A new barotropic model of the wind-driven circulation

Rationalized by the observational circulation pattern in the upper ocean of the North Pacific, meridional friction term is first incorporated in a barotropic theoretical model of the wind-driven circulation. The governing potential vorticity equation thence has β term and wind stress curl term (the two of the Sverdrup balance), zonal friction term and meridional friction term. The analytical solution satisfactorily captures many important features of the wind-driven circulation in the North Pacific: Kuroshio, Oyashio, Kuroshio extension, North Equatorial Current, and especially the eastern boundary currents in the North Pacific, i.e. California current and Alaska current.     

Statistical properties of an enstrophy conserving finite element discretisation for the stochastic quasi-geostrophic equation

ABSTRACT

A 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.     

准地转大洋风生环流的格子Boltzmann数值模拟

建立了求解准地转相当正压涡度方程的格子Boltzmann (LB)模型. 该模型将准地转相当正压涡度方程作为一个平流-扩散-反应方程来加以处理,在整体二阶精度下,通过Chapman_Enskog多尺度分析法,可将格子Boltzmann方程还原到相当正压涡度方程. 在不同Reynolds数、不同边界条件以及不同风应力驱动下的数值解表明,该模型正确反映了风生环流的基本结构和不同边界的耗散特征,并得到风生环流的多平衡态解等非线性特征. 此外,不同Rossby变形半径下的实验证明,小Rossby变形半径更容易激发环流的非线性模态. 通过与同等类型有限差方案的比较,表明本文的LB模型具有稳定性好、精度高等优点.     

Roles of forced and inertially unstable convection development in the onset process of Indian summer monsoon

The NCEP/NCAR R1 reanalysis data are employed to investigate the impact of forced and inertial instability in the lower troposphere over the Arabian Sea on the onset process of Indian summer monsoon(ISM),and to reveal the important role of zonal advection of zonal geostrophic momentum played in the forced unstable convection.Results show that during the ISM onset the zero absolute vorticity contour(??=0)shifts northward due to the strong cross-equatorial pressure gradient in the lower troposphere over southern Arabian Sea.Thus a region with negative absolute vorticity is generated near the equator in the northern hemisphere,manifesting the evident free inertial instability.When a southerly passes through this region,under the influence of friction a lower convergence that facilitates the convection flourishing at the lower latitudes appears to the north of zero absolute vorticity contour.However,owing to such a traditional inertial instability,the convection is confined near the equator which does not have direct influence on the ISM onset.On the contrary in the region to the north of the zero absolute vorticity contour and to the south of the low pressure center near the surface,although the atmosphere there is inertially stable,the lower westerly jet can develop and bring on the apparent zonal advection of zonal geostrophic momentum.Both theoretical study and diagnosing analysis present that such a zonal advection of geostrophic momentum is closely associated with the zonal asymmetric distribution of meridional land-sea thermal contrast,which induces a convergence center near and further north of the westerly jet in the lower troposphere over the southwestern coast of the Indian Peninsula,providing a favorable lower circulation for the ISM onset.It illustrates that the development of convection over the Arabian Sea in late spring and early summer is not only due to the frictional inertial instability but also strongly affected by the zonal asymmetric distribution of land-sea thermal contrast.Moreover,before the ISM onset due to the eastward development of the South Asian High(SAH)in the upper troposphere,high potential vorticity is transported to the region over the Arabian Sea.Then a local trumpet-shaped stream field is generated to cause the evident upper divergence-pumping effect which favors the ISM onset.When the upper divergence is vertically coupled with the lower convergence resulted from the aforementioned forced unstable convection development near the southwestern coast of Indian Peninsula,the atmospheric baroclinic unstable development is stimulated and the ISM onset is triggered.     

风驱动下f-平面准地转三维海洋环流的形成及总质量守恒的应用

将理想化的南中国海海盆在垂直方向上划分为Ekman层、惯性层和摩擦层. Ekman层中的运动由大气风应力驱动,其底部的扰动压力将作为其下惯性层中运动的上边界条件. 惯性层中的运动是由f 平面三维非线性方程在准地转近似下位势涡度守恒控制,由此得到控制惯性层中运动关于扰动压力的三维椭圆型方程. 在惯性层以下考虑到深层的海盆水平尺度很小,由此引进带有底部摩擦的线性控制方程,方程的边界条件为惯性层和摩擦层交界面上的扰动压力连续,沿海盆边界假定海水与相邻的固壁间无热量交换,由此设在海盆边界上扰动温度为零. 在此基础上分别利用惯性层和摩擦层中的椭圆型控制方程计算了相应层次上冬、夏季的扰动压力和准地转流. 结果表明冬季各层上以气旋式环流为主,且随深度的增加流速减小;夏季各层上以反气旋式环流为主,流速也随深度增加而减小. 这在一定程度上和观测事实相符.     

Decadal variability of the Kuroshio Extension: mesoscale eddies and recirculations

An eddy-resolving multidecadal ocean model hindcast simulation is analyzed to investigate time-varying signals of the two recirculation gyres present respectively to the north and south of the Kuroshio Extension (KE) jet. The northern recirculation gyre (NRG), which has been detected at middepth recently by profiling float and moored current meter observations, is a major focus of the present study. Low-frequency variations in the intensity of the recirculation gyres are overall highly correlated with decadal variations of the KE jet induced by the basin-wide wind change. Modulation of the simulated mesoscale eddies and its relationship with the time-varying recirculation gyres are also evaluated. The simulated eddy kinetic energy in the upstream KE region is inversely correlated with the intensity of the NRG, consistent with previous observational studies. Eddy influence on the low-frequency modulation of the NRG intensity at middepth is further examined by a composite analysis of turbulent Sverdrup balance, assuming a potential vorticity balance between the mean advection and the convergent eddy fluxes during the different states of the recirculation gyre. The change in the NRG intensity is adequately explained by that inferred by the turbulent Sverdrup balance, suggesting that the eddy feedback triggers the low-frequency modulation of the NRG intensity at middepth.     

Lateral friction in the oceans as an effect of potential vorticity mixing

Abstract

Applying a mixing-length calculation to potential vorticity rather than to momentum a new type of lateral friction appears in the oceanic mass transport equations. This friction is evaluated for the special case of horizontally homogeneous, quasi-geostrophic turbulence. The main effect is a westward force arising from the so-called β-term. This produces an additional southward interior transport and a strengthening of the western boundary current. A turbulent exchange coefficient K^H = 10⁸ em²s^?1 is sufficient to give a Gulf Stream transport twice that obtained by the classical Sverdrup model.     

An observational study of 300 mb winds in the tropical belt. Part II: Dynamical interpretation

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.     

On Production of Long-term Mean Zonal Current and Eddy Momentum and Heat Transports in Atmosphere

— The mean zonal velocity in the atmosphere is taken as being created continually by the global scale Hadley circulation produced by the differential solar heating through the balance between the Coriolis effect and vertical diffusion, and not by conservation of absolute momentum. Hence a proper determination of the diffusion coefficient becomes the key to the solution of the zonal flow problem. In this study we take the flow field as composed of a primary global scale Hadley circulation, and a secondary flow created by the convergences of the eddy transports of heat and momentum and surface friction, which give rise to the classical three cell structure of the meridional circulation but which only modifies the zonal velocity distribution slightly.¶Finally, we use the equilibrium solution of the perturbation potential vorticity equation to obtain the eddy transports of momentum and heat, with the zonal velocity given by the primary Hadley flow as the basic flow, and we found that they are close to the statistically observed values, demonstrating that the system can maintain itself.     

The nonlinear spin-up of a stratified ocean

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.     

冷空气入侵对热带气旋发生发展的影响

本文从梯度风方程出发,证明温度梯度增强对涡度起到增强作用.因此当冷空气侵入热带气旋外围时,只要没有破坏热带气旋的暖心结构,就会引起温度梯度的增长,从而促进热带气旋的发生发展.本文采用NCAR/PSU研制的非静力中尺度模式MM5,研究北半球冷暖空气入侵在热带气旋形成和加强过程中的作用.通过研究冷暖空气对热带气旋发展影响的试验发现,冷暖空气在入侵热带气旋外围时,最主要改变的是外围的环流场.北半球冷空气的入侵将会增强热带气旋北面的北风,形成指向热带气旋中心的推力,即辐合增强,暖空气入侵减弱北面的北风,形成背向热带气旋中心的拉力,即辐合减弱.由于拉力作用,一方面把边界上由于冷空气入侵而生成的能量往热带气旋中心输送,另一方面导致温度梯度的增加.因此从天气学形势来看,在热带气旋发生发展的过程中,北方的冷高压将会增强热带气旋北面的风速,从而导致热带气旋的增强;南半球澳高的增强,将使越赤道气流增强,热带气旋南面的风速也因此增强,从而引起热带气旋的增强.     

The processes of tropical semi-geostrophic adaptation

In tropical areas, when the zonal or meridional geostrophic equilibrium is destroyed, inertial gravity wave will be excited by ageostrophic motion, with the dispersion of the wave, a new zonal or meridional geostrophic balance will be established again, and it follows an invariant of semi-potential vorticity. Based on the invariant, it should be pointed out that the direction of the zonal or meridional semi-geostrophic adaptation depends mainly upon the meridional characteristic scale of initial disturbance. For the zonal (meridional) semi-geostrophic adaptation, if the zonal characteristic scale of initial disturbance is big (small) enough, then the adaptation process always represents the mutual adjustment between the pressure field and zonal (meridional) flow.     

Monsoonal quasi-stationary ultralong waves of the tropical troposphere predicted by a real data prediction over a global tropical belt

The mechanisms of the maintenance of the tropical upper tropospheric quasi-stationary ultralong waves during the northern hemisphere summer season are briefly reviewed and discussed. Diagnostic and prognostic studies indicate that the waves are maintained by the land-ocean contrast heating. These scales of motion as a whole (sum of the zonal wavenumbers 1, 2 and 3) are considered to supply kinetic energy to all other scales of motion.The ultralong waves predicted in the real data numerical prediction experiment over the global tropics using a multi-level primitive equation model are examined and compared with the observed climatological waves. The predicted waves are found to have several similarities with the observations. Further investigations of the baroclinic nature of the waves indicate that their thermal structure is essential for understanding their dynamics.The vorticity budget computations are performed for the predicted ultralong waves at 200 mb and also compared with the climatological observations. It is found that the advection term is one of the leading terms in the vorticity equation.This study indicates that the tropical quasi-stationary ultralong waves are fully nonlinear, non-geostrophic, three-dimensional waves forced mainly by the convective heating over the monsoon Indian subcontient.     

A numerical experiment on the general circulation of the middle atmosphere with a three-dimensional model explicitly representing internal gravity waves and their breaking

The general circulation of the middle atmosphere is simulated by means of a three-dimensional primitive equation model which covers from the south pole to the north pole but is limited to a ten-degree sector in the latitudinal direction; cyclic conditions are imposed at the east—west lateral boundaries. The model is capable of explicitly representing internal gravity waves of zonal wavelength greater than a few hundred kilometers with the use of a one-degree mesh, but planetary-scale waves were excluded. No parameterization is employed for subgrid-scale eddy viscosity (or diffusivity).With the assumption of a simple external-heating function corresponding to solstice conditions, a time integration was performed for about thirty days from the motionless state. During the whole period, random forcings were imposed on each grid of the lowest level in order to generate small-scale upwardly propagating internal gravity waves.The experiment has shown that small-scale waves were indeed excited, propagated upward, broke up near the mesopause, and greatly changed the thermally induced zonal mean motion and temperature fields in the upper mesosphere and lower thermosphere. As a result, important features of the general circulation at those levels, such as reversals of the zonal motion and the latitudinal gradient of zonal mean temperature were reproduced.     

Sill effects on physical dynamics in eastern Long Island Sound

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.     

冬季太阳11年周期活动对大气环流的影响

利用气象场的再分析资料和太阳辐射活动资料,对太阳11年周期活动影响北半球冬季(11月~3月)大气环流的过程进行了统计分析和动力学诊断.根据赤道平流层纬向风准两年振荡(QBO)的东、西风状态对太阳活动效应进行了分类讨论,结果表明：东风态QBO时,太阳活动效应主要集中在赤道平流层中、高层和南半球平流层,强太阳活动时增强的紫外辐射加热了赤道地区的臭氧层,造成平流层低纬明显增温,同时加强了南半球的Brewer-Dobson(B-D)环流,引起南极高纬平流层温度增加;而北半球中高纬的环流主要受行星波的影响,太阳活动影响很小.西风态QBO时,太阳活动效应在北半球更为重要,初冬时强太阳活动除了加热赤道地区臭氧层外,还抑制了北半球的B-D环流,造成赤道平流层温度增加和纬向风梯度在垂直方向的变化,从而改变了对流层两支行星波波导的强度;冬末时在太阳活动调制下,行星波向极波导增强,B-D环流逐渐恢复,造成北半球极地平流层明显增温,同时伴随着赤道区域温度的下降.     

Analysis on observing optimization for the wind-driven circulation by an adjoint approach

The adjoint approach is a variational method which is often applied to data assimilation widely in meteorology and oceanography. It is used for analyses on observing optimization for the wind-driven Sverdrup circulation. The adjoint system developed by Thacker and Long (1992), which is based on the GFDL Byran-Cox model, includes three components, i. e. the forward model, the adjoint model and the optimal algorithm. The GFDL Byran-Cox model was integrated for a long time driven by a batch of ideal wind stresses whose meridional component is set to null and zonal component is a sine function of latitudes in a rectangle box with six vertical levels and 2 by 2 degree horizontal resolution. The results are regarded as a "real" representative of the wind-driven Sverdrup circulation, from which the four dimensional fields are allowed to be sampled in several ways, such as sampling at the different levels or along the different vertical sections. To set the different samples, the fields of temperature, salinity and velocities function as the observational limit in the adjoint system respectively where the same initial condition is chosen for 4D VAR data assimilation. By examining the distance functions which measure the misfit between the circulation field from the control experiment of the adjoint system with a complete observation and those from data assimilation of adjoint approach in these sensitivity experiments respectively, observing optimizations for the wind-driven Sverdrup circulation will be suggested under a fixed observational cost.     

Some numerical experiments on surface albedo variation

Abstract

A two-level quasi-geostrophic general circulation model is developed to test various theories relating to surface albedo changes in the Sahara/Sahel regions of Africa. The heating function in the model is varied so as to examine the effects of both increases and decreases in surface albedo. Loss of vegetation cover is linked to increased surface albedo, and from the experiments, the delicate balance between the Sahara/Sahel is noted. Revegetating the Sahara would tend to decrease the surface albedo and the model shows that this experiment would be successful in reclaiming some of the desert.     

On Rossby wave propagation in a meridionally stratified channel

Rossby wave propagation in the presence of a nonseparable Brunt-Väisälä frequency,N(y,z), and the associated geostrophic zonal flow,U(y,z), is examined in this paper. The usual quasi-geostrophic potential vorticity equation only includes vertical variations in Brunt-Väisälä frequency (i.e.N(z)). We derive a linearised quasi-geostrophic potential vorticity equation which explicitly includesN(y, z), where variations inN may occur on the internal Rossby radius length scale. A mixed layer distribution that monotonically deepens in the poleward direction leads to a nonseparableN(y,z). The resulting meridional pressure gradient is balanced by an eastward zonal geostrophic flow.By assuming mixed layer depth changes occur slowly, relative to a typical horizontal wavelength of a Rossby wave, a local analysis is presented. The Rossby wave is found to have a strongly modulated meridional wavenumber,l, with amplitude proportional to |l|^–1/2. To elucidate whether the modulations of the Rossby wave are caused by the horizontal variations inN orU we also consider the cases where eitherN orU vary horizontally. Mixed layer depth changes lead to largestl where the mixed layer is deepest, whereasl is reduced in magnitude whereU is nonzero. When bothU(y,z) andN(y,z) are present, the two effects compete with one another, the outcome determined by the size of |c|/U _max, wherec is the Rossby wave phase speed. Finally, the slowly varying assumption required for the analytical approach is removed by employing a numerical model. The numerical model is suitable for studying Rossby wave propagation in a rectangular zonal channel with generalN(y, z) andU(y, z).     

Vortex evolution

Abstract

Friedmann's equation and the potential vorticity equation are generalised for turbulent motion. The generalised equations incorporate some new phenomena connected with turbulent transport of mass. It is proved that, if ?×[S×Ω+S(?·S)]≠0 where Ω is the absolute vorticity of the velocity and S is the turbulent density flux, then the Helmholtz-Kelvin theorem concerning the conservation of the velocity circulation around a closed path is violated and the potential vorticity is not a Lagrangian adiabatic invariant. The effects of this turbulent transport of mass on the creation or dissipation of vorticity discussed here is not equivalent to effects of baroclinicity or viscosity. Some possible implications of the new circulation theorem in geophysical and astrophysical fluid dynamics are discussed.