Wind-driven Circulation Research Articles

Decadal variability and trends of oceanic barrier layers in tropical Pacific

Decadal variability and trends of the isothermal layer depth (ILD), mixed layer depth (MLD), and barrier layer thickness (BLT) were analyzed for the tropical Pacific during 1979–2015. The decadal variability of ILD, MLD, and BLT shows a close connection with the Pacific Decadal Oscillation (PDO). At PDO positive phase, the eastward shift of precipitation and weakened trade winds result in thinner BLT in western Pacific and thicker BLT in central and eastern Pacific. The situation is reversed at PDO negative phase. The differences in BLT can be up to 9–15 m. The spatial distributions of decadal trends of ILD and MLD are complex, but a thickening of BLT in the western tropical Pacific is clearly present. The raw trends of ILD, MLD, and BLT averaged in the tropical Pacific (30° N–30° S, 120° E–75° W) from 1979 to 2015 are 1.62, 1.20, and 0.51 m per decade, respectively. PDO can explain about 25% of the increasing trends of BLT, while El Nino-Southern Oscillation (ENSO) only explains about 1.7%. Global warming and/or variability at longer time scales is responsible for the remaining increasing trends. The BLT change is related to the warming and freshening of the western Pacific warm pool in recent decades. The ocean-atmosphere interactions about trade winds, wind-driven ocean circulation, temperature, and precipitation/evaporation are discussed.

Steady Flow Regimes in the Problem of Intense Wind-Driven Circulation in a Thin Layer of Viscous Rotating Fluid

The problem of wind-driven circulation in a thin layer of homogeneous viscous rotating fluid is considered. In the limit of small Froude and Burger numbers it is described by two parameters—the Rossby number proportional to the forcing and the Ekman number. For small Ekman numbers and moderate Rossby numbers, the regimes of steady fluid circulation are investigated through numerical simulations of a Karmantype flow. Two different types of steady flows are shown to exist, and their physical interpretation based on a simple analytical model is proposed. A regime diagram on the plane of problem parameters is provided. The simultaneous existence of steady flows of two different types turns out to be possible in some domain of parameters, i.e., there is a dependence of the stationary solution to the problem on initial data. The asymptotic dependence of steady flow characteristics is investigated in the limit of small Ekman numbers.

Upgradient and Downgradient Potential Vorticity Fluxes Produced by Forced Rossby Waves. Part II: Parameter Sensitivity and Physical Interpretation

AbstractWe examine the potential vorticity (PV) flux produced by forced Rossby waves in a two-layer quasigeostrophic model, using a perturbation analysis. Rossby waves are excited by external forcing applied to the upper layer. The southward PV flux is produced in the lower layer by the higher-order Rossby waves that are excited by nonlinear wave–wave interactions, whereas the northward PV flux is produced in the upper layer. The direction of the PV flux is consistent with that obtained by an eddy-resolving model of the wind-driven circulation in previous studies. The southward PV flux is produced in a wide parameter range comparable to the eddy-resolving model. The basic features of the PV flux remain unchanged even in the limit of weak stratification. In this limit, stratification has nearly no effect on the flow, except that it isolates the lower layer from the direct effects of external forcing. The mechanism of the southward PV flux is explained using basic features of the barotropic Rossby waves and does not depend on details of the model. Furthermore, the resonant triad interaction of Rossby waves does not affect the PV flux. Stratification weakens or strengthens the PV flux depending on the horizontal scale of the external forcing.

Upgradient and Downgradient Potential Vorticity Fluxes Produced by Forced Rossby Waves. Part I: Basic Experiments

AbstractThe mean flow and potential vorticity (PV) flux produced by Rossby waves are examined, particularly by focusing on the effects of stratification and nonlinearity on upgradient and downgradient PV fluxes. Rossby waves are excited by an external forcing confined near the surface and produce a northward (upgradient) PV flux in the surface layer. While the meridional PV flux is considerably weak in the deep layer in the weakly nonlinear case, the southward (downgradient) PV flux is produced as nonlinearity increases. In both the surface and deep layers, the distribution of the PV flux and mean flow is qualitatively similar to that in recirculation gyres obtained in an eddy-resolving model of the wind-driven circulation. A perturbation analysis shows that the primary and harmonic waves are excited by external forcing and wave–wave interaction between the primary waves, respectively. The meridional PV fluxes in the surface and deep layers are mostly produced by the primary and harmonic waves, respectively. The southward PV flux in the deep layer is produced by the interaction between the barotropic harmonic wave and the first baroclinic component of nonlinear forcing by the primary waves. The irreversible processes that are implicitly assumed in the PV homogenization theory (Rhines and Young) do not substantially affect the southward PV flux. The qualitative features of the PV flux remain unchanged even when nonlinearity is increased beyond the range in which the perturbation theory is exactly applicable.

Extreme learning machine for reduced order modeling of turbulent geophysical flows.

We investigate the application of artificial neural networks to stabilize proper orthogonal decomposition-based reduced order models for quasistationary geophysical turbulent flows. An extreme learning machine concept is introduced for computing an eddy-viscosity closure dynamically to incorporate the effects of the truncated modes. We consider a four-gyre wind-driven ocean circulation problem as our prototype setting to assess the performance of the proposed data-driven approach. Our framework provides a significant reduction in computational time and effectively retains the dynamics of the full-order model during the forward simulation period beyond the training data set. Furthermore, we show that the method is robust for larger choices of time steps and can be used as an efficient and reliable tool for long time integration of general circulation models.

Large- to submesoscale surface circulation and its implications on biogeochemical/biological horizontal distributions during the OUTPACE cruise (southwest Pacific)

Abstract. The patterns of the large-scale, meso- and submesoscale surface circulation on biogeochemical and biological distributions are examined in the western tropical South Pacific (WTSP) in the context of the OUTPACE cruise (February–April 2015). Multi-disciplinary original in situ observations were achieved along a zonal transect through the WTSP and their analysis was coupled with satellite data. The use of Lagrangian diagnostics allows for the identification of water mass pathways, mesoscale structures, and submesoscale features such as fronts. In particular, we confirmed the existence of a global wind-driven southward circulation of surface waters in the entire WTSP, using a new high-resolution altimetry-derived product, validated by in situ drifters, that includes cyclogeostrophy and Ekman components with geostrophy. The mesoscale activity is shown to be responsible for counter-intuitive water mass trajectories in two subregions: (i) the Coral Sea, with surface exchanges between the North Vanuatu Jet and the North Caledonian Jet, and (ii) around 170∘ W, with an eastward pathway, whereas a westward general direction dominates. Fronts and small-scale features, detected with finite-size Lyapunov exponents (FSLEs), are correlated with 25 % of surface tracer gradients, which reveals the significance of such structures in the generation of submesoscale surface gradients. Additionally, two high-frequency sampling transects of biogeochemical parameters and microorganism abundances demonstrate the influence of fronts in controlling the spatial distribution of bacteria and phytoplankton, and as a consequence the microbial community structure. All circulation scales play an important role that has to be taken into account not only when analysing the data from OUTPACE but also, more generally, for understanding the global distribution of biogeochemical components.

Wind-Driven Circulation in a Shelf Valley. Part II: Dynamics of the Along-Valley Velocity and Transport

AbstractThe dynamics controlling the along-valley (cross shelf) flow in idealized shallow shelf valleys with small to moderate Burger number are investigated, and analytical scales of the along-valley flows are derived. This paper follows Part I, which shows that along-shelf winds in the opposite direction to coastal-trapped wave propagation (upwelling regime) force a strong up-valley flow caused by the formation of a lee wave. In contrast, along-shelf winds in the other direction (downwelling regime) do not generate a lee wave and consequently force a relatively weak net down-valley flow. The valley flows in both regimes are cyclostrophic with O(1) Rossby number. A major difference between the two regimes is the along-shelf length scales of the along-valley flows Lx. In the upwelling regime Lx depends on the valley width Wc and the wavelength λlw of the coastal-trapped lee wave arrested by the along-shelf flow Us. In the downwelling regime Lx depends on the inertial length scale |Us|/f and Wc. The along-valley velocity scale in the upwelling regime, given byis based on potential vorticity (PV) conservation and lee-wave dynamics (Hs and Hc are the shelf and valley depth scales, respectively, and f is the Coriolis parameter). The velocity scale in the downwelling regime, given by is based on PV conservation. The velocity scales are validated by the numerical sensitivity simulations and can be useful for observational studies of along-valley transports. The work provides a framework for investigating cross-shelf transport induced by irregular shelf bathymetry and calls for future studies of this type under realistic environmental conditions and over a broader parameter space.

Error estimates of B-spline based finite-element methods for the stationary quasi-geostrophic equations of the ocean

This paper presents theoretical error estimates of B-spline based finite-element methods for the streamfunction formulation of the stationary quasi-geostrophic equations, which describe the large scale wind-driven ocean circulation. We introduce variational formulations of the streamfunction formulation inspired by the interior penalty discontinuous Galerkin method. Dirichlet boundary conditions are weakly enforced in the formulations and stabilizations are achieved via Nitsche’s method. Existence and uniqueness of the approximation are proved and optimal error estimates in the energy norm are demonstrated under a small data assumption. Numerical experiments are performed to verify the theoretical error estimates on rectangular and L-shape geometries.

Three-dimensional hydrodynamic model for wind-driven circulation

This paper presents the development of a three-dimensional hydrodynamic model for wind-driven circulation using the moving element method in the vertical discretization. As most three-dimensional models use sigma coordinate transformation in the vertical discretization, the use of the moving element method is an alternative to the latter, with the advantage that there is no need for fixed subdivision of the water column. In the proposed model, the coupling of two- and three-dimensional hydrodynamic model is considered. The shallow-water equations are integrated in the vertical direction, finite elements are employed in the spatial discretization, and finite differences in the time discretization, to resolve the position of the free surface (ζ), and the vertically integrated velocities components. The three-dimensional module is used to compute the velocity profiles. In the three-dimensional module is employed the moving element method in the vertical discretization. The efficiency of the model is demonstrated through the comparison of its results with laboratory experimental results and with another model that uses sigma coordinate transformation in the vertical discretization.

Three-dimensional hydrodynamics numerical of wind-driven circulations in Danjiangkou Reservoir

This paper focuses on the analysis of the flow field of Danjiangkou Reservoir under the action of wind stress. Based on the analysis of the annual wind field data of Danjiangkou Reservoir, the three-dimensional hydrodynamic model of Danjiangkou Reservoir was established. The distribution of water flow field in the reservoir area under five different wind directions and two different wind speeds was studied. The simulation results were compared with the flow field without wind. The results show that when the wind speed in the reservoir area is 3.3m/s, the surface velocity and flow direction change less under the same wind conditions as the potential flow direction. Under the wind condition opposite to the potential flow direction, the reservoir area is locally generated. The small circulation and surface flow are more disordered; when the wind speed reaches 10.0m/s, under the same wind condition as the potential flow direction, the surface velocity of the reservoir area increases significantly. Under the wind condition opposite to the direction of the potential flow, a stable counterclockwise circulation is generated, and the wind direction dominates the surface layer. seriously affecting the flow field distribution in the reservoir area. The research results in this paper can provide support for the reservoir in the formulation of emergency water pollution emergency strategy and the formulation of real-time scheduling plan.

Adaptivity of a B-spline based finite-element method for modeling wind-driven ocean circulation

This paper presents an adaptive refinement algorithm of a B-spline based finite-element approximation of the streamfunction formulation for the large scale wind-driven ocean currents. In particular, we focus on a posteriori error analysis of the simplified linear model of the stationary quasi-geostrophic equations, namely the Stommel–Munk model, which is the fourth-order partial differential equation. The analysis provides a posteriori error estimator for the local refinement of the Nitsche-type finite-element formulation. Numerical experiments with several benchmark examples are performed to test the capability of the posteriori error indicator on rectangular and L-shape geometries.

Simulating the Agulhas system in global ocean models – nesting vs. multi-resolution unstructured meshes

Many questions in ocean and climate modelling require the combined use of high resolution, global coverage and multi-decadal integration length. For this combination, even modern resources limit the use of traditional structured-mesh grids. Here we compare two approaches: A high-resolution grid nested into a global model at coarser resolution (NEMO with AGRIF) and an unstructured-mesh grid (FESOM) which allows to variably enhance resolution where desired. The Agulhas system around South Africa is used as a testcase, providing an energetic interplay of a strong western boundary current and mesoscale dynamics. Its open setting into the horizontal and global overturning circulations also requires global coverage.Both model configurations simulate a reasonable large-scale circulation. Distribution and temporal variability of the wind-driven circulation are quite comparable due to the same atmospheric forcing. However, the overturning circulation differs, owing each model's ability to represent formation and spreading of deep water masses. In terms of regional, high-resolution dynamics, all elements of the Agulhas system are well represented. Owing to the strong nonlinearity in the system, Agulhas Current transports of both configurations and in comparison with observations differ in strength and temporal variability. Similar decadal trends in Agulhas Current transport and Agulhas leakage are linked to the trends in wind forcing.Although the number of 3D wet grid points used in FESOM is similar to that in the nested NEMO, FESOM uses about two times the number of CPUs to obtain the same model throughput (in terms of simulated model years per day). This is feasible due to the high scalability of the FESOM code.

Covariate-based stochastic parameterization of baroclinic ocean eddies

AbstractIn this study we investigate a covariate-based stochastic approach to parameterize unresolved turbulent processes within a standard model of the idealised, wind-driven ocean circulation. We focus on vertical instead of horizontal coarse-graining, such that we avoid the subtle difficulties of horizontal coarsegraining. The corresponding eddy forcing is uniquely defined and has a clear physical interpretation related to baroclinic instability.We propose to emulate the baroclinic eddy forcing by sampling from the conditional probability distribution functions of the eddy forcing obtained from the baroclinic reference model data. These conditional probability distribution functions are approximated here by sampling uniformly from discrete reference values. We analyze in detail the different performances of the stochastic parameterization dependent on whether the eddy forcing is conditioned on a suitable flow-dependent covariate or on a timelagged covariate or on both. The results demonstrate that our non-Gaussian, non-linear methodology is able to accurately reproduce the first four statistical moments and spatial/temporal correlations of the stream function, energetics, and enstrophy of the reference baroclinic model.

Wind-Driven Circulation in a Shelf Valley. Part I: Mechanism of the Asymmetrical Response to Along-Shelf Winds in Opposite Directions

AbstractMotivated by observations in Hudson shelf valley showing stronger onshore than offshore flows, this study investigates wind-driven flows in idealized shallow shelf valleys. This first part of a two-part sequence focuses on the mechanism of the asymmetrical flow response in a valley to along-shelf winds of opposite directions. Model simulations show that (i) when the wind is in the opposite direction to coastal-trapped wave (CTW) phase propagation, the shelf flow turns onshore in the valley and generates strong up-valley transport and a standing meander on the upstream side (in the sense of CTW phase propagation) of the valley, and (ii) when the wind is in the same direction as CTW phase propagation, the flow forms a symmetric onshore detour pattern over the valley with negligible down-valley transport. Comparison of the modeled upstream meanders in the first scenario with CTW characteristics confirms that the up-valley flow results from CTWs being arrested by the wind-driven shelf flow establishing lee waves. The valley bathymetry generates an initial excessive onshore pressure gradient force that drives the up-valley flow and induces CTW lee waves that sustain the up-valley flow. When the wind-driven shelf flow aligns with CTW phase propagation, the initial disturbance generated in the valley propagates away, allowing the valley flow to adjust to roughly follow isobaths. Because of the similarity in the physical setup, this mechanism of arrested CTWs generating stronger onshore than offshore flow is expected to be applicable to the flow response in slope canyons to along-isobath background flows of opposite directions.

Effects of ecological flow release patterns on water quality and ecological restoration of a large shallow lake

Large shallow lakes play an important role in providing water for domestic supply and landscape irrigation, and maintaining a healthy ecosystem. A lake ecosystem possesses abundant aquatic plants and animals. Changes of the hydrological regime affect the water level, water quality, and species distribution. In this study, a two-dimensional hydrodynamic and water quality model is applied to a large shallow lake, Baiyangdian Lake. The model was established based on measured lake bed elevation, hydrological data, and water quality data. This model was validated for two water transfer events and wind-driven circulation in local areas was observed in the model results. Influences of water transfer and wind effects on water flow and distribution of ammonium and phosphate were then evaluated and discussed. A total of eighteen water transfer scenarios were simulated. The entire lake flow field and water transfer routes in the lake and nutrient distributions were analyzed under each water transfer scenario. The water transfer suggestions proposed in this paper are based on hydraulic characteristics of the lake and make up for deficiencies that previous did not consider the effects of flow transfers on the flow field of receiving. The environmental flow patterns and ecological restoration measures for Baiyangdian Lake are proposed based on the lake hydrodynamics and flow routes under different water transfer scenarios.

SATELLITE MONITORING OF THE BLACK SEA ECOLOGICAL RISK AREAS

Results of multiyear monitoring of zones of persistent ecological risk in the Black Sea are presented. These ones are most affected by oil pollution, raised concentration of suspended particulate matter and harmful algae bloom. Studies are based on satellite remote sensing data obtained over the Black Sea from 2000 to 2017 from radar sensors ERS-2 SAR, Envisat ASAR, Sentinel -1A, -B, Radarsat 2, TerraSAR-X; visible and infrared data from Envisat MERIS, Landsat-5 TM, Landsat-7 ETM+, Landsat-8 OLI, MSI Sentinel-2A and Terra/Aqua Modis. An analysis of radar data indicated areas most affected by ship spills of bilge waters. Greatest polluted area were found along the main ship routes, near biggest ports and at sites of anchor positions.It is necessary to separate anthropogenic oil pollution and oil-containing slicks caused by natural hydrocarbon seeps including mud volcanoes, natural gas and oil outflows from the sea bottom, and gas hydrates. The geographical distribution of these slicks is defined by their permanent locations that well correlate with locations of natural hydrocarbon seeps from the sea bottom in this region.Areas characterized by increased concentration of suspended particulate matter were revealed at maps compiled from Envisat MERIS, MSI Sentinel-2A data and Landsat colour composites. Among the most notable ones are river plume zones, first of all, those of the Danube River and mountain rivers of Georgia. Results of satellite data processing were used for detecting impacts of various natural factors, such as precipitation, rivers flows, wind-driven water circulation and vortex activity, on suspended matter proliferation. Mapping of zones of maximum propagation of suspended solids in different seasons was performed for the examined areas. Eutrophication has recently become a very important problem worldwide. It is true also for the Black Sea, especially for its western part.

Implementation of a 3D ocean model to understand upland lake wind-driven circulation

A community numerical ocean model is used to extend the understanding of wind-driven circulation in small upland lakes. A 3D model of a case study lake (Llyn Conwy, Wales, UK) is calibrated against measured velocity profiles via adjustment of the bottom roughness coefficient. Validation against a separate set of measured velocity profiles confirms the ability of the model to resolve key features of the flow field. Sensitivity analysis shows that the velocity field responds rapidly to changes in the wind forcing. Analysis of the gross circulation using Empirical Orthogonal Functions reveals a persistent two-gyre circulation pattern in the upper half layer of the water column driven by the interaction of wind and bathymetry. At the bottom, the flow is characterised by locally strong currents and analysis of vertical circulation over short time scales shows strong currents in the deepest parts of the lake basin and the responsiveness of the water column to changes in wind speed and direction. Even in small lakes, the assumption of uniform wind stress across the water surface is not always justified and topographic sheltering or other catchment roughness effects give rise to heterogeneity in the wind field. An idealized experiment for the case study lake shows that differences in circulation emerge if the wind stress is allowed to vary across the lake. Energetic wind forcing in upland areas can drive an energetic lake circulation that has important implications for mixing and sediment dynamics. 3D numerical modelling of wind-driven circulation should be more widely used to provide insights into physical limnology to support a wide range of ecological, biogeochemical and palaeoenvironmental studies.

Applying a Simple Analytical Solution to Modelling Wind-Driven Coastal Upwelling of Two-Layered Fluid at the Head of Tokyo Bay, Japan

Blue tides at the head of Tokyo Bay are a hydro-environmental phenomenon where seawater appears to be milky blue because of the reflection of the sunlight off surface water containing large amounts of sulphur particles. Its appearance is due to the coastal upwelling of bottom oxygen-depleted water induced by northeasterly wind-driven circulation. Blue tides cause the death of many shellfish and other aquatic animals across the head of Tokyo Bay and consequently result in substantial economic losses to coastal fisheries. This paper examines the occurrence of wind-driven blue tides in Tokyo Bay, based on a simplified hydrodynamic model and observational analysis. The model assumed a two-layer structure with a wind-driven upper layer and an oxygen-depleted lower layer. In this study, we derived a simple analytical solution to determine a critical wind condition for which the lower layer outcrops at the surface if the wind forcing is sufficiently strong, resulting in the mixing of the two layers and giving rise to blue tide. The results of sensitivity analyses of the analytical solution to all incorporated factors were found to be in accordance with a qualitative understanding of the blue tide phenomenon. More importantly, comparisons of observational data with real cases of blue tide during 1978–2016 and without blue tide during 2003–2016 suggested that this analytical solution was mostly valid. This study would be helpful for gaining a better understanding of the hydro-dynamical mechanism of blue tide.

Extreme bottom velocities induced by wind wave and currents in the Gulf of Gda\u0144sk

The principal goal of this study is to get some preliminary insights about the intensity of water movement generated by wind waves, and due to the currents in the bottom waters of Gulf of Gdańsk, during severe storms. The Gulf of Gdańsk is located in the southern Baltic Sea. This paper presents the results of analysis of wave and current-induced velocities during extreme wind conditions, which are determined based on long-term historical records. The bottom velocity fields originated from wind wave and wind currents, during analysed extreme wind events, are computed independently of each other. The long-term wind wave parameters for the Baltic Sea region are derived from the 44-year hindcast wave database generated in the framework of the project HIPOCAS funded by the European Union. The output from the numerical wave model WAM provides the boundary conditions for the model SWAN operating in high-resolution grid covering the area of the Gulf of Gdańsk. Wind current velocities are calculated with the M3D hydrodynamic model developed in the Institute of Oceanography of the University of Gdańsk based on the POM model. The three dimensional current fields together with trajectories of particle tracers spreading out of bottom boundary layer are modelled, and the calculated fields of bottom velocities are presented in the form of 2D maps. During northerly winds, causing in the Gulf of Gdańsk extreme waves and most significant wind-driven circulation, the wave-induced bottom velocities are greater than velocities due to currents. The current velocities in the bottom layer appeared to be smaller by an order of magnitude than the wave-induced bottom orbital velocities. Namely, during most severe northerly storms analysed, current bottom velocities ranged about 0.1–0.15 m/s, while the root mean square of wave-induced near-seabed velocities reached maximum values of up to 1.4 m/s in the southern part of Gulf of Gdańsk.

Formula omitted]-discontinuous Galerkin methods for a wind-driven ocean circulation model: Two-grid algorithm

This paper presents a nonconforming finite element method for a streamfunction formulation of the stationary quasi-geostrophic equations, which describe the large scale wind-driven ocean circulation. The streamfunction formulation is a fourth order nonlinear PDE and the nonconforming method is based on C0-elements instead of C1-elements. Existence and uniqueness of the approximation are proved and optimal error estimates in several norms of interest are demonstrated under a small data assumption. Two-grid algorithms based on Picard and Newton type linearizations are then presented to efficiently resolve nonlinearities and computational results are given to demonstrate the efficiency of the algorithm. The Mediterranean sea example is tested with real world coastline data, which illustrates the effectiveness of the two-grid approach in the wind-driven ocean circulation simulation.