Turbulence modeling in ocean circulation problems

A physical formulation of the problem is considered. A mathematical model and a numerical algorithm of the turbulence model as part of the ocean circulation model for simulations for decades are formulated. The model is based on the evolution equations for turbulent kinetic energy (TKE) and the frequency of its viscous dissipation. A numerical solution algorithm for both the circulation model and the turbulence model is based on implicit schemes of splitting with respect to physical processes and geometric coordinates. For the turbulence model, this provided analytical solutions at a splitting step related to TKE generation and dissipation. Numerical experiments have been performed with a model of the joint circulation of the North Atlantic, the Arctic Ocean, and the Bering Sea to reproduce the annual cycle and synoptic disturbances of ocean characteristics. The model has a resolution of 0.25° in latitude and longitude and 40 levels in the vertical, which are compressed toward the surface to reproduce the process of developed turbulence better. The results are compared with observations and with the results of simulations using traditional parameterizations of the upper ocean mixing. It is shown that the model reproduces ocean characteristics correctly, only slightly increasing the computation time in comparison with simple parameterizations. Spatial and temporal characteristics of turbulence are analyzed.     

Eddy-resolving ocean circulation in the Asian-Australian region inferred from an ocean reanalysis effort

The first global ocean reanalysis with focus on the Asian-Australian region was performed for the period October 1992 to June 2006. The 14-year experiment assimilated available observations of altimetric sea-level anomaly, satellite SST and quality-controlled in situ temperature and salinity profiles from a range of sources, including field surveys and the Argo float array. This study focuses on dominant circulation patterns in the South-East Asian/Australian region as simulated by an eddy-resolving and data-assimilating ocean general circulation model. New estimates of the ocean circulation are provided which are largely in agreement with the limited number of observations. Transports of key currents in the region are as follows: The total (top-to-bottom) annual mean Indonesian Throughflow transport and its standard deviation are 9.7 ± 4.4 Sv from the Pacific to the Indian Ocean with a minimum in January (6.6 Sv) and a maximum in April (12.3 Sv). The Leeuwin Current along the west coast of Australia is dominated by eddy structures with a mean southward transport of 4.1 ± 2.0 Sv at 34°S. Along the southern coast of Australia a narrow shelf edge current known as the South Australian Current advects 4.5 ± 2.6 Sv eastward at 130°E. The South Australian Current converges east of Tasmania with the eddy-rich extension of East Australian Current. At 32°S this current transports 36.8 ± 18.5 Sv southward. A dominating feature of the circulation between north-eastern Australia and Papua-New Guinea is the strong and quasi-permanent Coral Sea Gyre. This gyre is associated with the highly variable Hiri Current which runs along the south coast of Papua-New Guinea and advects 8.2 ± 19.1 Sv into the Western Pacific Ocean. All of these transport estimates are subject to strong eddy variability.     

Effects of the deep ocean circulation on the reservoir characteristics of the ocean

To examine the effects of the deep ocean circulation on the characteristics of the ocean as a reservoir, age distributions of the material whose source and sink are at the ocean surface are calculated using an idealized vertical two-dimensional model of the ocean. The results show that the large-scale vertical circulation of the deep water accelerates the renewal of deep water and reduces the average age of the material. It is also shown that the multi-layered structures of the deep circulation are more realistic than the one-layered structure and promote the renewal of the deep water.     

Pacific ocean circulation based on observation

A thorough understanding of the Pacific Ocean circulation is a necessity to solve global climate and environmental problems. Here we present a new picture of the circulation by integrating observational results. Lower and Upper Circumpolar Deep Waters (LCDW, UCDW) and Antarctic Intermediate Water (AAIW) of 12, 7, and 5 Sv (10⁶ m³s⁻¹) in the lower and upper deep layers and the surface/intermediate layer, respectively, are transported to the North Pacific from the Antarctic Circumpolar Current (ACC). The flow of LCDW separates in the Central Pacific Basin into the western (4 Sv) and eastern (8 Sv) branches, and nearly half of the latter branch is further separated to flow eastward south of the Hawaiian Ridge into the Northeast Pacific Basin (NEPB). A large portion of LCDW on this southern route (4 Sv) upwells in the southern and mid-latitude eastern regions of the NEPB. The remaining eastern branch joins nearly half of the western branch; the confluence flows northward and enters the NEPB along the Aleutian Trench. Most of the LCDW on this northern route (5 Sv) upwells to the upper deep layer in the northern (in particular northeastern) region of the NEPB and is transformed into North Pacific Deep Water (NPDW). NPDW shifts southward in the upper deep layer and is modified by mixing with UCDW around the Hawaiian Islands. The modified NPDW of 13 Sv returns to the ACC. The remaining volume in the North Pacific (11 Sv) flows out to the Indian and Arctic Oceans in the surface/intermediate layer.     

Nonlinear dynamics of the circulation variability in the western ocean

The nonlinear dynamics of the low-frequency variability of a mid-latitude ocean are studied. The mechanism of the separation of the western boundary current from the western wall, as well as the meridional displacements of the separation point and the separated eastward jet, is analyzed. A regional barotropic quasigeostrophic eddy-resolving numerical model is used for the analysis. The flow in a rectangular domain is simulated by the constant inflow and outflow of fluid through the boundaries. A regime when the nonlinearity prevails over the dissipation and the advection and β terms are of the same order of magnitude is considered, which is characteristic of the actual ocean. When the nonlinearity exceeds the threshold value, a periodic solution is obtained. The solution is determined by the nonslip boundary condition at the western wall. The solution obtained is studied in detail. The meridional displacements of the western boundary current separation point with respect to the western wall and the separated eastward jet can reach a few hundred kilometers. Their intensities and the intensity of the recirculation gyre in the western boundary current are found to oscillate with a period of about five years.     

Towards the general circulation of the North Atlantic ocean

After reviewing the inverse method, we apply it to deducing the general circulation of the North Atlantic ocean. We argue that the method is purely classical in nature, being nothing more than a mathematical statement of the principles upon which nearly all previous circulation schemes have been based. The ‘smoothed’ solution is shown to represent the components of the flow field that are determinable independently of the initial reference level. We then produce two circulation schemes based upon two different initial reference levels — 2000 decibars and the bottom — called North Atlantic-1A and North Atlantic-1B respectively. The models share many features in common and are strikingly similar to several previous schemes, most notably those of Jacobsen and Defant in the region west of Bermuda. No simple level-of-no-motion emerges in the flow fields; rather the velocity sections exhibit a complex cellular structure. Zonally integrated meridional cells of models and of the uniquely determined components are very similar, showing a poleward movement of warm saline water compensated at depth by a return flow of cold, fresher water. The magnitudes of the implied polar sea overflows and the heat fluxes are in good agreement with previous estimates. Finally, it is argued that neither these model circulations nor any other circulation pattern based upon the existing data can be regarded as actually representing the true time average ocean circulation because the data are aliased in time; the frequency/wavenumber spectrum of the ocean is inadequately known to determine the resulting errors.     

A diagnostic stabilized finite-element ocean circulation model

A stabilized finite-element (FE) algorithm for the solution of oceanic large scale circulation equations and optimization of the solutions is presented. Pseudo-residual-free bubble function (RFBF) stabilization technique is utilized to enforce robustness of the numerics and override limitations imposed by the Babuška–Brezzi condition on the choice of functional spaces. The numerical scheme is formulated on an unstructured tetrahedral 3d grid in velocity–pressure variables defined as piecewise linear continuous functions. The model is equipped with a standard variational data assimilation scheme, capable to perform optimization of the solutions with respect to open lateral boundary conditions and external forcing imposed at the ocean surface. We demonstrate the model performance in applications to idealized and realistic basin-scale flows. Using the adjoint method, the code is tested against a synthetic climatological data set for the South Atlantic ocean which includes hydrology, fluxes at the ocean surface and satellite altimetry. The optimized solution proves to be consistent with all these data sets, fitting them within the error bars.The presented diagnostic tool retains the advantages of existing FE ocean circulation models and in addition (1) improves resolution of the bottom boundary layer due to employment of the 3d tetrahedral elements; (2) enforces numerical robustness through utilization of the RFBF stabilization, and (3) provides an opportunity to optimize the solutions by means of 3d variational data assimilation. Numerical efficiency of the code makes this a desirable tool for dynamically constrained analyses of large datasets.     

A modification to the Munk wind-driven ocean circulation theory

In order to fulfill the no-slip condition at the western and eastern boundaries of the ocean basin, introduced ＂effective wind stress＂, which has much larger spatial variations towards the boundaries than in the ocean interior. The effective wind stress can thus be decomposed into spatially slow-varying and fast varying components. Careful scale analysis on the classical Munk winddriven ocean circulation theory, which consists of the interior Sverdrup flow and the western boundary current but of no eastern boundary current, shows that the wind stress curl appearing in the Sverdrup equation must have negligible spatial variations. In the present model the spatially slow-varying component of the wind stress appears in the Sverdrup equation, and the spatially fastvarying component becomes the forcing term of the boundary equations. As a result, in addition to the classical Munk solution the present model has an extra term at the western boundary which （Northern Hemisphere） increases the northward transport as well as the southward return transport, and has a term at the eastern boundary corresponding to the eastern boundary current.     

Quasi-isopycnic layer model for large-scale ocean circulation

A hydrothermodynamic model of a multilayer ocean, incorporating the upper mixed layer (UML) is described. The model is based on a system of primitive equations integrated within each layer. All layers are assumed to be horizontally-inhomogeneous, however, the density in each thermocline layer changes within the limits determineda priori by the prescribed basic stratification. It is assumed that the layers may outcrop. Results of the numerical experiment on subduction simulation (downwelling of UML waters toward the main thermocline layers) are given.Translated by V. Puchkin.     

Seasonal variations of the ocean surface circulation in the vicinity of Palau

The surface circulation in the western equatorial Pacific Ocean is investigated with the aim of describing intra-annual variations near Palau (134°30′ E, 7°30′ N). In situ data and model output from the Ocean Surface Currents Analysis—Real-time, TRIangle Trans-Ocean buoy Network, Naval Research Laboratory Layered Ocean Model and the Joint Archive for Shipboard ADCP are examined and compared. Known major currents and eddies of the western equatorial Pacific are observed and discussed, and previously undocumented features are identified and named (Palau Eddy, Caroline Eddy, Micronesian Eddy). The circulation at Palau follows a seasonal variation aligned with that of the Asian monsoon (December–April; July–October) and is driven by the major circulation features. From December to April, currents around Palau are generally directed northward with speeds of approximately 20 cm/s, influenced by the North Equatorial Counter-Current and the Mindanao Eddy. The current direction turns slightly clockwise through this boreal winter period, due to the northern migration of the Mindanao Eddy. During April–May, the current west of Palau is reduced to 15 cm/s as the Mindanao Eddy weakens. East of Palau, a cyclonic eddy (Palau Eddy) forms producing southward flow of around 25 cm/s. The flow during the period July to September is disordered with no influence from major circulation features. The current is generally northward west of Palau and southward to the east, each with speeds on the order of 5 cm/s. During October, as the Palau Eddy reforms, the southward current to the east of Palau increases to 15 cm/s. During November, the circulation transitions to the north-directed winter regime.     

Upper ocean circulation in the western tropical Atlantic in boreal fall 2000

The upper ocean large-scale circulation of the western tropical Atlantic from 11.5°S to the Caribbean in November and December 2000 is investigated from a new type of shipboard ADCP able to measure accurate velocities to 600 m depth, combined with lowered ADCP measurements. Satellite data and numerical model output complement the shipboard measurements to better describe the large-scale circulation. In November 2000 the North Brazil Undercurrent (NBUC) was strongly intensified between 11 and 5°S by inflow from the east, hence the NBUC was formed further to the north than in the mean. The NBUC was transporting 23.1 Sv northward at 5°S, slightly less than the mean of six cruises (Geophysical Research Letters (2002) 29 (7) 1840). At 35°W the North Brazil Current (NBC) transported 29.4 Sv westward, less than the mean of 13 cruises (Geophysical Research Letters (2003) 30 (7) 1349). A strong retroflection ring had just pinched off the NBC retroflection according to the satellite information. The inflow into the Caribbean south of 16.5°N originated in part of a leakage from the NBC retroflection zone and in part from the North Equatorial Current. A thermocline intensified ring with a transport of about 30 Sv was located off Guadeloupe carrying South Atlantic Central Water towards the north. Observed deviations of the November/December 2000 flow field from the November long-term mean flow field were related to an enhanced Intertropical Convergence Zone (ITCZ) associated with an increased North Equatorial Countercurrent (NECC), as well as to boundary current rings and Rossby waves with zonal wavelength of the order of 1000 km. At 44°W the presence of a Rossby wave associated with an anticyclonic circulation led to a strongly enhanced NBC of 65.0 Sv as well as to a combined NECC and Equatorial Undercurrent transport of 52.4 Sv, much stronger than during earlier cruises. While the 1/3°-FLAME model is unable to reproduce details of the vertical distribution of the observed horizontal flow at 44 °W for November 2000 as well as the horizontal distribution of some of the observed permanent current bands, a climatological simulation with the 1/12°-FLAME agrees much better with the observations and provides information on the spreading path between the sections. E.g., the interpretation that the widening in the Antarctic Intermediate Water layer of the westward flowing NBC at 44°W in November was caused by water from the Equatorial Intermediate Current was further supported by the model results.     

海洋环流模式中卫星遥感资料同化的应用进展

物理海洋研究长久以来一直受到观测资料不足的制约,然而这一状况随着现代观测技术的迅猛发展得到了很大的改善。卫星遥感技术的发展提供了覆盖全球的、连续、实时的卫星观测数据,这是其他任何资料都无法比拟的。这些数据大部分难以直接运用来改善气候预测或数值模拟分析,然而资料同化技术的出现和发展改善了这一情况。     

Approximations to the ocean’s residual circulation in arbitrary tracer coordinates

The residual circulation is the flow which transports tracers. Its utility is tempered by the challenge associated with its computation: velocity must be mapped into tracer coordinates on a timescale which is short compared to eddy timescales. Several approximations have been introduced which allow the residual circulation to be evaluated using a small number of flow statistics, including the transformed Eulerian mean (TEM), the temporal residual mean (TRM), and the recently introduced statistical transformed Eulerian mean (STEM). This paper discusses the relationship between these approximations and illustrates their differences with a series of analytical and numerical examples. The STEM is found to be superior to the TEM and TRM in both its handling of the surface boundary condition and its ease of implementation.     

Rapid changes of the oceanic circulation in a hierarchy of ocean models

The response time of the large-scale oceanic circulation due to freshwater perturbations is investigated with models of different complexity. A three-dimensional ocean general circulation model (OGCM) and a zonally averaged ocean model are employed. In order to distinguish advection and diffusion from fast baroclinic processes (e.g. waves in the OGCM) a color tracer is injected at the same time and location as the freshwater discharges. In spite of the inability of the zonally averaged model to represent wave processes in a realistic way similarities with the OGCM are found for the propagation patterns of density anomalies and of color tracer. In the OGCM as well as in the zonally averaged model, density anomalies propagate faster than anomalies of a passive color tracer in the case of vertical density stratification. The progression of density anomalies leads to changes of the oceanic circulation, and both oceanic models exhibit circulation changes in areas distant from the discharge places long before the passively entrained color tracer has reached these regions. The fact that a zonally averaged model simulates baroclinic processes faster than advection even if internal gravity waves are not represented due to neglected acceleration terms, is clarified with a conceptual box model.     

Tidally driven mixing in a numerical model of the ocean general circulation

Astronomical data reveals that approximately 3.5 terawatts (TW) of tidal energy is dissipated in the ocean. Tidal models and satellite altimetry suggest that 1 TW of this energy is converted from the barotropic to internal tides in the deep ocean, predominantly around regions of rough topography such as mid-ocean ridges. A global tidal model is used to compute turbulent energy levels associated with the dissipation of internal tides, and the diapycnal mixing supported by this energy flux is computed using a simple parameterization.The mixing parameterization has been incorporated into a coarse resolution numerical model of the global ocean. This parameterization offers an energetically consistent and practical means of improving the representation of ocean mixing processes in climate models. Novel features of this implementation are that the model explicitly accounts for the tidal energy source for mixing, and that the mixing evolves both spatially and temporally with the model state. At equilibrium, the globally averaged diffusivity profile ranges from 0.3 cm² s⁻¹ at thermocline depths to 7.7 cm² s⁻¹ in the abyss with a depth average of 0.9 cm² s⁻¹, in close agreement with inferences from global balances. Water properties are strongly influenced by the combination of weak mixing in the main thermocline and enhanced mixing in the deep ocean. Climatological comparisons show that the parameterized mixing scheme results in a substantial reduction of temperature/salinity bias relative to model solutions with either a uniform vertical diffusivity of 0.9 cm² s⁻¹ or a horizontally uniform bottom-intensified arctangent mixing profile. This suggests that spatially varying bottom intensified mixing is an essential component of the balances required for the maintenance of the ocean’s abyssal stratification.     

Description of coastline variations in an ocean general circulation model

A wetting and drying algorithm is considered and implemented in a three-dimensional sigma–z coordinate model of ocean thermo- and hydrodynamics. The algorithm is tested in two idealized experiments simulating the run-up of a tidal wave on the coast and in a realistic experiment simulating the evolution of the Caspian Sea coastline in the 20th century.