共查询到20条相似文献，搜索用时 421 毫秒
1.
Abstract The adjustment of a nonlinear, quasigeostrophic, stratified ocean to an impulsively applied wind stress is investigated under the assumption that barotropic advection of vortex tube length is the most important nonlinearity. The present study complements the steady state theories which have recently appeared, and extends earlier, dissipationless, linear models. In terms of Sverdrup transport, the equation for baroclinic evolution is a forced advection-diffusion equation. Solutions of this equation subject to a “tilted disk” Ekman divergence are obtained analytically for the case of no diffusion and numerically otherwise. The similarity between the present equation and that of a forced barotropic fluid with bottom topography is shown. Barotropic flow, which is assumed to mature instantly, can reverse the tendency for westward propagation, and thus produce regions of closed geostrophic contours. Inside these regions, dissipation, or equivalently the eddy field, plays a central role. We assume that eddy mixing effects a lateral, down-gradient diffusion of potential vorticity; hence, within the closed geostrophic contours, our model approaches a state of uniform potential vorticity. The solutions also extend the steady-state theories, which require weak diffusion, by demonstrating that homogenization occurs for moderately strong diffusion. The evoiution of potential vorticity and the thermocline are examined, and it is shown that the adjustment time of the model is governed by dissipation, rather than baroclinic wave propagation as in linear theories. If dissipation is weak, spin-up of a nonlinear ocean may take several times that predicted by linear models, which agrees with analyses of eddy-resolving general circulation models. The inclusion of a western boundary current may accelerate this process, although dissipation will still play a central role. 相似文献
2.
Abstract Merilees and Warn's (1975) nonlinear interaction analysis of two-dimensional nondivergent flow is extended to examine the quasi-geostrophic two-layer model. Two sets of triads exist in this model (Salmon, 1978). The purely barotropic triads are the same as the triads examined by Merilees and Warn. Baroclinic-barotropic triads are found to exchange more energy or potential enstrophy with smaller or larger scales depending on the scale of motion as compared with the internal Rossby deformation radius and the relative wavenumber position of baroclinic and barotropic components. 相似文献
3.
Abstract Severe unidirectional Fourier truncation of the equations for 2-D incompressible flow leads to a system of three coupled PDEs in one space dimension with the same quadratic invariants as the original set (i.e. energy and enstrophy). Numerically generated equilibria for inviscid, truncated versions of the reduced system are well approximated by Kraichnan's energy-enstrophy equipartition spectra. Viscous calculations for decaying turbulence at moderate resolution (1024 degrees of freedom) also appear to be consistent with a direct, k ?3, enstrophy cascading inertial range when the dissipation is small. Dissipation range intermittency in the form of spatially intermittent enstrophy dissipation with occasional strong bursts producing linear phase locking is also observed. In contrast to full 2-D simulations, no tendency towards the emergence of isolated, coherent vorticity structures is observed. The model consequently mimics some, but not all, of the properties of the full 2-D set. 相似文献
4.
A. D. McEwan 《地球物理与天体物理流体动力学》2013,107(1):283-311
AbstractIt is successfully demonstrated that substantial redistribution of the angular momentum within a completely liquid-filled cylinder in uniform rotation can be brought about by the induction of turbulent mixing through the resonant excitation of standing inertial waves. This means of mixing is accomplished without significant net circulation in the meridional plane, or strong boundary restraint.Intense cyclonic vortices are created with an apparently high conversion of energy from the inertial wave excited. Visualizations and measurements of vortex strength and circulation distribution are presented and dimensional arguments are applied to interpret from the measurements the partition of the turbulence into relative velocity- and angular momentum-diffusing elements. This indicates tentatively the mechanism responsible; momentum advected by the inertial wave is irreversibly diffused by turbulence of smaller scale. Anisotropy with enhanced radial transport is an essential feature of the nett turbulence in such a mechanism. Similar combinations of large-scale waves and turbulence can be expected to occur in the geophysical situations to which the phenomenon of angular momentum mixing relates. The experiment does not, however, test the effectiveness of isotropic turbulence in the same rôle. 相似文献
5.
Abstract We describe the high-resolution spectral modelling of nondivergent barotropic linearized flow over steep irregular topography. We use collocation to evaluate spatial derivatives in the barotropic vorticity equation, and a spectral multigrid technique to accelerate the iterative solution of the vorticity—stream function relation. The computational domain is a rectangular channel, which can be conformally mapped into more interesting shapes, as we also discuss. A Fourier-series representation is used in the (periodic) direction parallel to the walls of the channel, and a sine series in the cross-channel direction. For much of the paper we concentrate on the numerical techniques, though results are provided, including an application to the Bass Strait region of southeast Australia. 相似文献
6.
An estimate of the magnitudes of the absolute vorticity advection terms and the terms in the balance equation suggest that
the use of the barotropic vorticity equation within 5 degrees of latitude of the equator is not very good and that the linear
balance equation is as good as the nonlinear balance equation in the equatorial region.
Zonal Fourier analysis has revealed that the contribution from planetary scale waves is much larger than that from synoptic
scale waves, being more in the winter hemisphere than in the summer hemisphere.
In classical scale analysis there must be a distinction in wavelength between the zonal and the meridional directions for
planetary scale waves. This distinction does not appear to be necessary for synoptic scale waves. 相似文献
7.
Michelle S. Cho Felipe Solano Neil R. Thomson Michael G. Trefry Daniel R. Lester Guy Metcalfe 《Ground Water Monitoring & Remediation》2019,39(3):23-39
Chaotic advection is a novel approach that has the potential to enhance contact between an injected reagent and target contaminants, and thereby improve the effectiveness of in situ treatment technologies. One configuration that is capable of generating chaotic advection is termed the rotated potential mixing (RPM) flow. A conventional RPM flow system involves periodically reoriented dipole flow driven by transient switching of pressures at a series of radial wells. To determine whether chaotic advection can be engineered using such an RPM flow system, and to assess the consequent impact on the spatial distribution of a conservative tracer, a series of field-scale experiments were conducted. These experiments involved the injection of a tracer in the center of a circular array of wells followed by either mixing using an engineered RPM flow system to invoke chaotic advection, or by natural processes (advection and diffusion) as the control. Pressure fluctuations from the mixing tests using the RPM flow system showed consistent peak amplitudes during injection and extraction at a frequency corresponding to the switching time, suggesting that the target hydraulic behavior was achieved with the time-dependent flow field. The tracer breakthrough responses showed oscillatory behavior at all monitoring locations during the mixing tests which indicated that the desired RPM flow was generated. The presence of chaotic advection was supported by comparisons to observations from a previous laboratory experiment using RPM flow, and the Fourier spectrum of the temporal tracer data. Results from several quantitative metrics adopted to demonstrate field-scale evidence of chaotic advection showed that mixing led to improved lateral tracer spreading and approximately uniform concentrations across the monitoring network. The multiple lines of evidence assembled in this proof-of-concept study conclusively demonstrated that chaotic advection can be engineered at the field scale. This investigation is a critical step in the development of chaotic advection as a viable and efficient approach to enhance reagent delivery. 相似文献
8.
Abstract The problem of topographic forcing by an obstacle against the boundary of a rotating flow is considered in various parameter regimes. The timescale for the motion is the topographic vortex-stretching time, which is inversely proportional to the background rotation rate and the fractional height of the obstacle. For slow flows this time is short compared with the advection time and the governing equation of conservation of potential vorticity is linear. The final state satisfies the non-linear equation for the advection of potential vorticity, however, and so time dependence has given a specific solution to a non-linear problem. The presence of the sidewall causes a stagnant Taylor column to be set up far more rapidly than cases with no sidewall. It is shown that viscosity and mixing arrests the inviscid evolution at some stage, thus some fluid still crosses the obstacle in the steady state. These solutions suggest that experimental results on separation obtained by Griffiths and Linden (1983) can tentatively be ascribed to entrainment and expulsion of fluid through vertical shear layers at the edge of the topography. 相似文献
9.
Chaotic advection at the pore scale: Mechanisms,upscaling and implications for macroscopic transport
The macroscopic spreading and mixing of solute plumes in saturated porous media is ultimately controlled by processes operating at the pore scale. Whilst the conventional picture of pore-scale mechanical dispersion and molecular diffusion leading to persistent hydrodynamic dispersion is well accepted, this paradigm is inherently two-dimensional (2D) in nature and neglects important three-dimensional (3D) phenomena. We discuss how the kinematics of steady 3D flow at the pore scale generate chaotic advection—involving exponential stretching and folding of fluid elements—the mechanisms by which it arises and implications of microscopic chaos for macroscopic dispersion and mixing. Prohibited in steady 2D flow due to topological constraints, these phenomena are ubiquitous due to the topological complexity inherent to all 3D porous media. Consequently 3D porous media flows generate profoundly different fluid deformation and mixing processes to those of 2D flow. The interplay of chaotic advection and broad transit time distributions can be incorporated into a continuous-time random walk (CTRW) framework to predict macroscopic solute mixing and spreading. We show how these results may be generalised to real porous architectures via a CTRW model of fluid deformation, leading to stochastic models of macroscopic dispersion and mixing which both honour the pore-scale kinematics and are directly conditioned on the pore-scale architecture. 相似文献
10.
This study investigates how Mattituck Sill influences circulation patterns and physical dynamics in eastern Long Island Sound, a major estuary on the U.S. east coast. Observations show there is pronounced across-estuary transport in the area and suggest there may be subtidal anticyclonic flow around the sill. Model runs, with and without sill bathymetry, exhibit this across-estuary transport and anticyclonic circulation. Comparison between these runs indicates that the sill intensifies the anticyclonic circulation. This study finds the sill does not exert internal hydraulic control during neap, mean, or spring tidal conditions. Nevertheless, along-estuary exchange is reduced over the sill and across-estuary fluxes are increased. The Connecticut River plume enters close to the estuary mouth. The sill deflects more of the plume waters towards the mouth, causing less freshwater to take the long looping route through the estuary. The subtidal circulation balance around the sill indicates a barotropic balance between the tidal advection of tidal vorticity and friction. The subtidal vorticity balance indicates the net effect of tidal advection of relative vorticity is balanced with frictional curl associated with lateral speed gradients and vorticity dissipation. Previously developed scalings based on the circulation balance (Nature 290:549–555, 1981), frictional vorticity generation mechanisms (Deep-Sea Res 28:195–212, 1981), and tidal diffusion of potential vorticity (J Phys Oceanogr 29:821–827, 1999) are applicable to Mattituck Sill and predict circulation with a similar magnitudes to model results. 相似文献
11.
Thomas M. Bendall 《地球物理与天体物理流体动力学》2019,113(5-6):491-504
ABSTRACTA framework of variational principles for stochastic fluid dynamics was presented by Holm, and these stochastic equations were also derived by Cotter, Gottwald and Holm. We present a conforming finite element discretisation for the stochastic quasi-geostrophic equation that was derived from this framework. The discretisation preserves the first two moments of potential vorticity, i.e. the mean potential vorticity and the enstrophy. Following the work of Dubinkina and Frank, who investigated the statistical mechanics of discretisations of the deterministic quasi-geostrophic equation, we investigate the statistical mechanics of our discretisation of the stochastic quasi-geostrophic equation. We compare the statistical properties of our discretisation with the Gibbs distribution under assumption of these conserved quantities, finding that there is an agreement between the statistics under a wide range of set-ups. 相似文献
12.
A subgrid-scale parameterization scheme motivated by statistical closure theory, but employing statistics obtained from high-resolution direct numerical simulations, is applied to large eddy simulations of two-level quasigeostrophic turbulence on the sphere. It is shown that these parameterizations are consistent with the phenomenology of quasigeostrophic turbulence. The parameterizations consist of 2 × 2 dissipation and stochastic forcing covariance matrices at each wavenumber, with the off-diagonal elements of the matrices representing vertical mixing. Two flow regimes, characterized by their deformation scales, are considered, namely atmospheric and oceanic. In the former, the deformation scale is fully resolved, and the truncation scale is within the enstrophy cascading interial range. In the latter, the deformation scale is not fully resolved, and the truncation scale is within the energy cascading inertial range. It is demonstrated through numerical experiments that both stochastic and deterministic variants of the scheme give comparable results for the energy spectra in the atmospheric regime. In the oceanic regime, the stochastic variant again gives excellent results, but the deterministic variant is found to be numerically unstable. 相似文献
13.
This paper describes numerical models of advection/diffusion between enclaves and host magmas, applied with the aim of estimating
time-scales during which enclaves can be homogenised. In particular, advection was simulated using a numerical system consisting
of regular and chaotic regions. Results indicate that the homogenisation time of enclaves in chaotic regions is several orders
of magnitude faster than in regular regions. For instance, an enclave with a diameter of 100 cm may be homogenised in the
chaotic region in ∼ 380 years, assuming an advection velocity of 10 cm/year, whereas in the regular region it would require
6.5×105 years for complete homogenisation. This implies that, in the same magmatic system, large differences in the degree of homogenisation
may co-exist, generating magmatic masses with large spatial and temporal inhomogeneities.
The results of this study may have significant petrological and volcanological implications. From a petrological point of
view, mafic enclaves dispersed in felsic host rocks are regarded as portions of mafic magma which, trapped inside regular
regions, survived the hybridisation process. Instead, host rocks are regarded as regions where efficient mixing dynamics generated
hybrid magmas. The fact that a single magmatic mass may display large compositional differences at the same time undermines
the assumption of most geochemical models, which assume the temporal and spatial homogeneity of the magma body. From the volcanological
perspective, the presence of magmatic enclaves in volcanic rocks allows us to estimate the mixing times of magmas by analysing
chemical diffusion patterns between host rocks and enclaves.
Editorial responsibility: D. Dingwell 相似文献
14.
Abstract Non-Markovian closure theories are compared with ensemble averaged direct numerical simulations (DNS) for decaying two-dimensional turbulence at large scale Reynolds numbers ranging from ≈ 50 to ≈ 4000. The closures, as well as DNS, are formulated for discrete wave numbers relevant to flows on the doubly periodic domain and are compared with the results of continuous wave number closures. The direct interaction approximation (DIA), self-consistent field theory (SCFT) and local energy-transfer theory (LET) closures are also compared with cumulant update versions of these closures (CUDIA, CUSCFT, CULET). The cumulant update closures are shown to have comparable performance to the standard closures but are much more efficient allowing long time integrations. The discrete wave number closures perform considerably better than continuous wave number closures as far as evolved energy and transfer spectra and skewness are concerned. The discrete wave number closures are in reasonable agreement with DNS in the energy containing range of the large scales for Reynolds numbers ranging from ≈ 50 to ≈ 4000. The closures tend to underestimate the enstrophy flux to high wave numbers, increasingly so with increasing Reynolds number, resulting in underestimation of small-scale kinetic energy. 相似文献
15.
Initially the development of shallow sea three-dimensional barotropic tidal models is briefly reviewed with a view to determining what were the key measurements that allowed progress in this field and rigorous model validation. Subsequently this is extended to a brief review of baroclinic tidal models to try to determine a “way forward” for baroclinic model development. The difficulty of high spatial variability, and wind influence are identified as possibly important issues that must be considered in validating baroclinic tidal models. These are examined using a three-dimensional unstructured grid model of the M2 internal tide on the shelf edge region off the west coast of Scotland. The model is used to investigate the spatial variability of the M2 internal tide, and associated turbulence energy and mixing in the region. Initial calculations are performed with tidal forcing only, with subsequent calculations briefly examining how the tidal distribution is modified by down-welling and up-welling favourable winds. Calculations with tidal forcing only, show that there is significant spatial variability in the internal tide and associated mixing in the region. In addition, these are influenced by wind effects which may have to be taken into account in any model validation exercise. The paper ends by discussing the comprehensive nature of data sets that need to be collected to validate internal tidal models to the same level currently attained with three dimensional barotropic tidal models. 相似文献
16.
Abstract Collisions between isolated(i.e. localized) dipolar vortex states, called modons, are examined in various numerical solutions of the quasigeostrophic, equivalent barotropic equation. For a range of parameters, the collision interactions are soliton-like in that the vorticity maxima are displaced (phase-shifted) with only small speed changes and little excitation of internal degrees of freedom. For other parameters, new “inelastic” effects are observed, including speed changes due to vorticity rearrangement, vorticity filamentation, modon “capture” or “fusion” in an overtaking collision, and the “fission” of a modon into its component vorticity monopoles in a head-on collision. 相似文献
17.
A. M. Treguier 《地球物理与天体物理流体动力学》2013,107(1-4):43-68
Abstract Steady currents develop in oceanic turbulence above topography even in the absence of steady forcing. Mesoscale steady currents are correlated with mesoscale topography with anticyclonic eddies above topographic bumps, and large scale westward flows develop when β is non-zero. The relationship between those two kinds of steady currents, as well as their dependence on various parameters, is studied using a barotropic quasi-geostrophic channel model. The percentage of steady energy is found to depend on the forcing, friction and topography in a non-monotonic fashion. For example, the percentage of steady currents grows with the energy level in the linear regime (low energies) and decreases when the energy level increases in the nonlinear regime (high energies). Mesoscale steady currents are the energy source for the steady westward flow U, and therefore U is the maximum when large scale and mesoscale currents are of the same order of magnitude. This happens when the ratio S of the large scale slope βH/f 0 and the mesoscale rms topographic slope α is of order one. U decreases for both small and large values of S. 相似文献
18.
Abstract The generation of stationary Rossby waves by sources of potential vorticity in a westerly flow is examined here in the context of a two-layer, quasi-geostrophic, β-plane model. The response in each layer consists of a combination of a barotropic Rossby wave disturbance that extends far downstream of the source, and a baroclinic disturbance which is evanescent or wave-like in character, depending on the shear and degree of stratification. Contributions from each of these modes in each layer are strongly dependent on the basic flows in each layer; the degree of stratification; and the depths of the two layers. The lower layer response is dominated by an evanescent baroclinic mode when the upper layer westerlies are much larger than those in the lower layer. In this case, weak stationary Rossby waves of large wavelengths are confined to the upper layer and the disturbance in the lower layer is confined to the source region. Increasing the upper layer flow (with the lower layer flow fixed) increases the Rossby wavelength and decreases the amplitude. Decreasing the lower layer flow (with the upper layer flow fixed) decreases the wavelength and increases the amplitude. Stratification increases the contribution from the barotropic wave-like mode and causes the response to be confined to the lower layer. The finite amplitude response to westerly flow over two sources of potential vorticity is also considered. In this case stationary Rossby waves induced by both sources interact to reinforce or diminish the downstream wave pattern depending on the separation distance of the sources relative to the Rossby wavelength. For fixed separation distance, enhancement of the downstreatm Rossby waves will only occur for a narrow range of flow variables and stratification. 相似文献
19.
A variety of studies of magnetised plasma turbulence invoke theories for the advection of a passive scalar by turbulent fluctuations. Examples include modelling the electron density fluctuations in the interstellar medium, understanding the chemical composition of galaxy clusters and the intergalactic medium, and testing the prevailing phenomenological theories of magnetohydrodynamic turbulence. While passive scalar turbulence has been extensively studied in the hydrodynamic case, its counterpart in MHD turbulence is significantly less well understood. Herein we conduct a series of high-resolution direct numerical simulations of incompressible, field-guided, MHD turbulence in order to establish the fundamental properties of passive scalar evolution. We study the scalar anisotropy, establish the scaling relation analogous to Yaglom’s law, and measure the intermittency of the passive scalar statistics. We also assess to what extent the pseudo Alfvén fluctuations in strong MHD turbulence can be modelled as a passive scalar. The results suggest that the dynamics of a passive scalar in MHD turbulence is considerably more complicated than in the hydrodynamic case. 相似文献
20.
Abstract Analysis of a two-layer, flat-bottom, steady-wind driven, eddy-resolving general circulation model reveals a distinct separation in frequency of baroclinic and barotropic motion in the region distant from the model Gulf Stream. The far-field motions at periods less (greater) than about 100 days are predominantly barotropic (baroclinic), unlike the near-field, eddy-generating, free-jet region which contains barotropic and baroclinic energy throughout the modei frequency range. The far-field barotropic energy produces a peak in the model sea-level spectra between 25 and 50 days with a magnitude comparable to energy levels observed in spectra of sea level from oceanic island tide gauges. The far-field barotropic motion is clearly composed of large-scale, resonant, barotropic normal modes drive by mesoscale activity of the turbulent, free-jet region. Oceanic mesoscale turbulence may therefore provide for planetary normal modes an excitation mechanism distinct from atmospheric forcing. The open-ocean, barotropic, model response is very similar to that of a fluctuating-wind driven model, which suggests that atmospheric and intrinsic forcing of mid-ocean eddies may be of comparable importance. 相似文献