On the exact shape of the horizontal profile of a topographically rectified tidal flow

Abstract

Starting from the nonlinear shallow water equations of a homogeneous rotating fluid we derive the equation describing the evolution of vorticity by a fluctuating bottom topography of small amplitude, using a multiple scale expansion in a small parameter, which is the topographic length scale relative to the tidal wave length. The exact response functions of residual vorticity for a sinusoidal bottom topography are compared with those obtained by a primitive perturbation series and by harmonic truncation, showing the former to be invalid for small topographic length scales and the latter to be only a fair approximation for vorticity produced by planetary vortex stretching. In deriving the exact shape of the horizontal residual velocity profile at a step-like break in the bottom topography, it is shown that the Lagrangian profile only exists in a strip having the width of the amplitude of the tidal excursion at both sides of the break, and that it vanishes outside that interval. Moreover, in the limit of small amplitude topography at least, it vanishes altogether for the generation mechanism by means of planetary vortex stretching. The Eulerian profile is shown to extend over twice the interval of the Lagrangian profile both for production by vortex stretching and by differential bottom friction. These finite intervals over which the residual velocity profiles exist for a step-like topography are not reproduced by harmonic truncation of the basic equation. This method gives exponentially decaying profiles, indicating spurious horizontal diffusion of vorticity. In terms of orders of magnitude, the method of harmonic truncation is reliable for residual velocity produced by vortex stretching but it overestimates the residual velocity produced by differential bottom friction by a factor 2.     

The Red Sea outflow regulated by the Indian monsoon

To investigate why the Red Sea water overflows less in summer and more in winter, we have developed a locally high-resolution global OGCM with transposed poles in the Arabian peninsula and India. Based on a series of sensitivity experiments with different sets of idealized atmospheric forcing, the present study shows that the summer cessation of the strait outflow is remotely induced by the monsoonal wind over the Indian Ocean, in particular that over the western Arabian Sea. During the southwest monsoon (May–September), thermocline in the Gulf of Aden shoals as a result of coastal Ekman upwelling induced by the predominantly northeastward wind in the Gulf of Aden and the Arabian Sea. Because this shoaling is maximum during the southwest summer monsoon, the Red Sea water is blocked at the Bab el Mandeb Strait by upwelling of the intermediate water of the Gulf of Aden in late summer. The simulation also shows the three-dimensional evolution of the Red Sea water tongue at the mid-depths in the Gulf of Aden. While the tongue meanders, the discharged Red Sea outflow water (RSOW) (incoming Indian Ocean intermediate water (IOIW)) is always characterized by anticyclonic (cyclonic) vorticity, as suggested from the potential vorticity difference.     

Reconstruction of the upper ocean 3D dynamics from high-resolution sea surface height

The present study investigates the reconstruction of the 3D dynamics of a turbulent mesoscale eddy field driven at a depth by a baroclinic instability of the Phillips type. It uses a high-resolution primitive equation simulation as a testbed. The method of reconstruction is based on potential vorticity principles and extends an earlier approach (Lapeyre and Klein, J Phys Oceanogr 36:165–176, 2006) to a regime where the signature of surface density anomalies on the dynamics is weak. The crux and the originality of the reconstruction lie in the estimation from sea surface height and surface density anomalies of the interior quasigeostrophic potential vorticity (PV) anomalies and its subsequent inversion. The estimation of PV anomalies relies on the vertical correlation between PV anomalies and on the knowledge on stratification and horizontal gradients of background PV. PV anomalies are accurately estimated over the first 500 m of the water column and over a wide range of wavenumbers. Density anomalies play a minor role in the PV estimation, though their omission leads to an overestimation of PV by a factor of less than 2 at scales of order 20 km and less. Inversion of the estimated PV leads to a geostrophic streamfunction which in turn provides reliable reconstructions of the relative vorticity and vertical velocity (via the omega equation).     

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.     

Role of the Himalayan Orography in Simulation of the Indian Summer Monsoon using RegCM3

In this study, sensitivity of the Indian summer monsoon simulation to the Himalayan orography representation in a regional climate model (RegCM) is examined. The prescribed height of the Himalayan orography is less in the RegCM model than the actual height of the Himalayas. Therefore, in order to understand the impact of the Himalayan orography representation on the Indian summer monsoon, the height of the Himalayan orography is increased (decreased) by 10 % from its control height in the RegCM model. Three distinct monsoon years such as deficit (1987), excess (1988) and normal rainfall years are considered for this study. The performance of the RegCM model is tested with the use of a driving force from the reanalysis data and a global model output. IMD gridded rainfall and the reanalysis-2 data are used as verification analysis to validate the model results. The RegCM model has the potential to represent mean rainfall distribution over India as well as the upper air circulation patterns and some of the semi-permanent features during the Indian summer monsoon season. The skill of RegCM is reasonable in representing the variation in circulation and precipitation pattern and intensity during two contrasting rainfall years. The simulated seasonal mean rainfall over many parts of India especially, the foothills of the Himalaya, west coast of India and over the north east India along with the whole of India are more when the orography height is increased. The low level southwesterly wind including the Somali jet stream as well as upper air circulation associated with the tropical easterly jet stream become stronger with the enhancement of the Himalayan orography. Statistical analysis suggests that the distribution and intensity of rainfall is represented better with the increased orography of RegCM by 10 % from its control height. Thus, representation of the Himalayan orography in the model is close to actual and may enhance the skill in seasonal scale simulation of the Indian summer monsoon.     

Western Boundary Current Separation Caused by a Deep Countercurrent

It is shown that the deep western boundary current (DWBC) in the North Atlantic may contribute to premature separation of the Gulf Stream. A simple analytical study is made based on the linear barotropic vorticity equation in which a possible effect of the DWBC is introduced as anomalous stretching of the water column in a manner consistent with certain qualitative aspects of the observed features. This additional positive vorticity may be generated by a deep downwelling associated with horizontal shears of the DWBC. It is found that separation latitudes are farther to the south as the stretching is strengthened. Vertical motion required for a southward shift of order unity (e.g., 500 km) is estimated to be of the order of 0.05 mm s m 1 , in reasonable agreement with the observed values. It is suggested that since the DWBC is intimately linked with the thermohaline circulation, a meridional migration of the Gulf Stream separation might reflect long-term variations in the North Atlantic.     

Mapping radar-derived sea surface currents with a variational method

High-frequency radars measure projections of surface velocity vectors on the directions of the radar beams. A variational method for reconstruction of the 2d velocity field from such observations is proposed. The interpolation problem is regularized by penalizing high-frequency variability of the surface vorticity and divergence fields. Twin-data experiments are used to assess the method's skill and compare it with two well-known approaches to HFR data processing: conventional local interpolation and more sophisticated non-local scheme known as open-boundary modal analysis (OMA). It is shown that the variational method and OMA have a significant advantage over local interpolation because of their ability to reconstruct the velocity field within the gaps in data coverage, near the coastlines and in the areas covered only by one radar. Compared to OMA, the proposed variational method appears to be more flexible in processing gappy observations and more accurate at noise levels below 30%.     

Finite-frequency tomography in a crustal environment: Application to the western part of the Gulf of Corinth

In this paper we investigate finite-frequency effects in crustal tomography. We developed an inversion procedure based on an exact numerical computation of the sensitivity kernels. In this approach we compute the 3D travel-time sensitivity kernels by using (1) graph theory and an additional bending to estimate accurately both rays and travel-times between source/receiver and diffraction points and (2) paraxial ray theory to estimate the amplitude along theses rays. We invert both the velocity and the hypocentre parameters, using these so-called banana-doughnut kernels and the LSQR iterative solver. We compare the ray-theoretical and the finite-frequency tomography to image the intermediate structures beneath the Gulf of Corinth (Greece), which has long been recognized as the most active continental rifting zone in the Mediterranean region. Our dataset consists of 451 local events with 9233 P- first-arrival times recorded in the western part of the Gulf (Aigion area) in the framework of the 3F-Corinth European project. Previous tomographic images showed a complex velocity crustal model and a low-dip surface that may accommodate the deformation. Accurate velocity models will help to better constrain the rifting process, which is still a subject of debate. The main results of this study show that finite-frequency tomography improves crustal tomographic images by providing better resolved images of the 3D complicated velocity structure. Because the kernels spread the information over a volume, finite-frequency tomography results in a sharpening of layer boundaries as we observed for the shallower part of the crust (down to 5 km depth) beneath the Gulf of Corinth.     

The use of EPROM memories with a conventional tide-well gauge to record short period seiches

A low cost electronic apparatus is presented, which increases considerably the useful frequency range of mechanical floating type tide-gauges. The detection and the measurement of sea level oscillations in the range of 5 to 60 min is then possible. In a preliminary application, the presence in the Gulf of Genoa of shelf oscillations, predicted by a numerical model, have been detected.     

On the theory of thin rotating jets: A quasi‐geostrophic time dependent model

The time‐dependent meandering in a thin baroclinic jet over bottom topography is discussed in the quasi‐geostrophic approximation. The motion of the axis of the jet is taken to be vertically coherent and the axis itself is defined as inextensible. The motion is examined from a frame of reference moving with the axis but fixed at an arbitrary longitude in terms of an open ocean spatial initial value problem. The velocities of the axis and of the jet are quasi‐geostrophic, and vorticity conservation for the first non‐geostrophic components constrains the evolution of the axis and gives a path equation. The spatial linearized stability problem is studied and the jet is found to be baroclinically unstable to path disturbances of sufficiently high frequency which amplify downstream. An exact solution is obtained to the nonlinear path equation over a flat bottom with no ß‐effect. The evolution of the path of these unstable meanders is such that the path closes itself and forms rings (at which point the analysis breaks down). It is proposed that the baroclinic jet processes studied here are fundamental to the dynamics of Gulf Stream meandering and isolated eddy production.     

Urban seagrass: status of Posidonia oceanica facing the Genoa city waterfront (Italy) and implications for management

A system of five adjacent Posidonia oceanica meadows facing the waterfront of Genoa city (Ligurian Sea, NW Mediterranean) was investigated over different spatial scales (meters-kilometers) using three environmental indices: conservation index (CI), substitution index (SI) and phase-shift index (PSI). CI revealed differences mostly at large spatial scale, distinguishing the poor condition of the meadows closest to Genoa centre and harbour from the comparatively healthy condition of the farthest meadows. SI showed differences mostly at small spatial scale (i.e., within meadows), suggesting the influence of local factors in the re-colonisation of regressed meadows by the seagrass Cymodocea nodosa and/or the invasive alga Caulerpa racemosa. Mapping of PSI showed that the meadows closest to Genoa centre and harbour have undergone a nearly total phase shift and have no real potential for recovery: attempts to re-establish P. oceanica there might be a waste of time and money. On the contrary, the meadows farthest from Genoa centre and harbour showed a comparatively low level of phase shift and could still fully recover given specific management actions.     

On cumulus-scale transport of horizontal momentum in monsoon depression over India

A diagnostie method of cumulus parameterization is suggested in which vertical transport of horizontal momentum by cumulus-scale is derived by making use of large-scale vorticity as well as divergence budget equations. Data for composite monsoon depression over India available from our earlier studies used to test the method. As a first approximation, the results are obtained using only the vorticity budget equation.The results show that in the southwest sector of the monsoon depression, which is characterized by maximum cloudiness and precipitation, there is an excess of cyclonic vorticity in the lower troposphere and anticyclonic vorticity in the upper troposphere associated with the large-scale motion. The distribution of eddy vertical transport of horizontal momentum is such that anticyclonic vorticity is generated in the lower troposphere and cyclonic vorticity aloft. Cumulus-scale eddies thus work against the large-scale system and tend to off-set the large-scale imbalance in vorticity.     

Numerical computation of the tidally induced Lagrangian residual current in a model bay

With a depth-averaged numerical model, the tidally induced Lagrangian residual current in a model bay was studied. To correctly reflect the long-term mass transport, it is appropriate to use the Lagrangian residual velocity (LRV) rather than the Eulerian residual velocity (ERV) or the Eulerian residual transport velocity (ETV) to describe the residual current. The parameter κ, which is defined as the ratio of the typical tidal amplitude at the open boundary to the mean water depth, is considered to be the indicator of the nonlinear effect in the system. It is found that the feasibility of making the mass transport velocity (MTV) approximate the LRV is strongly dependent on κ. The error between the MTV and the LRV tends to increase with a growing κ. An additional error will come from the various initial tidal phases due to the Lagrangian drift velocity (LDV) when κ is no longer small. According to the residual vorticity equation based on the MTV, the Coriolis effect is found to influence the residual vorticity mainly through the curl of the tidal stress. A significant difference in the flow pattern indicates that the LRV is sensitive to the bottom friction in different forms.     

Cold anticyclonic eddies formed from cold pool water in the southern Middle Atlantic Bight

AVHRR satellite imagery of the southern Mid-Atlantic Bight during May 1993 revealed a large area of cold water over the shelf break and slope that appeared to spin up into a series of southward propagating anticyclonic eddies. The eddies had diameters of 35–45 km at the surface and moved southward at about 20 cm/sec. A radial TOYO CTD (to 50m) and ADCP velocity (to 400m) transect was conducted across the southern-most of these eddies. The upper 50 meters had minimum temperatures of less than 7°C and salinities of about 33 pss, characteristics similar to cold pool waters usually found over the continental shelf. ADCP velocity data from one of the eddies revealed anticyclonic flow extending to a depth of about 250m. The transport of cold pool water by the eddies was estimated to be 0.1 to 0.2 Sv which is of the same order as the annual mean alongshore transport of shelf water in this region. The origin of the deeper water within the eddy is unlikely to be the continental shelf because the shelf break is less than 100 m. The depth and velocity profiles along the TOYO transect were consistent with the constant potential vorticity eddy model of Flierl (1979) although the source of the eddy kinetic energy is uncertain. The cause for the exodus of cold pool water from the shelf, which extended northward to at least 38°N, is unclear but must involve the establishment of an alongshore baroclinic pressure gradient against the usual southwestward shelf flow. It is possible that the intrusion of Gulf Stream waters onto the shelf near Cape Hatteras was a precursor of this off shelf transport. The southern-most eddy was marked by high biological productivity and very high oxygen supersaturation. The phytoplankton bloom detected within the exported cold pool water, located over the continental slope, suggests a mechanism whereby production fueled by nutrients derived from the shelf can be locally exported into deep water.     

On a generalized potential vorticity equation for quasi-geostrophic flow

Summary It is shown that the general nonlinear potential vorticity equation for viscous and conductive fluid in a rotating system can be expressed in terms of the geostrophic stream function for the horizontal velocity alone, provided that the motions are hydrostatic and quasi-geostrophic and the Richardson number is much larger than unity. The form of this equation is identical with that obtained from an asymptotic expansion for a small Rossby number.     

斜压大气中热带气旋运动特征的动力分析

从绝热、无摩擦、无环境场作用条件下的原始方程组出发,讨论了热带气旋的动力平衡特征,并分别导出了正、斜压大气中综合描述热带气旋中心强度变化的物理量(dI/dt)及其动力平衡关系式,进而分析了正、斜压大气中的热带气旋强度变化及移动的特征.结果表明:热带气旋的定常运动具有"相当地转风平衡”的特征,其等"压能”线和等位涡线均与流线重合;"β涡旋对”及由高(低)层水平风正(负)垂直切变产生的"切变涡旋对”之间的"通风气流”均使热带气旋的强度减弱,高(低)层涡度的负(正)垂直平流则增强热带气旋的强度;热带气旋的中心有向极、向高(低)层涡度垂直平流的梯(升)度方向移动的趋势,垂直运动及高、低层水平风速垂直切变的非对称结构对热带气旋的移动有影响;"γ效应”则是"通风气流”牵引热带气旋移动的动力机制之一.     

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.     

Observations of submesoscale eddies using high-frequency radar-derived kinematic and dynamic quantities

The spatio-temporal variability of submesoscale eddies off southern San Diego is investigated with two-year observations of subinertial surface currents [O(1) m depth] derived from shore-based high-frequency radars. The kinematic and dynamic quantities — velocity potential, stream function, divergence, vorticity, and deformation rates — are directly estimated from radial velocity maps using optimal interpolation. For eddy detection, the winding-angle approach based on flow geometry is applied to the calculated stream function. A cluster of nearly enclosed streamlines with persistent vorticity in time is identified as an eddy. About 700 eddies were detected for each rotation (clockwise and counter-clockwise). The two rotations show similar statistics with diameters in the range of 5–25 km and Rossby number of 0.2–2. They persist for 1–7 days with weak seasonality and migrate with a translation speed of 4–15 cm s⁻¹ advected by background currents. The horizontal structure of eddies exhibits nearly symmetric tangential velocity with a maximum at the defined radius of the eddy, non-zero radial velocity due to background flows, and Gaussian vorticity with the highest value at the center. In contrast divergence has no consistent spatial shape. Two episodic events are presented with other in situ data (subsurface current and temperature profiles, and local winds) as an example of frontal-scale secondary circulation associated with drifting submesoscale eddies.     

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.