｌｉｄｆｒｏｍｗａｔｅｒｂｙｇｒａｖｉｔｙ,ｗｉｄｅｌｙｕｓｅｄｉｎｗａｔｅｒａｎｄｗ...  相似文献   

13.
Net sediment transport in tidal basins is a subtle imbalance between large fluxes produced by the flood/ebb alternation. The imbalance arises from several mechanisms of suspended transport. Lag effects and tidal asymmetries are regarded as dominant, but defined in different frames of reference (Lagrangian and Eulerian, respectively). A quantitative ranking of their effectiveness is therefore missing. Furthermore, although wind waves are recognized as crucial for tidal flats’ morphodynamics, a systematic analysis of the interaction with tidal mechanisms has not been carried out so far. We review the tide-induced barotropic mechanisms and discuss the shortcomings of their current classification for numerical process-based models. Hence, we conceive a unified Eulerian framework accounting for wave-induced resuspension. A new methodology is proposed to decompose the sediment fluxes accordingly, which is applicable without needing (semi-) analytical approximations. The approach is tested with a one-dimensional model of the Vlie basin, Wadden Sea (The Netherlands). Results show that lag-driven transport is dominant for the finer fractions (silt and mud). In absence of waves, net sediment fluxes are landward and spatial (advective) lag effects are dominant. In presence of waves, sediment can be exported from the tidal flats and temporal (local) lag effects are dominant. Conversely, sand transport is dominated by the asymmetry of peak ebb/flood velocities. We show that the direction of lag-driven transport can be estimated by the gradient of hydrodynamic energy. In agreement with previous studies, our results support the conceptualization of tidal flats’ equilibrium as a simplified balance between tidal mechanisms and wave resuspension.  相似文献   

14.
—?A set of procedures is described for estimating network-averaged teleseismic P-wave spectra for underground nuclear explosions and for analytically inverting these spectra to obtain estimates of m b /yield relations and individual yields for explosions at previously uncalibrated test sites. These procedures are then applied to the analyses of explosions at the former Soviet test sites at Shagan River, Degelen Mountain, Novaya Zemlya and Azgir, as well as at the French Sahara, U.S. Amchitka and Chinese Lop Nor test sites. It is demonstrated that the resulting seismic estimates of explosion yield and m b /yield relations are remarkably consistent with a variety of other available information for a number of these test sites. These results lead us to conclude that the network-averaged teleseismic P-wave spectra provide considerably more diagnostic information regarding the explosion seismic source than do the corresponding narrowband magnitude measures such as m b , M s and m b (L g ), and, therefore, that they are to be preferred for applications to seismic yield estimation for explosions at previously uncalibrated test sites.  相似文献   

15.
The development of numerical wave models for coastal applications, including coupling with ocean circulation models, has spurred an ongoing effort on theoretical foundations, numerical techniques, and physical parameterizations. Some important aspects of this effort are reviewed here, and results are shown in the case of the French Atlantic and Channel coast using version 4.18 of the WAVEWATCH III R model. Compared to previous results, the model errors have been strongly reduced thanks to, among other things, the introduction of currents, coastal reflection, and bottom sediment types. This last item is described here for the first time, allowing unprecedented accuracy at some sites along the French Atlantic Coast. The adequate resolution, necessary to represent strong gradients in tidal currents, was made possible by the efficiency brought by unstructured grids. A further increase in resolution, necessary to resolve surf zones and still cover vast regions,will require further developments in numerical methods.  相似文献   

16.
Fractional derivatives can be viewed either as handy extensions of classical calculus or, more deeply, as mathematical operators defined by natural phenomena. This follows the view that the diffusion equation is defined as the governing equation of a Brownian motion. In this paper, we emphasize that fractional derivatives come from the governing equations of stable Lévy motion, and that fractional integration is the corresponding inverse operator. Fractional integration, and its multi-dimensional extensions derived in this way, are intimately tied to fractional Brownian (and Lévy) motions and noises. By following these general principles, we discuss the Eulerian and Lagrangian numerical solutions to fractional partial differential equations, and Eulerian methods for stochastic integrals. These numerical approximations illuminate the essential nature of the fractional calculus.  相似文献   

17.
This paper is concerned with application of the h-adaptive finite element method to dynamic analysis of a pile in liquefiable soil considering large deformation. In finite element analysis of pile behavior in liquefiable soil during an earthquake, especially considering large deformation of liquefied ground, error due to discretization in the zone near the pile becomes very large. Our purpose was to refine the approximation of the finite element method. The updated Lagrangian formulation and a cyclic elasto-plastic model based on the kinematic hardening rule were adopted to deal with the nonlinearity of the soil. The mixed finite element and finite difference methods together with the u-p formulation and Biot's two-phase mixture theory were used. To improve the accuracy and increase the efficiency of finite element analysis, an h-adaptive scheme that included a posteriori error estimation and h-version mesh refinement was applied to the analysis. The calculated results of effective stress were smoothed locally by the extrapolation method and smoothed stress was used to calculate the L2 norm of the effective stress error in the last step of the calculation of each time increment. The mesh was refined by a fission procedure based on the indication of the error estimate As a numerical example, a soil–pile interaction system loaded cyclically was analyzed by our method.  相似文献   

18.
This study proposes a recording-based approach to characterize and quantify earthquake-induced site nonlinearity, exemplified as soil nonlinearity and/or liquefaction. Alternative to Fourier spectral analysis (FSA), the paper introduces time–frequency analysis of earthquake ground motion recordings with the aid of so-called Hilbert-Huang transform (HHT), and offers justification for the HHT in addressing the nonlinear features shown in the recordings. With the use of the 2001 Nisqually earthquake recordings, this study shows that the proposed approach is effective in characterizing site nonlinearity and quantifying the influences in seismic ground responses. Major results from this study are listed below.
1. HHT-based site amplification is defined as the ratio of marginal Hilbert amplitude spectra, similar to the Fourier-based one that is the ratio of Fourier amplitude spectra. The HHT-based site amplification can be used in effectively quantifying site nonlinearity in terms of frequency downshift in the low-frequency range and amplification-reduction factor in intermediate-frequency range in comparison with the Fourier-based one.
2. Instantaneous damping, and Hilbert and marginal Hilbert damping spectra are defined in ways similar to instantaneous frequency, and Hilbert and marginal Hilbert amplitude spectra, respectively. Consequently, the HHT-based site damping is found as the difference of marginal Hilbert damping spectra, which can be used as an alternative, complementary index to measure the influences of site nonlinearity in seismic ground responses.
Keywords: Site nonlinearity; Site amplification; Site damping; Hilbert-Huang transform (HHT); Liquefaction; 2001 Nisqually earthquake  相似文献   

19.
Retrospective data of monitoring under conditions of low seismic activity are used to identify free oscillations of the Earth, including the fundamental mode, the oscillation with a central period of 54 min (0 S 2 m multiplet), split into five lines with azimuthal numbers m = ?2, ?1, 0, 1, 2. It is shown that some lines of this oscillation are also recorded in atmospheric pressure variation spectra and group in ensembles of observations around frequencies predicted by the 0 S 2 m splitting theory. This phenomenon is discovered in data recorded both synchronously and in different time intervals. A causal relationship involved in the oscillation under study is determined on the basis of the examination of the direction of the acoustic energy flux. The energy flux in the region of the 0 S 2 m multiplet is shown to be directed from the Earth toward the atmosphere. This suggests that deep processes in the Earth are capable of exciting its upper shells.  相似文献   

20.
Relationships describing response times for landscape saturation and subsurface flow for idealised hillslopes after a change in water balance are derived in terms of similarity parameters given by their topographic, soil and climatic attributes. The study was carried out under a set of specific assumptions.The work quantitatively describes effects of each of these attributes on travel time. For example, divergent hillslopes can exhibit travel times that are double those of convergent hillslopes, and concave slopes tend to have lower travel times than planar or convex slopes. It is shown that the hillslope travel time T is dependent on hillslope length L, hydraulic conductivity K and slope S such that T = f(L/KS, B, CR, Δq/smd) and if saturation does not occur in the lower reaches of a hillslope, this can be simplified to T = f(L/KS, B). Here, Δq is change in net external flux and smd is soil moisture deficit; CR and B are the convergence ratio and profile factor respectively. The relative importance of these attributes on response time is discussed.It is shown that subsurface flow hydrographs of simple hillslopes of different scale, derived numerically, can be collapsed into a single curve by normalising them by means of a form of response time, the time constant.Results from the analytical derivation were compared with numerical analysis with good agreement. The theory was applied to a natural catchment using observed data from a bushfire event. Comparison of analytically calculated response time with observed response time for the event showed a large discrepancy. The reason is discussed.  相似文献   

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