共查询到20条相似文献，搜索用时 31 毫秒
1.
Abstract Starting from the nonlinear shallow water equations of a homogeneous rotating fluid we derive the equation describing the evolution of vorticity by a fluctuating bottom topography of small amplitude, using a multiple scale expansion in a small parameter, which is the topographic length scale relative to the tidal wave length. The exact response functions of residual vorticity for a sinusoidal bottom topography are compared with those obtained by a primitive perturbation series and by harmonic truncation, showing the former to be invalid for small topographic length scales and the latter to be only a fair approximation for vorticity produced by planetary vortex stretching. In deriving the exact shape of the horizontal residual velocity profile at a step-like break in the bottom topography, it is shown that the Lagrangian profile only exists in a strip having the width of the amplitude of the tidal excursion at both sides of the break, and that it vanishes outside that interval. Moreover, in the limit of small amplitude topography at least, it vanishes altogether for the generation mechanism by means of planetary vortex stretching. The Eulerian profile is shown to extend over twice the interval of the Lagrangian profile both for production by vortex stretching and by differential bottom friction. These finite intervals over which the residual velocity profiles exist for a step-like topography are not reproduced by harmonic truncation of the basic equation. This method gives exponentially decaying profiles, indicating spurious horizontal diffusion of vorticity. In terms of orders of magnitude, the method of harmonic truncation is reliable for residual velocity produced by vortex stretching but it overestimates the residual velocity produced by differential bottom friction by a factor 2. 相似文献
2.
In a compound meandering channel, patterns of flow structures and bed variations change with increasing water depth owing to complex momentum exchange between high-velocity flow in a main channel and low-velocity flows in flood plains. We have developed a new quasi-three-dimensional model without the shallow water assumption, i.e., hydrostatic pressure distribution; our method is known as the general bottom velocity computation (BVC) method. In this method, a set of depth-integrated equations, including depth-integrated momentum and vorticity equations, are prepared for evaluating bottom velocity and vertical velocity distributions. The objective of this study is to develop a bed variation calculation method for both single and compound meandering channels by using the BVC method coupled with a sediment transport model. This paper shows that the BVC method can reproduce the pattern change of bed variation in a compound meandering channel flow with increasing relative depth. The variation in sediment transport rate due to overbank flow is explained by experimental and computational results. 相似文献
3.
In this paper, we are concerned with sediment transport models consisting of a shallow water system coupled with the so called Exner equation to describe the evolution of the topography. We show that, for some bedload transport models like the well-known Meyer-Peter and Müller model, the system is hyperbolic and, thus, linearly stable, only under some constraint on the velocity. In practical situations, this condition is hopefully fulfilled. Numerical approximations of such system are often based on a splitting method, solving first shallow water equation on a time step and, updating afterwards the topography. It is shown that this strategy can create spurious/unphysical oscillations which are related to the study of hyperbolicity. Using an upper bound of the largest eigenvector may improve the results although the instabilities cannot be always avoided, e.g. in supercritical regions. 相似文献
4.
R. T. Pierrehumbert 《地球物理与天体物理流体动力学》2013,107(1-4):285-319
Abstract We consider the mixing of passive tracers and vorticity by temporally fluctuating large scale flows in two dimensions. In analyzing this problem, we employ modern developments stemming from properties of Hamiltonian chaos in the particle trajectories; these developments generally come under the heading “chaotic advection” or “Lagrangian turbulence.” A review of the salient properties of this kind of mixing, and the mathematics used to analyze it, is presented in the context of passive tracer mixing by a vacillating barotropic Rossby wave. We then take up the characterization of subtler aspects of the mixing. It is shown the chaotic advection produces very nonlocal mixing which cannot be represented by eddy diffusivity. Also, the power spectrum of the tracer field is found to be k ? l at shortwaves—precisely as for mixing by homogeneous, isotropic two dimensional turbulence,—even though the physics of the present case is very different. We have produced two independent arguments accounting for this behavior. We then examine integrations of the unforced barotropic vorticity equation with initial conditions chosen to give a large scale streamline geometry similar to that analyzed in the passive case. It is found that vorticity mixing proceeds along lines similar to passive tracer mixing. Broad regions of homogenized vorticity ultimately surround the separatrices of the large scale streamline pattern, with vorticity gradients limited to nonchaotic regions (regions of tori) in the corresponding passive problem. Vorticity in the chaotic zone takes the form of an arrangement of strands which become progressively finer in scale and progressively more densely packed; this process transfers enstrophy to small scales. Although the enstrophy cascade is entirely controlled by the large scale wave, the shortwave enstrophy spectrum ultimately takes on the classical k ? l form. If one accepts that the enstrophy cascade is indeed mediated by chaotic advection, this is the expected behavior. The extreme form of nonlocality (in wavenumber space) manifest in this example casts some doubt on the traditional picture of enstrophy cascade in the Atmosphere, which is based on homogeneous two dimensional turbulence theory. We advance the conjecture that these transfers are in large measure attributable to large scale, low frequency, planetary waves. Upscale energy transfers amplifying the large scale wave do indeed occur in the course of the above-described process. However, the energy transfer is complete long before vorticity mixing has gotten very far, and therefore has little to do with chaotic advection. In this sense, the vorticity involved in the enstrophy cascade is “fossil vorticity,” which has already given up its energy to the large scale. We conclude with some speculations concerning statistical mechanics of two dimensional flow, prompted by our finding that flows with identical initial energy and enstrophy can culminate in very different final states. We also outline prospects for further applications of chaotic mixing in atmospheric problems. 相似文献
5.
For a proper understanding of flow patterns in curved tidal channels, quantification of contributions from individual physical
mechanisms is essential. We study quantitatively how such contributions are affected by cross-channel bathymetry and three
alternative eddy viscosity parameterisations. Two models are presented for this purpose, both describing flow in curved but
otherwise prismatic channels with an (almost) arbitrary transverse bathymetry. One is a numerical model based on the full
three-dimensional shallow water equations. Special feature of this diagnostic model is that assumptions regarding the relative
importance of particular physical mechanisms can be incorporated in the computations by switching corresponding terms in the
model equations on or off. We also present an idealized model that provides semi-analytical approximate solutions of the shallow
water equations for all three considered alternative eddy viscosity parameterisations. It forms an aid in explaining and theorising
about results obtained with the numerical model. Observations regarding Chesapeake Bay serve as a reference case for the present
study. We find that the relative importance of both along-channel advective forcing and transverse diffusive forcing depends
on local characteristics of the cross-sectional bottom profile rather than global ones. In our reference case, tide-residual
along-channel flow induced by these forcings is not small compared to the total tidal residual. Building on this observation,
we present an indicative test to judge whether advective processes should be included in leading order in modelling tide-dominated
estuarine flow. Furthermore, depending on the applied eddy viscosity parameterisation (uniformly or parabolically distributed
over the vertical), we find qualitatively different spatial patterns for the along-channel advective forcing. 相似文献
6.
Hydraulic redistribution defined as the translocation of soil moisture by plant root systems in response to water potential gradients is a phenomenon widely documented in different climate, vegetation, and soil conditions. Past research has largely focused on hydraulic redistribution in deep tree roots with access to groundwater and/or winter rainfall, while the case of relatively shallow (i.e., ≈1–2 m deep) tree roots has remained poorly investigated. In fact, it is not clear how hydraulic redistribution in shallow root zones is affected by climate, vegetation, and soil properties. In this study, we developed a model to investigate the climate, vegetation, and soil controls on the net direction and magnitude of hydraulic redistribution in shallow tree root systems at the growing season to yearly timescale. We used the model to evaluate the effect of hydraulic redistribution on the water stress of trees and grasses. We found that hydraulic lift increases with decreasing rainfall frequency, depth of the rooting zone, root density in the deep soil and tree leaf area index; at the same time for a given rainfall frequency, hydraulic lift increases with increasing average rainstorm depth and soil hydraulic conductivity. We propose that water drainage into deeper soil layers can lead to the emergence of vertical water potential gradients sufficient to explain the occurrence of hydraulic lift in shallow tree roots without invoking the presence of a shallow water table or winter precipitation. We also found that hydraulic descent reduces the water stress of trees and hydraulic lift reduces the water stress of grass with important implications on tree–grass interactions. 相似文献
7.
Rick Salmon 《地球物理与天体物理流体动力学》2013,107(2):167-179
Abstract The equations for a relativistic perfect fluid result from the requirement that the total mass-energy be stationary with respect to variations δxα(a, b, c, s) in the space-time location of the fluid particle identified by Lagrangian labels (a, b, c) at the point s on its world-line. By considering variations of the Lagrangian labels that leave the specific volume and entropy unchanged, we obtain a general covariant statement of vorticity conservation. The conservation laws for circulation, potential vorticity, and helicity are simple corollaries. This Noether-theorem derivation shows that the vorticity laws have no analogues in particle mechanics, where the corresponding particle labels cannot be continuously vaned. 相似文献
8.
9.
The 3D structure of the tide-induced Lagrangian residual current was studied using the particle image velocimetry (PIV) technique in a long shallow narrow tank in the laboratory. At the mouth of the tank, a wave generator was used to make periodic wave which represents the tide movement, and at the head of the tank, a laterally sloping topography with the length of one fifth of the water tank was installed, above which the tide-induced Lagrangian residual current was studied. Under the weakly nonlinear condition in the present experiment setup, the results show that the Lagrangian residual velocity (LRV) field has a three-layer structure. The residual current flows inwards (towards the head) in the bottom layer and flows outwards in the middle layer, while in the surface layer, it flows inwards along the shallow side of the sloping topography and outwards along the deep side. The depth-averaged and breadth-averaged LRV are also analyzed based on the 3D LRV observations. Our results are in good agreement with the previous experiment studies, the analytical solutions with similar conditions and the observational results in real bays. Moreover, the volume flux comparison between the Lagrangian and Eulerian residual currents shows that the Eulerian residual velocity violates the mass conservation law while the LRV truly represents the inter-tidal water transport. This work enriches the laboratory studies of the LRV and offers valuable references for the LRV studies in real bays. 相似文献
10.
《Advances in water resources》2001,24(5):505-519
A regional model of tides in the Eastern North Pacific Ocean is developed through the use of inversion with two-dimensional finite element codes. Since global tide models are least accurate in coastal environments, modeling tides on a regional scale allows tidal propagation and interaction along the coast to be more accurately represented. In this respect, a regional model can act as a liaison between open ocean dynamics and physical processes more pertinent to coastal systems. The region of interest in this study extends from the Aleutian Islands to Southern California and includes deep ocean, continental shelf, and shallow water features. Boundary conditions are determined from nonlinear inversion of harmonic data from both shallow water and deep ocean tide gauges. Spatial patterns of amplitudes and phases from the model are examined for major constituents. Results are also compared to global tide models at selected stations. 相似文献
11.
Infiltrating river water carries the temperature signal of the river into the adjacent aquifer. While the diurnal temperature fluctuations are strongly dampened, the seasonal fluctuations are much less attenuated and can be followed into the aquifer over longer distances. In one-dimensional model with uniform properties, this signal is propagated with a retarded velocity, and its amplitude decreases exponentially with distance. Therefore, time shifts in seasonal temperature signals between rivers and groundwater observation points may be used to estimate infiltration rates and near-river groundwater velocities. As demonstrated in this study, however, the interpretation is nonunique under realistic conditions. We analyze a synthetic test case of a two-dimensional cross section perpendicular to a losing stream, accounting for multi-dimensional flow due to a partially penetrating channel, convective-conductive heat transport within the aquifer, and heat exchange with the underlying aquitard and the land surface. We compare different conceptual simplifications of the domain in order to elaborate on the importance of different system elements. We find that temperature propagation within the shallow aquifer can be highly influenced by conduction through the unsaturated zone and into the underlying aquitard. In contrast, regional groundwater recharge has no major effect on the simulated results. In our setup, multi-dimensionality of the flow field is important only close to the river. We conclude that over-simplistic analytical models can introduce substantial errors if vertical heat exchange at the aquifer boundaries is not accounted for. This has to be considered when using seasonal temperature fluctuations as a natural tracer for bank infiltration. 相似文献
12.
Irrespective of their spatial extent, free-surface shallow flows are challenging measurement environments for most instruments due to the relatively small depths and velocities typically associated with these flows. A promising candidate for enabling measurements in such conditions is Large-scale Particle Image Velocimetry (LSPIV). This technique uses a non-intrusive approach to measure two-dimensional surface velocity fields with high spatial and temporal resolutions. Although there are many publications documenting the successful use of LSPIV in various laboratory and field open-channel flow situations, its performance has not been equally substantiated for measurement in shallow flows. This paper aims at filling in this gap by demonstrating the capabilities of LSPIV to: (a) accurately evaluate complex flow patterns in shallow channel flows; and (b) estimate depth in shallow flows using exclusively LSPIV measurements. The demonstration is provided by LSPIV measurements in three shallow flow laboratory situations with flow depths ranging from 0.05 to 0.31 m. The obtained measurements illustrate the LSPIV flexibility and reliability in measuring velocities in shallow and low-velocity (near-zero) flows. Moreover, the technique is capable to evaluate and map velocity-derived quantities that are difficult to document with alternative measurement techniques (e.g. vorticity and shear stress distributions and mapping of large-scale structure in the body of water). 相似文献
13.
Kalman filtering for stochastic dynamic tidal models, is a hyperbolic filtering problem. The questions of observability and stability of the filter as well as the effects of the finite difference approximation on the filter performance are studied. The degradation of the performance of the filter, in case an erroneous filter model is used, is investigated. In this paper we discuss these various practical aspects of the application of Kalman filtering for tidal flow identification problems. Filters are derived on the basis of the linear shallow water equations. Analytical methods are used to study the performance of the filters under a variety of circumstances. 相似文献
14.
Abstract The acceptability of zero potential vorticity models as approximations for natural systems of small, but finite, potential vorticity is studied for bounded frontal flows of arbitrary profile. It is demonstrated that all (infinitely) long-wave solutions of the zero potential vorticity front are asymptotic limits for some (not necessarily long-wave) solutions of the small potential vorticity front. In contrast, for downstream-varying solutions there is no simple way of demonstrating this property. These findings suggest that the use of zero potential vorticity models should be carefully examined in other, non-frontal, problems as well. Finally we show that the longwave solutions of the zero potential vorticity flow are at most neutral (quasi-stable). 相似文献
15.
Station Helgoland Roads in the south-eastern North Sea (German Bight) hosts one of the richest long-term time series of marine
observations. Hydrodynamic transport simulations can help understand variability in the local data brought about by intermittent
changes of water masses. The objective of our study is to estimate to which extent the outcome of such transport simulations
depends on the choice of a specific hydrodynamic model. Our basic experiment consists of 3,377 Lagrangian simulations in time-reversed
mode initialized every 7 h within the period Feb 2002–Oct 2004. Fifty-day backward simulations were performed based on hourly
current fields from four different hydrodynamic models that are all well established but differ with regard to spatial resolution,
dimensionality (2D or 3D), the origin of atmospheric forcing data, treatment of boundary conditions, presence or absence of
baroclinic terms, and the numerical scheme. The particle-tracking algorithm is 2D; fields from 3D models were averaged vertically.
Drift simulations were evaluated quantitatively in terms of the fraction of released particles that crossed each cell of a
network of receptor regions centred at the island of Helgoland. We found substantial systematic differences between drift
simulations based on each of the four hydrodynamic models. Sensitivity studies with regard to spatial resolution and the effects
of baroclinic processes suggest that differences in model output cannot unambiguously be assigned to certain model properties
or restrictions. Therefore, multi-model simulations are needed for a proper identification of uncertainties in long-term Lagrangian
drift simulations. 相似文献
16.
Landslides in partially saturated colluvium on Seattle, WA, hillslopes have resulted in property damage and human casualties. We developed statistical models of colluvium and shallow‐groundwater distributions to aid landslide hazard assessments. The models were developed using a geographic information system, digital geologic maps, digital topography, subsurface exploration results, the groundwater flow modeling software VS2DI and regression analyses. Input to the colluvium model includes slope, distance to a hillslope–crest escarpment, and escarpment slope and height. We developed different statistical relations for thickness of colluvium on four landforms. Groundwater model input includes colluvium basal slope and distance from the Fraser aquifer. This distance was used to estimate hydraulic conductivity based on the assumption that addition of finer‐grained material from down‐section would result in lower conductivity. Colluvial groundwater is perched so we estimated its saturated thickness. We used VS2DI to establish relations between saturated thickness and the hydraulic conductivity and basal slope of the colluvium. We developed different statistical relations for three groundwater flow regimes. All model results were validated using observational data that were excluded from calibration. Eighty percent of colluvium thickness predictions were within 25% of observed values and 88% of saturated thickness predictions were within 20% of observed values. The models are based on conditions common to many areas, so our method can provide accurate results for similar regions; relations in our statistical models require calibration for new regions. Our results suggest that Seattle landslides occur in native deposits and colluvium, ultimately in response to surface‐water erosion of hillslope toes. Regional groundwater conditions do not appear to strongly affect the general distribution of Seattle landslides; historical landslides were equally dispersed within and outside of the area potentially affected by regional groundwater conditions. Published in 2007 by John Wiley & Sons, Ltd. 相似文献
17.
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
18.
Jean N. Reinaud 《地球物理与天体物理流体动力学》2017,111(1):32-64
Shielded vortices consist of a core of potential vorticity (PV) of a given sign surrounded (or shielded) by a layer of opposite-signed PV. Such vortices have specific properties and have been the focus of numerous studies, first in two dimensional geometries (where PV is just the vertical component of the vorticity vector) and in geophysical applications (mostly in layered models). The present paper focuses on three-dimensional, spheroidal shielded vortices. In particular, we focus on vortical structures whose overall volume-integrated PV is zero. We restrict attention to vortices of piecewise uniform PV in the present research. We first revisit the problem within the quasi-geostrophic model, then we extend the results to the non-hydrostatic regime. We show that the stability of the structure depends on the ratio of PV between the inner core and the outer shield. In particular it depends on the polarity of the core and of the wavenumber of the azimuthal mode perturbed. 相似文献
19.
P. G. J. ten Brummelhuis A. W. Heemink 《Stochastic Environmental Research and Risk Assessment (SERRA)》1990,4(3):193-208
In this paper a parameter estimation algorithm is developed to estimate uncertain parameters in two dimensional shallow water flow models. Since in practice the open boundary conditions of these models are usually not known accurately, the uncertainty of these boundary conditions has to be taken into account to prevent that boundary errors are interpreted by the estimation procedure as parameter fluctuations. Therefore the open boundary conditions are embedded into a stochastic environment and a constant gain extended Kalman filter is employed to identify the state of the system. Defining a error functional that measures the differences between the filtered state of the system and the measurements, a quasi Newton method is employed to determine the minimum of this functional. To reduce the computational burden, the gradient of the criterium that is required using the quasi Newton method is determined by solving the adjoint system. 相似文献
20.
MASCON方法是直接利用GRACE任务的卫星跟踪卫星技术研究地表浅层物质运动的一种有效技术手段.该方法相较Stokes球谐系数法在一定程度上克服了时变信号的滤波问题,能有效解决该方法时变重力场的南北条带效应.本文在对现有MASCON方法深入研究的基础上对其进行了改进,提出引入卫星精密轨道作为观测值,联合高低跟踪和低低跟踪两类观测数据,实现MASCON参数及有关动力学模型参数求解的思路,在不影响时变信号主要由星间距离变率观测值提供的前提下,采用方差分量估计方法合理定权,充分利用轨道数据的绝对基准作用,用一种改进的途径实现了MASCON方法.利用2008年GRACE的卫星重力观测数据,获得了亚马逊地区的地表物质迁移结果,并与GLDAS水文模型、CSR RL05球谐系数和JPL MASCON方法计算的水储量变化进行比较,表明一致性较好,验证了本文所提MASCON方法解算思路的可靠性,该方法为研究局部地区的地表物质迁移提供了一种可行手段. 相似文献