Computed rotational energy spectra of two energy and enstrophy conserving schemes on semi-staggered grids

Summary Rotational energy spectra are examined in experiments with two energy and enstrophy conserving schemes defined on the semi-staggered grid. One of the schemes conserved enstrophy as defined on an equivalent staggered grid, and the other conserved enstrophy as defined on the semi-staggered grid.As predicted by the theory (Janji, 1984), the rotational energy corresponding to the scheme conserving enstrophy as defined on an equivalent staggered grid decreases faster with increasing intensity of the wave number vector than that of the scheme conserving enstrophy as defined on the semistaggered grid. Moreover, the spectrum obtained with the scheme conserving the equivalent staggered grid enstrophy resembles the observed atmospheric spectra in a large part of the admissible wave number range.With 2 Figures     

Nonlinear evolution of a layered stratified shear flow

We investigate numerically and theoretically the nonlinear evolution of a parallel shear flow at moderate Reynolds number which has embedded within it a mixed layer of intermediate fluid. The two relatively thin strongly stratified density interfaces are centered on the edges of the shear layer. We are particularly interested in the development of primary and secondary instabilities. We present the results of a stability analysis which predicts that such flows may be unstable to stationary vortical disturbances which are a generalization of an inviscid instability first considered by G.I. Taylor. We investigate the behavior of these “Taylor billows” at finite amplitude through two-dimensional numerical simulations. We observe that the braid regions connecting adjacent primary Taylor billows are susceptible to secondary, inherently two-dimensional instabilities. We verify that these secondary instabilities, which take the form of small elliptical vortices, arise due to a local intensification of the spanwise vorticity in the braid region.     

Improved representation of ocean heat content in energy balance models

Climatic Change - Anomaly-diffusing energy balance models (AD-EBMs) are routinely employed to analyze and emulate the warming response of both observed and simulated Earth systems. We demonstrate a...     

Potential vorticity and eddy potential enstrophy in the North Atlantic Ocean simulated by a global eddy-resolving model

Eight-year daily mean output of a quasi-global eddy-resolving model is examined with a focus on the large-scale dynamical characteristics of the North Atlantic Ocean in a framework of potential vorticity (PV) and its derivatives. The model has reproduced some of the observed features of the mean potential vorticity field well. The three-dimensional structure of the mean potential vorticity supports baroclinic instability in most of the basin. Eddies are found to play important roles in the formation and maintenance of the mean potential vorticity fields. The contribution of relative vorticity to the mean potential vorticity field is found to be negligible for the most part. However, relative vorticity contribution to the source/sink of potential vorticity and eddy potential enstrophy is not negligible. We also find that eddies are not necessarily diffusive even on a basin-scale.     

Similarity vortices in a stratified atmosphere

Similarity equations relating to steady and unsteady vortices in a stratified atmosphere are shown to possess more general solutions than hitherto reported. Solutions with n cells, where n = 1,2,3, ..., are possible such that the axial and radial velocities tend to zero far from the axis of the vortex. For solutions with a finite number of cells, far from the axis the radial mass flow is directed towards the axis, with the exception of a subclass of solutions relating to one-cell and two-cell vortices associated with the unsteady configuration where the radial velocity is directed outwards.     

有限区域湿有效能量的层结、斜压、正压分量及其收支方程

本文探讨了将湿有效能量分解成层结、斜压、正压分量的方法,并讨论了它们的收支方程式.其中层结分量与实际大气中对流不稳定有较好的对应关系,但在干有效位能中分解不出这一项.在斜压、正压分量的收支方程中,除附加项外都与干有效位能的方程类似.由三个分量的收支方程看出,湿有效能量向动能的转换只可能发生在层结不稳定或(与)有斜压存在的大气中.这与天气分析经验以及经典的马古列斯(M.Margules)模式是一致的.     

Towards a parametrization of river discharges into ocean general circulation models: a closure through energy conservation

Diagnostic methods are defined in order to compare two numerical simulations of ocean dynamics in a region of freshwater influence. The first one is a river plume simulation based on a high resolution numerical configuration of the POM coastal ocean model in which mixing parametrizations have been previously defined. The second one is a simulation based on the NEMO Global Ocean Model used for climate simulations in its half-a-degree configuration in which a river inflow is represented as precipitation on two coastal grid cells. Both simulations are forced with the same freshwater inflows and wind stresses. The divergence of volumetric fluxes above and below the halocline are compared. Results show that when an upwelling wind blows, the two models display similar behavior although the impact of lack of precision can be observed in the NEMO configuration. When a downwelling wind blows, the NEMO Global Ocean configuration can not reproduce the coastally trapped baroclinic dynamics because its grid resolution is too coarse. To find a parametrization to help represent these dynamics in ocean general circulation models, a method based on energy conservation is investigated. This method shows that it is possible to link the energy fluxes provided by river inflows to the divergence of energy fluxes integrated over the grid cells of ocean general circulation models. A parametrization of the dynamics created by freshwater inflows is deduced from this method. This enabled creation of a box model that proved to have the same behavior as the fluxes previously computed from the high resolution configuration.     

Geostrophic adjustment and frontogenesis in a continuously stratified fluid

The structure of geostrophic flows that are formed from smooth initial unbalanced data with zero or uniform potential vorticity has been investigated in the work. Using methods of the theory of complex-variable functions, a class of exact analytical solutions describing these flows has been constructed. It has been shown that if the amplitude of a smooth initial disturbance exceeds the critical one, the final state will contain discontinuities of frontal type. A closed system of equations for discontinuity surfaces determination in the final states has been formulated. This system includes the Margules formula as a condition at the jump. It has been established that geometric configurations of discontinuity surfaces have an universal character, i.e. they do not depend on the details of initial distributions. To describe the nonstationary wave-processes of adjustment, a numerical hydrostatic model and a simplified analytical model based on the linearized dynamic equations in the Lagrange variables have been proposed. It has been shown that the establishment of discontinuious geostrophic flows has a clearly defined wave character with the alternations of smooth and multivalued phases. At the initial rather short interval, these phases are repeated with the inertial period, i.e. a nonstationary oscillatory front is formed.     

The atmospheric energy budget and implications for surface fluxes and ocean heat transports

Comprehensive diagnostic comparisons and evaluations have been carried out with the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) and European Centre for Medium Range Weather Forecasts (ECMWF) reanalyses of the vertically integrated atmospheric energy budgets. For 1979 to 1993 the focus is on the monthly means of the divergence of the atmospheric energy transports. For February 1985 to April 1989, when there are reliable top-of-the-atmosphere (TOA) radiation data from the Earth Radiation Budget Experiment (ERBE), the implied monthly mean surface fluxes are derived and compared with those from the assimilating models and from the Comprehensive Ocean Atmosphere Data Set (COADS), both locally and zonally integrated, to deduce the implied ocean meridional heat transports. While broadscale aspects and some details of both the divergence of atmospheric energy and the surface flux climatological means are reproducible, especially in the zonal means, differences are also readily apparent. Systematic differences are typically ∼20 W m⁻². The evaluation highlights the poor results over land. Land imbalances indicate local errors in the divergence of the atmospheric energy transports for monthly means on scales of 500 km (T31) of 30 W m⁻² in both reanalyses and ∼50 W m⁻² in areas of high topography and over Antarctica for NCEP/NCAR. Over the oceans in the extratropics, the monthly mean anomaly time series of the vertically integrated total energy divergence from the two reanalyses correspond reasonably well, with correlations exceeding 0.7. A common monthly mean climate signal of about 40 W m⁻² is inferred along with local errors of 25 to 30 W m⁻² in most extratropical regions. Except for large scales, there is no useful common signal in the tropics, and reproducibility is especially poor in regions of active convection and where stratocumulus prevails. Although time series of monthly anomalies of surface bulk fluxes from the two models and COADS agree very well over the northern extratropical oceans, the total fields all contain large systematic biases which make them unsuitable for determining ocean heat transports. TOA biases in absorbed shortwave, outgoing longwave and net radiation from both reanalysis models are substantial (>20 W m⁻² in the tropics) and indicate that clouds are a primary source of problems in the model fluxes, both at the surface and the TOA. Time series of monthly COADS surface fluxes are shown to be unreliable south of about 20^∘N where there are fewer than 25 observations per 5^∘ square per month. Only the derived surface fluxes give reasonable implied meridional ocean heat transports. Received: 21 March 2000 / Accepted: 21 June 2000     

Quasigeostrophic, ellipsoidal vortices in a stratified fluid

As a very simple model of some of the lens-like vortices of Mediterranean origin that drift in the eastern North Atlantic, we consider an ellipsoidal volume of uniform potential vorticity embedded in an otherwise quiescent, uniformly stratified fluid of infinite extent. We show that, under the quasigeostrophic approximation, such a vortex is a steadily rotating equilibrium solution and obtains its rotation rate as a function of the lengths of the principal axes. We also determine the dispersion relations for normal modes propagating on the ellipsoid. We find that unstable eigenmodes exist over a considerable range of the geometrical parameters that characterise the ellipsoid.     

Velocity profiles,the resistance law and the dissipation rate of mean flow kinetic energy in a neutrally and stably stratified planetary boundary layer

The logarithmic + polynomial approximation is suggested for vertical profiles of velocity components in a planetary boundary layer (PBL) at neutral and stable stratification. The resistance law functions A and B are determined on the basis of this approximation, using integral relations derived from the momentum equations, the Monin-Obukhov asymptotic formula for the wind profile in a stably stratified near-surface layer and the known expressions for the PBL depth. This result gives a realistic and convenient method for calculating the surface friction velocity and direction and the total dissipation rate of mean flow kinetic energy in terms of geostrophic velocity, buoyancy flux at the surface, the roughness parameter and the Coriolis parameter. In the course of these derivations a review is given of current views on the main problems of the neutral and stable PBL.     

西北太平洋海域风浪、涌浪、混合浪波浪能资源特征

用ECMWF的ERA-40海浪再分析资料,应用波浪能流密度计算方法,对西北太平洋海域的风浪能、涌浪能、混合浪能展开研究。结果表明:(1)波浪能流密度呈现出显著季节性差异。混合浪能流密度表现为冬高夏低;春、夏、秋季的涌浪能流密度明显大于风浪能流密度,冬季相反;(2)混合浪能流密度的大值区主要分布于阿留申群岛附近海域,高值中心可达60 kW/m以上;近海的大值区主要分布于琉球群岛—巴士海峡—传统的南海大风区一带,年平均值在4 kW/m以上,南海北部可达12 kW/m以上;(3)黄渤海的涌浪和混合浪能流密度峰值出现在8—9月,波谷出现在6月。风浪能流密度峰值出现在11月—次年3月,波谷出现在6—8月,均呈现双峰型月变化特征。东海、南海北部、南海中南部海域能流密度的月变化特征相似,都为双峰型,12月—次年4月的能流密度整体较高,波峰出现在12月,波谷出现在5—7月;(4)2 kW/m以上混合浪能流密度出现的频率较高,近海低于大洋;(5)0.5 m以上有效波高出现的频率都非常高,中国近海稍低于大洋;(6)涌浪能流密度的稳定性明显好于风浪能流密度;大洋的能流密度稳定性明显强于近岸。1月份能流密度的稳定性最好,4月和7月次之,10月的稳定性最差。     

Momentum and heat transfers in the surface layer over a frozen sea

Wind and temperature profiles from a 10-m mast were measured over the frozen Baltic Sea. The Monin-Obukhov similarity theory applies well to runs carefully selected according to stationarity criteria. This provides relatively low-scattered results with the roughness length z ₀ 0.04 cm, the drag coefficient C _D 1.5 × 10^-3 and the Stanton number C _H 1.00 × 10^-3 under near-neutral conditions. The roughness length, however, behaves in a peculiar way under intense stratification conditions. The reasons proposed for this could lead to an extension of the theory. The mechanisms for momentum and heat transfers are also examined, revealing that there are two different regimes, the smooth and the rough, for the wall friction but not for the heat transfer. Further, the scatter of the data for momentum and heat transfer under the aerodynamically rough regime can be explained by the distinction between the type of thermal stability conditions.     

Global ocean circulation and equator-pole heat transport as a function of ocean GCM resolution

To determine whether resolution of smaller scales is necessary to simulate large-scale ocean climate correctly, I examine results from a global ocean GCM run with different horizontal grid spacings. The horizontal grid spacings span a range from coarse resolutions traditionally used in climate modeling to nearly the highest resolution attained with today's computers. The experiments include four cases employing 4°, 2°, 1° and 1/2° spacing in latitude and longitude, which were run with minimal differences among them, i.e., in a controlled experiment. Two additional cases, 1/2° spacing with a more scale-selective sub-gridscale mixing of heat and momentum, and approximate 1/2° spacing, are also included. The 1/2° run resolves most of the observed mesoscale eddy energy in the ocean. Artificial constraints on the model tend to minimize differences among the different resolution cases. Nevertheless, the simulations show significant changes as resolution increases. These changes generally but not always bring the model into better agreement with observations. Differences are typically more noticeable when comparing the 4° and 2° runs than when comparing the 2° and 1° runs or the 1° and 1/2° runs. A reasonable conclusion to draw for current studies with coupled ocean-atmosphere GCMs is that the ocean grid spacing could be set to about 1° to accrue the benefits of enhanced resolution without paying an excessively steep price in computer-time cost. The model's poleward heat transport at 1/2° grid spacing peaks at about 1 × 10¹⁵ W in the Northern Hemisphere and 0.5 × 10¹⁵ W in the Southern Hemisphere. These values are significantly below observations, a problem typical of ocean GCMs even when they are less constrained than in the present study. This present problem is alleviated somewhat in the 1/2° run. In this case, however, the eddies resolved by the model generally act to counter rather than to reinforce the heat transport of the mean flow. Improved heat transport may result less from enhanced resolution than from other changes made in this version of the model, such as more accurate wind forcing.     

Shelf wave dispersion in a geophysical ocean

We consider subinertial, free waves trapped along three coastlines (i.e., shelf waves) in an ocean governed by a geophysical model in which stratification is explicitly obtained by taking the Vaisala frequency N much greater than the inertial frequency f. The behavior is generalized in terms of the parameter S = (N/f)a where a is the bottom slope of the trapping region. Only when $\text{S}\text{\$}\text{?}\text{0.2}$, are the predicted shelf waves like those predicted by Laplace's tidal equations (LTE) on an f-plane. When 0.2 ? S < 1, LTE are inappropriate because the shelf waves are only qualitatively like those predicted by LTE, and when S 1, the shelf waves are like baroclinic Kelvin waves in that they can occur at any subinertial frequency up to f (in qualitative disagreement with the predictions of LTE). Since N/f is usually a large number in the real ocean (of order 50–250), S is likely to be large unless the bottom slope is very gentle throughout the trapping region. Some applications to coastal current observations are discussed.     

Stably stratified flow in a marine atmospheric surface layer

Data from the marine atmospheric surface layer have been analysed. The data set consists of about two weeks with tower measurements up to 31 m of mean profiles of wind, temperature, and humidity, together with 20 Hz turbulence data. Mean wind, temperature, and humidity profiles up to 2000 m are also available from pibal trackings and radio soundings. Wave height was measured at 2 Hz, using an inverted echo-sounder.It was found from pibal wind profiles that low level jets were present during 2/3 of the measurements, having their maxima in the height interval 40 to 300 m. Here only data from the remaining 1/3 of the measurements, without low level jets, have been analysed.Non-dimensional wind and temperature gradients agree with results over homogeneous land surfaces as regards stability dependence during stable conditions that prevailed during this experiment. Linear regression gave _m = 1 + 6.8z/L and _m = 1 + 8.3z/L. No significant sea wave influence was found. The same was vrue for me dimensionless standard deviations of the three wind components, except for the vertical component. The expected wind speed dependence was found for the neutral drag coefficient, givingC _dN = 0.109U + 0.33 at 10 m, and a dependence on the wave parameter,C/u _*, was confirmed. Note, however, that the data set was restricted to low and moderate wind speeds and that stratification was mainly stable.Power spectra, non-dimensionalized according to suface-layer theories, do not follow the expected stability dependence. It was shown that this may be a consequence of the presence of gravity waves in the stable marine boundary layer. Indicators of gravity waves were found in most runs. The TKE budget agrees with findings over homogeneous land areas. The pressure transport term was found to be a source of energy also for near neutral conditions.     

Internal gravity waves in a stably stratified boundary layer

Often, a combination of waves and turbulence is present in the stably stratified atmospheric boundary layer. The presence of waves manifest itself in the vertical profiles of variances of fluctuations and in low-frequency contributions to the power spectra. In this paper we study internal waves by means of a linear stability analysis of the mean profiles in a stably stratified boundary layer and compare the results with observed vertical variance profiles of fluctuating wind and temperature along a 200 m mast. The linear stability analysis shows that the observed mean flow is unstable for disturbances in a certain frequency and wavenumber domain. These disturbances are expected to the detectable in the measurements. It is shown that indeed the calculated unstable frequencies are present in the observed spectra. Furthermore, the shape of the measured vertical variance profiles, which increase with height, is explained well by the calculated vertical structure of the amplitude of unstable Kelvin-Helmholtz waves, confirming the contribution of waves to the variances. Because turbulence and waves have quite distinct transport properties, estimates of diffusion from measurements of variances would strongly overestimate this diffusion. Therefore it is important to distinguish between them.     

Laboratory observations of shear-layer instability in a stratified fluid

Instability and transition to turbulence is studied in a shear layer between two streams of different salinities and velocities. The viscous layer between the two streams is 15–18 times thicker than the diffusion layer. When the initial layer Richardson number is low, the instability organizes the shear-layer vorticity into discrete lumps as in the homogeneous case. Here the similarity ends. The homogeneous shear layer continues to grow by the combination of neighboring vertical lumps (vortex pairing). In the stratified shear layer, the pairing process is stopped completely, and the vorticity is redistributed along the interface. This redistribution generates interfacial waves. The interfacial waves and the residual turbulence eventually decay, and the shear flow approaches a laminar state.