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1.
Etienne Mémin 《地球物理与天体物理流体动力学》2014,108(2):119-146
We present a derivation of a stochastic model of Navier Stokes equations that relies on a decomposition of the velocity fields into a differentiable drift component and a time uncorrelated uncertainty random term. This type of decomposition is reminiscent in spirit to the classical Reynolds decomposition. However, the random velocity fluctuations considered here are not differentiable with respect to time, and they must be handled through stochastic calculus. The dynamics associated with the differentiable drift component is derived from a stochastic version of the Reynolds transport theorem. It includes in its general form an uncertainty dependent subgrid bulk formula that cannot be immediately related to the usual Boussinesq eddy viscosity assumption constructed from thermal molecular agitation analogy. This formulation, emerging from uncertainties on the fluid parcels location, explains with another viewpoint some subgrid eddy diffusion models currently used in computational fluid dynamics or in geophysical sciences and paves the way for new large-scales flow modeling. We finally describe an applications of our formalism to the derivation of stochastic versions of the Shallow water equations or to the definition of reduced order dynamical systems. 相似文献
2.
A complex and highly dynamical ocean region, the Agulhas Current System plays an important role in the transfer of energy, nutrients and organic material from the Indian to the Atlantic Ocean. Its dynamics are not only important locally, but affect the global ocean-atmosphere system. In working towards improved ocean reanalysis and forecasting capabilities, it is important that numerical models simulate mesoscale variability accurately—especially given the scarcity of coherent observational platforms in the region. Data assimilation makes use of scarce observations, a dynamical model and their respective error statistics to estimate a new, improved model state that minimises the distance to the observations whilst preserving dynamical consistency. Qualitatively, it is unclear whether this minimisation directly translates to an improved representation of mesoscale dynamics. In this study, the impact of assimilating along-track sea-level anomaly (SLA) data into a regional Hybrid Coordinate Ocean Model (HYCOM) is investigated with regard to the simulation of mesoscale eddy characteristics. We use an eddy-tracking algorithm and compare the derived eddy characteristics of an assimilated (ASSIM) and an unassimilated (FREE) simulation experiment in HYCOM with gridded satellite altimetry-derived SLA data. Using an eddy tracking algorithm, we are able to quantitatively evaluate whether assimilation updates the model state estimate such that simulated mesoscale eddy characteristics are improved. Additionally, the analysis revealed limitations in the dynamical model and the data assimilation scheme, as well as artefacts introduced from the eddy tracking scheme. With some exceptions, ASSIM yields improvements over FREE in eddy density distribution and dynamics. Notably, it was found that FREE significantly underestimates the number of eddies south of Madagascar compared to gridded altimetry, with only slight improvements introduced through assimilation, highlighting the models’ limitation in sustaining mesoscale activity in this region. Interestingly, it was found that the threshold for the maximum eddy propagation velocity in the eddy detection scheme is often exceeded when data assimilation relocates an eddy, causing the algorithm to interpret the discontinuity as eddy genesis, which directly influences the eddy count, lifetime and propagation velocity, and indirectly influences other metrics such as non-linearity. Finally, the analysis allowed us to separate eddy kinetic energy into contributions from detected mesoscale eddies and meandering currents, revealing that the assimilation of SLA has a greater impact on mesoscale eddies than on meandering currents. 相似文献
3.
Modeling of suspended sediment particle movement in surface water can be achieved by stochastic particle tracking model approaches.In this paper,different mathematical forms of particle tracking models are introduced to describe particle movement under various flow conditions,i.e.,the stochastic diffusion process,stochastic jump process,and stochastic jump diffusion process.While the stochastic diffusion process can be used to represent the stochastic movement of suspended particles in turbulent flows,the stochastic jump and the stochastic jump diffusion processes can be used to describe suspended particle movement in the occurrences of a sequence of extreme flows.An extreme flow herein is defined as a hydrologic flow event or a hydrodynamic flow phenomenon with a low probability of occurrence and a high impact on its ambient flow environment.In this paper,the suspended sediment particle is assumed to immediately follow the extreme flows in the jump process（i.e.the time lag between the flow particle and the sediment particle in extreme flows is considered negligible）.In the proposed particle tracking models,a random term mainly caused by fluid eddy motions is modeled as a Wiener process,while the random occurrences of a sequence of extreme flows can be modeled as a Poisson process.The frequency of occurrence of the extreme flows in the proposed particle tracking model can be explicitly accounted for by the Poisson process when evaluating particle movement.The ensemble mean and variance of particle trajectory can be obtained from the proposed stochastic models via simulations.The ensemble mean and variance of particle velocity are verified with available data.Applicability of the proposed stochastic particle tracking models for sediment transport modeling is also discussed. 相似文献
4.
The results of numerical models or of new observational programs are checked by comparing them with past observations. Also, it is desirable that the eddy diffusion coefficients used in two-dimensional models be derived from the same data set as the circulation statistics which the model outputs are checked against, so that all results refer to the same atmospheric conditions. For the first time, the three components of the eddy diffusion matrix, from 30–60 km, 80°N–10°S are computed, together with the means, variances and covariances of the wind and temperature through the same region using the same data set for 1960–76 and the same handling and analysis methods for all variables. Horizontal diffusivities,K
yy
, are obtained from the variance and integral time scale of the meridional wind speed. The present values are generally smaller than past estimates, presumably because temporal variations longer than a month have been removed in this work. Estimates ofK
yz
are based on the tentative assumption that the diffusivity is proportional to the slope of isentropic surfaces, and estimates ofK
zz
are based on the assumption that small-scale gravity waves are primarily responsible for vertical mixing. 相似文献
5.
ABSTRACTThe clustering of catchments is important for prediction in ungauged basins, model parameterization and watershed development and management. The aim of this study is to explore a new measure of similarity among catchments, using a data depth function and comparing it with catchment clustering indices based on flow and physical characteristics. A cluster analysis was performed for each similarity measure using the affinity propagation clustering algorithm. We evaluated the similarity measure based on depth–depth plots (DD-plots) as a basis for transferring parameter sets of a hydrological model between catchments. A case study was developed with 21 catchments in a diverse New Zealand region. Results show that clustering based on the depth–depth measure is dissimilar to clustering on catchment characteristics, flow, or flow indices. A hydrological model was calibrated for the 21 catchments and the transferability of model parameters among similar catchments was tested within and between clusters defined by each clustering method. The mean model performance for parameters transferred within a group always outperformed those from outside the group. The DD-plot based method was found to produce the best in-group performance and second-highest difference between in-group and out-group performance.
EDITOR D. Koutsoyiannis; ASSOCIATE EDITOR A. Viglione 相似文献
6.
Lagrangian trajectory methods are often applied as deterministic transport models, where transport is due strictly to advection without taking into account stochastic elements of particle dispersion, which raises questions about validity of the model results. The present work investigates the impact of horizontal eddy diffusivity for a case study of coastal pollution in the Gulf of Finland, where the pollutants are assumed to originate from a major fairway and are transported to the coast by surface currents. Lagrangian trajectories are calculated using the TRACMASS model from velocity fields calculated by the Rossby Centre circulation model for 1982 to 2001. Three cases are investigated: (1) trajectory calculation without eddy diffusivity, (2) stochastic modelling of eddy diffusivity with a constant diffusion coefficient and (3) stochastic modelling of eddy diffusivity with a time- and space-variable diffusion coefficient. It is found that the eddy diffusivity effect increases the spreading rate of initially closely packed trajectories and the number of trajectories that eventually reach the coast. The pattern of most frequently hit coastal sections, the probability of hit to each such section and the time the pollution spends offshore are virtually invariant with respect to inclusion of eddy diffusivity. 相似文献
7.
In this study, we examine the effects of conditioning spatially variable transmissivity fields using head and/or transmissivity measurements on well-capture zones. In order to address the challenge posed by conditioning a flow model with spatially varying parameters, an innovative inverse algorithm, the Representers method, is employed. The method explicitly considers this spatial variability.
A number of uniform measurement grids with different densities are used to condition transmissivity fields using the Representers method. Deterministic and stochastic analysis of well-capture zones are then examined. The deterministic study focuses on comparison between reference well-capture zones and their estimated mean conditioned on head data. It shows that model performance due to head conditioning on well-capture zone estimation is related to pumping rate. At moderate pumping rates transmissivity observations are more crucial to identify effects arising from small-scale variations in pore water velocity. However, with more aggressive pumping these effects are reduced, consequently model performance, through incorporating head observations, markedly improves. In the stochastic study, the effect of conditioning using head and/or transmissivity data on well-capture zone uncertainty is examined. The Representers method is coupled with the Monte Carlo method to propagate uncertainty in transmissivity fields to well-capture zones. For the scenario studied, the results showed that a combination of 48 head and transmissivity data could reduce the area of uncertainty (95% confidence interval) in well-capture zone location by over 50%, compared to a 40% reduction using either head or transmissivity data. This performance was comparable to that obtained through calibrating on three and a half times the number of head observations alone. 相似文献
8.
Richard John Greatbatch Xiaoming Zhai Jan-Dirk Kohlmann Lars Czeschel 《Ocean Dynamics》2010,60(3):617-628
Eddy momentum fluxes, i.e. Reynold stresses, are computed for the latitude bands of the Gulf Stream and Kuroshio extensions
using 13 years of data from the merged satellite altimeter product of Le Traon et al. The spatial pattern and amplitude of
the fluxes is remarkably similar to that found by Ducet and Le Traon using the 5 years of data that were available to them.
In addition to updating the work of Ducet and Le Traon, we provide new insight into the role played by the underlying variable
bottom topography, both for determining the structure of the eddy momentum fluxes seen in the satellite data and for influencing
the way these fluxes feedback on the mean flow. While there is no clear evidence that eddies locally flux momentum into the
eastward jets of the Gulf Stream and Kuroshio extensions, a clearer picture emerges after zonally integrating across each
of the North Atlantic and North Pacific basins. We argue that the eddy momentum fluxes do indeed drive significant transport,
a conclusion supported by preliminary results from a 3-D model calculation. We also present evidence that in the North Pacific,
the Reynolds stresses are important for driving the recirculation gyres associated with the Kuroshio extension, taking advantage
of new data from both observations and high-resolution model simulations. 相似文献
9.
Estimates of the molecular values of magnetic, viscous and thermal diffusion suggest that the state of the Earth’s core is turbulent and that complete numerical simulation of the geodynamo is not realizable at present. Large eddy simulation of the geodynamo with modelling of the sub-grid scale turbulence must be used. Current geodynamo models effectively model the sub-grid scale turbulence with isotropic diffusivities larger than the molecular values appropriate for the core. In the Braginsky and Meytlis (1990) picture of core turbulence the thermal and viscous diffusivities are enhanced up to the molecular magnetic diffusivity in the directions of the rotation axis and mean magnetic field. We neglect the mean magnetic field herein to isolate the effects of anisotropic thermal diffusion, enhanced or diminished along the rotation axis, and explore the instability of a steady conductive basic state with zero mean flow in the Boussinesq approximation. This state is found to be more stable (less stable) as the thermal diffusion parallel to the rotation axis is increased (decreased), if the transverse thermal diffusion is fixed. To examine the effect of simultaneously varying the diffusion along and transverse to the rotation axis, the Frobenius norm is used to control for the total thermal diffusion. When the Frobenius norm of the thermal diffusion tensor is fixed, it is found that increasing the thermal diffusion parallel to the rotation axis is destabilising. This result suggests that, for a fixed total thermal diffusion, geodynamo codes with anisotropic thermal diffusion may operate at lower modified Rayleigh numbers. 相似文献
10.
Homogeneous, nonrotating flow over a backward-facing rounded step is simulated using the 2D vertical version of two general
circulation models, a z-coordinate model—the Massachusetts Institute of Technology general circulation model (MITgcm)—and a σ-coordinate model—the Bergen Ocean Model (BOM). The backward-facing step is a well-known testcase since it is geometrically
simple but still embodies important flow characteristics such as separation point, reattachment length, and recirculation
of the flow. The study compares the core of the two models and uses constant eddy viscosities and diffusivities. The Reynolds
numbers ranges from 2·102 to 2·106. The results correspond with previously published results having a relatively stationary separation point and a fluctuating
reattachment length due to downslope propagating eddies released from the reattachment zone for Reynolds numbers higher than
or equal to 2 · 104. For Reynolds number within the laminar regime, the flow is stationary. The discrepancies between the models increase by
enhancing Reynolds numbers. The σ-coordinate model experiences a reduction in eddy sizes with increasing resolution and Reynolds numbers in correspondence
with published experiments, while the size of the eddies are independent of the Reynolds number using the MITgcm. Due to mixing
generated by the staircase topography, the z-coordinate model gives a better convergence of the separation point and reattachment length compared with the BOM; however,
this conclusion might change with the inclusion of a relevant turbulence scheme. 相似文献
11.
An analysis of infiltration with moisture content distribution in a two‐dimensional discretized water content domain 
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下载免费PDF全文 On the basis of unsaturated Darcy's law, the Talbot–Ogden method provides a fast unconditional mass conservative algorithm to simulate groundwater infiltration in various unsaturated soil textures. Unlike advanced reservoir modelling methods that compute unsaturated flow in space, it only discretizes the moisture content domain into a suitable number of bins so that the vertical water movement is estimated piecewise in each bin. The dimensionality of the moisture content domain is extended from one dimensional to two dimensional in this study, which allows us to distinguish pore shapes within the same moisture content range. The vertical movement of water in the extended model imitates the infiltration phase in the Talbot–Ogden method. However, the difference in this extension is the directional redistribution, which represents the horizontal inter‐bin flow and causes the water content distribution to have an effect on infiltration. Using this extension, we mathematically analyse the general relationship between infiltration and the moisture content distribution associated with wetting front depths in different bins. We show that a more negatively skewed moisture content distribution can produce a longer ponding time, whereas a higher overall flux cannot be guaranteed in this situation. It is proven on the basis of the water content probability distribution independent of soil textures. To illustrate this analysis, we also present numerical examples for both fine and coarse soil textures. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
12.
An idealized numerical study of the influence of a tidal flow around an island has been undertaken with ROMS. The study focusses on coastal island wakes which are mainly controlled by elliptical tidal current flows on shallow shelves. This model is typical of some isolated continental shelf islands. The model is forced by a semi-diurnal barotropic inertia gravity wave imposed on the four open boundaries of a rectangular domain and its propagation results in an elliptical tidal flow within the domain in which the circular island lies. The influence of the surrounding island bathymetry and of the ellipse shape has been studied both in two and three dimensions. In the island vicinity, the residual circulation patterns over a tidal period show alongshore flow divergence along the major axis and convergence along the minor axis. A thin tidal ellipse (i.e. with a large ratio between major and minor axes) leads to strong eddy activity periods in the lee of the island during the flood and ebb phases, with eddy dissipation phases in between. By contrast, an almost round ellipse (axis ratio nearly 1) leads to vorticity filaments which continuously progress around the island without eddy shedding. The presence of a topographic slope in the vicinity of the island strengthens the eddy activity. This study suggests that the tidal current rotation favors the development of the eddy rotating in the same direction and weakens the development of the second eddy. In three dimensions with a surrounding bathymetry, an intense upwelling occurs in a large area in the lee of the island and the vertical velocities are stronger with thinner ellipses. With a flat bottom the vertical motions are almost fully generated by convergence and divergence of the secondary flow. With a varying bottom topography, the vertical motions come from a combination of this mechanism with convergence and divergence of the depth averaged flow. 相似文献
13.
Daniel Conti Alejandro Orfila Evan Mason Juan Manuel Sayol Gonzalo Simarro Salvador Balle 《Ocean Dynamics》2016,66(11):1415-1427
This work introduces a new method for ocean eddy detection that applies concepts from stationary dynamical systems theory. The method is composed of three steps: first, the centers of eddies are obtained from fixed points and their linear stability analysis; second, the size of the eddies is estimated from the vorticity between the eddy center and its neighboring fixed points, and, third, a tracking algorithm connects the different time frames. The tracking algorithm has been designed to avoid mismatching connections between eddies at different frames. Eddies are detected for the period between 1992 and 2012 using geostrophic velocities derived from AVISO altimetry and a new database is provided for the global ocean. 相似文献
14.
QingYe Wang 《中国科学:地球科学(英文版)》2017,60(9):1719-1731
The three-dimensional structure of mesoscale eddies in the western tropical Pacific(6°S–20°N, 120°E–150°E)is investigated using a high-resolution ocean model simulation. Eddy detection and eddy tracking algorithms are applied to simulated horizontal velocity vectors, and the anticyclonic and cyclonic eddies identified are composited to obtain their three-dimensional structures. The mean lifetime of all long-lived eddies is about 52 days, and their mean diameter is 147 km. Two typical characteristics of mesoscale eddies are revealed and possible dynamic explanations are analyzed. One typical characteristic is that surface eddies are generally separated from subthermocline eddies along the bifurcation latitude(~13°N) of the North Equatorial Current in the western tropical Pacific, which may be associated with different eddy energy sources and vertical eddy energy fluxes in subtropical and tropical gyres. Surface eddies have maximum swirl velocities of 8–9 cm s~(-1) and can extend to about 1500 m depth. Subthermocline eddies occur below 200 m, with their cores at about 400–600 m depth, and their maximum swirl velocities can reach 10 cm s~(-1). The other typical characteristic is that the meridional velocity component of the eddy is much larger than the zonal component. This characteristic might be due to more zonal eddy pairs(two eddies at the same latitude),which is also supported by the zonal wavelength(about 200 km) in the high-frequency meridional velocity component of the horizontal velocity. 相似文献
15.
While tomographic inversion has been successfully applied to laboratory- and field-scale tests, here we address the new issue of scale that arises when extending the method to a basin. Specifically, we apply the hydraulic tomography (HT) concept to jointly interpret four multiwell aquifer tests in a synthetic basin to illustrate the superiority of this approach to a more traditional Theis analysis of the same tests. Transmissivity and storativity are estimated for each element of a regional numerical model using the geostatistically based sequential successive linear estimator (SSLE) inverse solution method. We find that HT inversion is an effective strategy for incorporating data from potentially disparate aquifer tests into a basin-wide aquifer property estimate. The robustness of the SSLE algorithm is investigated by considering the effects of noisy observations, changing the variance of the true aquifer parameters, and supplying incorrect initial and boundary conditions to the inverse model. Ground water flow velocities and total confined storage are used as metrics to compare true and estimated parameter fields; they quantify the effectiveness of HT and SSLE compared to a Theis solution methodology. We discuss alternative software that can be used for implementing tomography inversion. 相似文献
16.
Formulated as an inverse problem, the diffusion parameters associated with length-scale dependent eddy diffusivities can be viewed as the unknowns in the mass conservation equation for coastal zone transport problems. The values of the diffusion parameters can be optimized according to an error function incorporated with observed concentration data. Examples are given for the Fickian, shear diffusion and inertial subrange diffusion models. Based on a new set of dyeplume data collected in the coastal zone off Bronte, Lake Ontario, it is shown that the predictions of turbulence closure models can be evaluated for different flow conditions. The choice of computational schemes for this diagnostic approach is based on tests with analytic solutions and observed data. It is found that the optimized shear diffusion model produced a better agreement with observations for both high and low advective flows than, e.g., the unoptimized semi-empirical model, Ky=0.075 σy1.2, described by Murthy and Kenney. 相似文献
17.
S. K. Kao R. J. Okrasinski N. J. Lordi F. J. Schmidlin 《Pure and Applied Geophysics》1978,117(3):537-547
Meterological rocket soundings, launched between 1969–74 at six locations representative of low, middle, and high altitudes, are employed with the use of the statistical theory of diffusion, to determine the zonal and meridional component of eddy diffusivity between 30 and 55 km as a function of season, latitude, and altitude. A comparison is also made between annually-averaged eddy diffusivities above and below 30 km.It is shown that the zonal component of eddy diffusivity is approximately three to five times as large as the meridional component, in most cases. Both components of eddy diffusivity vary greatly with season, latitude, and altitude. Highest eddy diffusivities, found in the vicinity of the winter westerly jet, are approximately one order of magnitude higher than those present during the summer. Tropical eddy diffusivities, however, remain relatively small throughout the year. Annually, a minimum is indicated near 25 km between maximums located at the stratopause and tropopause. 相似文献
18.
Geophysical flows with anisotropic turbulence and dispersive waves: flows with stable stratification
The quasi-normal scale elimination (QNSE) is an analytical spectral theory of turbulence based upon a successive ensemble
averaging of the velocity and temperature modes over the smallest scales of motion and calculating corresponding eddy viscosity
and eddy diffusivity. By extending the process of successive ensemble averaging to the turbulence macroscale one eliminates
all fluctuating scales and arrives at models analogous to the conventional Reynolds stress closures. The scale dependency
embedded in the QNSE method reflects contributions from different processes on different scales. Two of the most important
processes in stably stratified turbulence, internal wave propagation and flow anisotropization, are explicitly accounted for
in the QNSE formalism. For relatively weak stratification, the theory becomes amenable to analytical processing revealing
just how increasing stratification modifies the flow field via growing anisotropy and gravity wave radiation. The QNSE theory
yields the dispersion relation for internal waves in the presence of turbulence and provides a theoretical reasoning for the
Gargett et al. (J Phys Oceanogr 11:1258–1271, 1981) scaling of the vertical shear spectrum. In addition, it shows that the internal wave breaking and flow anisotropization
void the notion of the critical Richardson number at which turbulence is fully suppressed. The isopycnal and diapycnal viscosities
and diffusivities can be expressed in the form of the Richardson diffusion laws thus providing a theoretical framework for
the Okubo dispersion diagrams. Transitions in the spectral slopes can be associated with the turbulence- and wave-dominated
ranges and have direct implications for the transport processes. We show that only quasi-isotropic, turbulence-dominated scales
contribute to the diapycnal diffusivity. On larger, buoyancy dominated scales, the diapycnal diffusivity becomes scale independent.
This result underscores the well-known fact that waves can only transfer momentum but not a scalar and sheds a new light upon
the Ellison–Britter–Osborn mixing model. It also provides a general framework for separation of the effects of turbulence
and waves even if they act on the same spatial and temporal scales. The QNSE theory-based turbulence models have been tested
in various applications and demonstrated reliable performance. It is suggested that these models present a viable alternative
to conventional Reynolds stress closures. 相似文献
19.
We examine velocity statistics from a numerical simulation of the Nordic Seas with 4 km resolution, with a focus on the Norwegian shelf and slope. The model mean flow is dominated by its version of the Norwegian Atlantic Current, with two branches, one near the shelfbreak and the other near the 2000 m isobath. The model variances are surface-intensified and increase with water depth over the shelf; the variance ellipses also indicate topographic steering. Seasonality is more pronounced on the shelf than on the slope and the velocity probability distributions are weakly non-Gaussian, reflecting an excess of extreme velocities. All these aspects are broadly consistent with the observations. There are, however, differences with the observations. The topographic steering of the mean flow and of the variance ellipses is less pronounced in the model, a probable consequence of the model bathymetry, etopo5, being too smooth. The temporal and spatial coherence scales are too large by about a factor of 2, probably due to the model resolution. And correlations between velocity time series from the model and in situ moorings are generally small, despite the model having realistic forcing. The low predictability presumably reflects the degree of chaos in the flow and highlights the need for data assimilation. 相似文献
20.
Numerical simulations with the Regional Ocean Modeling System (ROMS) are used to study the initial spin-up and the evolution of a mesoscale, topographically linked eddy under steady and variable wind conditions. The development of a pool of dense water on the southern Vancouver Island shelf allows cyclonic eddies formed by coastal upwelling off Cape Flattery to spread westward, ultimately contributing to the shelf-wide circulation known as the Juan de Fuca Eddy. This dense water arises through upwelling of water present in the underlying canyon system and tidal mixing over several shallow banks to the north. Tidal mixing is critical to the separation of the eddy from the coast. Although steady upwelling winds with a seasonal mean magnitude (combined with estuarine flow and tides) produce an eddy, only fluctuating winds with timescales and magnitudes typical of the region result in an eddy with a westward extent similar to seasonal observations. With each period of upwelling-favorable winds, newly upwelled water from the coast is entrained into the eddy which grows in size and moves westward. Wind events also significantly affect the baroclinic structure of the eddy. Specifically, during typical summer wind reversals, model surface drifters continue to move cyclonically within the eddy for several days after each downwelling wind event. Under upwelling-favorable wind conditions, model drifters exit the eddy to the southeast as the eddy and coastal upwelling fronts merge into a continuous southeastward shelf break jet. 相似文献