Modeling vertical motion at ocean fronts: Are nonhydrostatic effects relevant at submesoscales?

Through a suite of three-dimensional, high-resolution numerical modeling experiments, we examine the role of nonhydrostatic effects on O(1 km) submesoscale processes at ocean fronts, with particular focus on the vertical velocity field. Several differences between nonhydrostatic and hydrostatic models are pointed out using a framework that enables precise comparison, but it is difficult to identify categorical differences between the model solutions at the grid resolutions afforded. The instantaneous vertical velocity structure is sensitive to the model choice and, even more so, to grid resolution, but the average vertical flux is similar in both hydrostatic and nonhydrostatic cases.When a frontal region with horizontal density gradients is perturbed by wind, a profusion of submesoscale, O(1 km), secondary circulation features develops in the upper 50 m. Narrow, elongated cells of intense up- and down-welling are found to occur close to the surface, overlying broader regions of weaker up- and down-welling associated with the mesoscale meanders of the baroclinically unstable front. The submesoscale down-welling is considerably stronger than up-welling and is concentrated in 1–2 km width filaments within which velocities can attain magnitudes as high as 200 m day⁻¹. The submesoscale features are found to be robust at horizontal grid resolutions varying between 1 and 0.25 km and exist even in the hydrostatic model. Submesoscale circulation is difficult to observe or resolve in coarser resolution circulation models, but is likely to play a significant role in the exchange of energy and properties between the surface ocean and thermocline. Possible mechanisms for the generation of these features are investigated in a follow-on paper.     

A numerical study of the effects of wind forcing on the Chile Current System

A high-resolution, multi-level, primitive equation ocean model is used to examine the response of the coastal region from 22.5°S to 35°S of the Chile Current System to both equatorward and climatological wind forcing. The results from both types of forcing show that an equatorward surface current, a poleward undercurrent, upwelling, meanders, filaments and eddies develop in response to the predominant equatorward wind forcing. When climatological wind forcing is used, an offshore branch of the equatorward surface current is also generated. These features are consistent with available observations of the Chile Current System. The model results support the hypothesis that wind forcing is an important mechanism for generating currents, eddies and filaments in the Chile eastern boundary current system and in other eastern boundary current regions which have predominantly equatorward wind forcing.     

The role of nonhydrostatic dynamics in controlling development of a surface ocean front

Numerical studies of surface ocean fronts forced by inhomogeneous buoyancy loss show nonhydrostatic convective plumes coexisting with baroclinic eddies. The character of the vertical overturning depends sensitively on the treatment of the vertical momentum equation in the model. It is less well known how the frontal evolution over scales of O(10 km) is affected by these dynamics. Here, we compare highly resolved numerical experiments using nonhydrostatic and hydrostatic models and the convective-adjustment parametrization. The impact of nonhydrostatic processes on average cross-frontal transfer is weak compared to the effect of the O(1 km) scale baroclinic motions. For water-mass distribution and formation rate nonhydrostatic dynamics have similar influence to the baroclinic eddies although adequate resolution of the gradients in forcing fluxes is more important. The overall implication is that including nonhydrostatic surface frontal dynamics in ocean general circulation models will have only a minor effect on scales of O(1 km) and greater.     

A numerical study on the generation of the small meander of the Kuroshio off southern Kyûshû

The generation of small meanders of the Kuroshio off southern Kyûshû is investigated. Basing on the fact that the small meanders tend to follow an increase in velocity of the Kuroshio in the Satsunan region (Sekine andToba, 1981), the influence of this velocity increase on the quasi-stationary path of the Kuroshio is studied numerically. Simplified bottom and coastal topographies are employed in a two layer model ocean. A quasi-stationary numerical solution with a constant inflow is used for the initial condition, and a temporal increase in the inflow with corresponding leakage is employed as the boundary condition to investigate nonlinear effects due to the increase in current velocity. Experiments for four different physical models are carried out to determine the specific roles of the continental slope, the planetary-effect, and density stratification. Temporal increase in the inflow tends to cause offshore shift of the current path. But the topographic effect of the continental slope is strong enough that no significant shift of the current path occurs in the case of the barotropic ocean. However, in the case of a baroclinic ocean, temporal increase in the inflow does cause generation of small meanders, because density stratification diminishes the topographic effect. A larger density stratification provides more favorable condition for the appearance of the small meander, and a cyclonic eddy is formed on the continental side of the small meander path.     

A Large-Scale Seasonal Modeling Study of the California Current System

A high-resolution, multi-level, primitive equation ocean model has been used to investigate the combined role of seasonal wind forcing, seasonal thermohaline gradients, and coastline irregularities on the formation of currents, meanders, eddies, and filaments in the entire California Current System (CCS) region, from Baja to the Washington-Canada border. Additional objectives are to further characterize the meandering jet south of Cape Blanco and the seasonal variability off Baja. Model results show the following: All of the major currents of the CCS (i.e., the California Current, the California Undercurrent, the Davidson Current, the Southern California Countercurrent, and the Southern California Eddy) as well as filaments, meanders and eddies are generated. The results are consistent with the generation of eddies from instabilities of the southward current and northward undercurrent via barotropic and baroclinic instability processes. The meandering southward jet, which divides coastally-influenced water from water of offshore origin, is a continuous feature in the CCS, and covers an alongshore distance of over 2000 km from south of Cape Blanco to Baja. Off Baja, the southward jet strengthens (weakens) during spring and summer (fall and winter). The area off southern Baja is a highly dynamic environment for meanders, filaments, and eddies, while the region off Point Eugenia, which represents the largest coastline perturbation along the Baja peninsula, is shown to be a persistent cyclonic eddy generation region. This revised version was published online in July 2006 with corrections to the Cover Date.     

The rôle of the complete Coriolis force in cross-equatorial flow of abyssal ocean currents

Ocean currents flowing close to or across the equator are strongly constrained by the change in sign of f, the locally vertical component of the Earth’s rotation vector, across the equator. We investigate these currents using a shallow water model that includes both the locally vertical and locally horizontal components of the Earth’s rotation vector, thus accounting for the complete Coriolis force. We therefore avoid making the so-called “traditional approximation” that retains only the part of the Coriolis force associated with the locally vertical component of the rotation vector. Including the complete Coriolis force contributes an additional term to the fluid’s potential vorticity, which may partially balance the change in sign of f as fluid crosses the equator over suitably shaped bathymetry.We focus on the Antarctic Bottom Water, which crosses the equator northwards in the western Atlantic ocean where the local bathymetry forms an almost-zonal channel. We show that this bathymetry facilitates the current’s equatorial crossing via the action of the “non-traditional” component of the Coriolis force. We illustrate this process using both analytical and numerical solutions for flow of an abyssal current over idealised equatorial topography. We also consider the one-dimensional geostrophic adjustment of a body of fluid across the equator, and show that the “non-traditional” contribution to the fluid’s angular momentum permits a larger cross-equatorial transport. These results underline the importance of including the complete Coriolis force in studies of the equatorial ocean, particularly in the weakly-stratified abyssal ocean where the non-traditional component is most pronounced.     

Evaluation of drift current parameters using an analytical model

The paper is concerned with the evaluation of the drift current parameters derived through the use of an analytical model. In this model, effective when stratification is stable and indifferent, the vertical turbulence coefficient profile is prescribed by the power function, and hydrodynamic quantities are prescribed using the external parameters of the problem (wind stress, the Coriolis parameter, and the dimensionless stratification parameter). Model data are compared with the observations of the upper mixed layer in the vicinity of the oceanic Station C, conducted during one year. It is shown that, under the spring-summer-time warming conditions, the model at issue is capable of adequately simulating the upper ocean layer dynamics. Translated by Vladimir A. Puchkin.     

Generation of internal waves in a three-layer ocean

Within the framework of the linear theory of long waves taking into account the action of the Coriolis force, we solve the problem of generation of internal waves by a barotropic tide impinging on a bottom irregularity of the sea-ridge type. The cross section of the ridge is assumed to be rectangular and the stratification of the ocean is regarded as stepwise with two thermoclines (three-layer model). We study the dependences of the characteristics of generated waves on the parameters of stratification and the period of the impinging barotropic tide. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Analysis of a simplification strategy in a nonhydrostatic model for surface and internal wave problems

This paper examines the simplification strategy of retaining only the nonhydrostatic effect of local acceleration in a three-dimensional fully nonhydrostatic model regarding the submesoscale wave phenomenon in the ocean.Elaborate scale analysis of the vertical component of the Reynold-averaged Navier–Stokes(RANS) equation was performed, confirming the rationalization of this simplification. Then, the simplification was implemented in a RANS equation-based nonhydrostatic model NHWAVE(nonhydrostat...     

Generation of internal waves by barotropic tidal flow over a steep ridge

A three-dimensional nonhydrostatic numerical model is used to study the generation of internal waves by the barotropic tidal flow over a steep two-dimensional ridge in an ocean with strong upper-ocean stratification. The process is examined by varying topographic width, amplitude of the barotropic tide, and stratification at three ridge heights. The results show that a large amount of energy is converted from the barotropic tide to the baroclinic wave when the slope parameter, defined as the ratio of the maximum ridge slope to the maximum wave slope, is greater than 1. The energy flux of internal waves can be normalized by the vertical integral of the buoyancy frequency over the ridge depths and the kinetic energy of the barotropic tides in the water column. A relationship between the normalized energy flux and the slope parameter is derived. The normalized energy flux reaches a constant value independent of the slope parameter when the slope parameter is greater than 1.5. It is inferred that internal wave generation is most efficient at the presence of strong upper-ocean stratification over a steep, tall ridge. In the Luzon Strait, the strength of the shallow thermocline and the location of the Kuroshio front could affect generation of internal solitary waves in the northern South China Sea.     

Numerical model of nonhydrostatic ocean dynamics based on methods of artificial compressibility and multicomponent splitting

An algorithm is proposed for solving three-dimensional ocean hydrodynamics equations without hydrostatic approximation and traditional simplification of Coriolis acceleration. It is based on multicomponent splitting of the modified model with artificial compressibility. The original system of equations is split into two subsystems describing the transport of three velocity components and adjustment of the density and velocity fields. At the adjustment stage, the horizontal velocity components are represented as a sum of the depth means and deviations; the two corresponding subsystems are derived. For barotropic dynamics, the compressibility effect is represented as the boundary condition at the free surface, while for the baroclinic subsystem, it is introduced as ε-regularization of the continuity equation. Then, the baroclinic equations are split into two subsystems describing the hydrostatic and nonhydrostatic dynamics. The nonhydrostatic dynamics is computed at a separate splitting stage. The algorithm is included into the Institute of Numerical Mathematics of the Russian Academy of Sciences model based on “primitive” equations and verified by solving the hydrodynamics problem for the Sea of Marmara.     

太湖夏季环流成因的数值研究

强潮河口盐水入侵对饮用水源地危害极大。基于平面二维水动力盐度模型, 对典型强潮河口—钱塘江的水动力及盐水入侵过程进行了数值模拟研究。结果表明枯水径流时盐度变化与潮位过程曲线类似, 潮差对盐度大小影响显著, 径流量的增加将逐渐减小其相似程度。当流量增加到一定程度后, 继续增加的一定径流量所产生的抑咸效果减弱, 水资源有效利用率降低, 此时允许水源地盐度超标并改从蓄淡避咸水库取水可有效节约水资源。盐度平面分布显示, 盐水入侵在强潮河口弯道处受涨潮流主流线影响明显, 靠近主流线一岸的盐度大于对岸, 单从盐水入侵角度考虑, 强潮河口弯道段的取水口应设置在远离涨潮流主流线一岸。钱塘江河口盐度数值模拟对于研究减轻盐水入侵对水源地危害的措施具有指导意义。     

冬季黄海暖流的诊断计算

采用ECOMSED三维水动力模式，诊断计算了冬季渤海、黄海和东海的近海环流状况，重点分析了黄海暖流的演变过程及其垂直结构，并探讨了黄海暖流的形成机理。结果表明，黄海暖流于12月初步形成，次年2月发展最强盛，3月开始衰退。黄海暖流在表层和次表层（0-30m）并不是一支持续稳定的流，其持续稳定性仅在近底层得到很好的体现。对黄海暖流形成机理的分析表明，压强梯度力、垂向摩擦力和柯氏力占主要地位。在表层及次表层，主要表现为风的正压作用，而在近底层，则由海平面起伏造成的正压梯度力和密度场引起的斜压梯度力形成的总压强梯度力与柯氏力基本平衡，因而黄海暖流可基本认为是准地转流。     

Application of interleaving models for the description of intrusive layering at the fronts of deep polar water in the Eurasian Basin (Arctic)

Interleaving models of pure thermohaline and baroclinic frontal zones are applied to describe intrusions at the fronts found in the upper part of the Deep Polar Water (DPW) when the stratification was absolutely stable. It is assumed that differential mixing is the main mechanism of the intrusion formation. Important parameters of the interleaving such as the growth rate, vertical scale, and slope of the most unstable modes relative to the horizontal plane are calculated. It was found that the interleaving model for a pure thermohaline front satisfactory describes the important intrusion parameters observed at the frontal zone. In the case of a baroclinic front, satisfactory agreement over all the interleaving parameters is observed between the model calculations and observations provided that the vertical momentum diffusivity significantly exceeds the corresponding coefficient of mass diffusivity. Under specific (reasonable) constraints of the vertical momentum diffusivity, the most unstable mode has a vertical scale approximately two-three times smaller than the vertical scale of the observed intrusions. A thorough discussion of the results is presented.     

Product water mass formation by turbulent density currents from a high-order nonhydrostatic spectral element model

In light of the pressing need for development of parameterizations of gravity current entrainment in ocean general circulation models, the behavior of turbulent gravity currents in the presence of ambient stratification is studied via numerical simulation, for cases in which equilibrated product water masses are formed. The main objective is to explore how the ambient stratification impacts entrainment and the properties of product water masses, which are of ultimate interest to ocean and climate modelers. Numerical experiments are conducted by employing the high-order nonhydrostatic spectral element model Nek5000. It is investigated how the separation level of the current from the bottom, the propagation speed, the salinity of the product water masses, and the transport and entrainment of the gravity current are affected as a function of the strength of the ambient stratification and the slope angle. Results show that, for the case of constant slope angle and linear ambient stratification, the gravity current separates from the bottom such that the entrained mass flux is independent of the slope angle. The entrainment mass transport, product mass transport, and product salinity then depend only on the ambient stratification, and these quantities are approximated as simple algebraic functions of the ambient stratification parameter that modify the source properties.     

Vertical structure of time-dependent currents in a mid-ocean ridge axial valley

Velocity measurements with high vertical resolution, and a two-dimensional linear quasianalytic model for subinertial oscillatory flows, are used to analyze the vertical structure of flow in the axial valley at Endeavour Segment, Juan de Fuca Ridge. At a site away from hydrothermal vents, observed semidiurnal flows are independent of depth, rectilinear and parallel to the valley axis, while subinertial flows are intensified and re-aligned along-valley toward the bottom. This behavior is consistent with solutions from the model, which show attenuation of subinertial across-valley flow with depth. This cross-flow attenuation is most pronounced for valleys with widths less than the internal Rossby radius of deformation. Reduction of across-valley flow with depth results in a weakened Coriolis force that cannot fully balance the along-valley pressure-gradient force. The resulting force imbalance yields a directly accelerated bottom-intensified along-valley flow. The importance of this physical process in other submarine valleys depends on their geometry, stratification and latitude. If active, this mechanism provides a dynamic background environment for the axial valley to which hydrothermal venting would add complexity. The strong vertical shears and spiraling flows observed within the axial valley for diurnal tidal and lower-frequency flows have important implications in the transport of hydrothermal vent fluid and the dispersal of larvae of vent organisms by bottom currents.     

The onset of the Spring Bloom in the MEDOC area: mesoscale spatial variability

In the northwestern Mediterranean Sea, Coastal Zone Color Scanner images suggest that the eddies that participate in the restratification following deep convection interact with the spring phytoplankton bloom. The mechanisms for this interaction are studied using a biogeochemical model embedded in an eddy-resolving primitive equation ocean model. The model is initialized with a patch of dense water surrounded by a stratified ocean, which is characteristic of the winter situation. The atmospheric forcing is artificially held constant, in order to focus solely on the mesoscale variability. After a few days, meanders develop at the periphery of the patch, inducing its sinking and spreading. Mesoscale upward motions are responsible for the shoaling of the mixing layer in the trough of the meanders. As sunlight is the main factor regulating primary production at this time of year, this shoaling increases the mean exposure time of the phytoplankton cells and thus enhances productivity. Consequently, the majority of phytoplankton production is obtained at the edge of the patch, in agreement with in situ data. Through advection, phytoplankton is then subducted from these sources towards the crest of the meanders. Our results suggest that this mesoscale transport is responsible for a decorrelation between phytoplankton biomass and primary production.     

Generation of internal waves by a barotropic tide in the coastal zone

Within the framework of the linear theory of long waves, we study internal waves generated by a barotropic tide in a two-layer ocean of variable depth taking into account the influence of the Coriolis force. Barotropic waves run over an extended unevenness of the bottom at an arbitrary angle. This unevenness is regarded as a model of the continental slope and shelf. We establish the dependences of the amplitudes of generated internal waves on the angle of incidence of the barotropic tide, topography of the bottom, and stratification. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Circulation, exchange and water masses at the ocean margin: the role of physical processes at the shelf edge

The coastal ocean meets the deep sea at the continental shelf edge. Questions of global change entail elucidation of the processes that determine the quantities, transformation and fate of materials transported between the shelf and ocean, the measurement and definition of exchange processes, and the development of prognostic models of exchanges.Physical processes control the large-scale movement and irreversible small-scale mixing of water and its constituents. At the shelf edge, steep bathymetry may inhibit ocean-shelf exchange, but in combination with stratification gives rise to special processes and modelling challenges.A preliminary assessment is made of coastal-trapped waves; along-slope currents, instability and meanders; eddies; upwelling, fronts and filaments; downwelling, cascading; tides, surges; internal tides and waves as potentially influential processes in ocean-shelf exchange, water-mass structure and general circulation, according to their scales and context. For this purpose, theory and previous measurements are interpreted.Future studies needed to improve this assessment are discussed.     

A numerically effective calculation of sea water density

Accurate density calculation that includes pressure effects is achieved with negligible computational cost in the context of three-dimensional ocean modelling. Local linear (or quadratic) fits to the full UNESCO (Anon, 1981) equation of state can be used in many model applications where the potential temperature and salinity at a model grid point vary slightly in each model time step. The local polynomial fit is achieved by computing a Taylor series expansion about a local reference state. The terms in the Taylor series are calculated analytically for optimal accuracy and minimal computational cost. All calculations can be done with single precision arithmetic, without compromising accuracy. In a three-dimensional nonhydrostatic ocean model applied to a deep convection problem, the local density calculation reduced the total computational cost of the model by 7% relative to that when the full UNESCO density calculation was used. The computational advantage is 15% for an application in which the nonhydrostatic part of the calculation is turned off. The computational advantage is, however, a function of the nature of both the model being used and the problem being solved.The principal algorithms are coded in Fortran 90, fortran 77, and as Matlab functions. The complete set of routines and test programs is coded in Fortran 90.