Wind-driven Ocean Circulation Research Articles

Nonstationarity in the NAO–Gulf Stream SST Front Interaction

Abstract The interaction between the North Atlantic Oscillation (NAO) and the latitudinal shifts of the Gulf Stream sea surface temperature front (GSF) has been the subject of extensive investigations. There are indications of nonstationarity in this interaction, but differences in the methodologies used in previous studies make it difficult to draw consistent conclusions. Furthermore, there is a lack of consensus on the key mechanisms underlying the response of the GSF to the NAO. This study assesses the possible nonstationarity in the NAO–GSF interaction and the mechanisms underlying this interaction during 1950–2020, using reanalysis data. Results show that the NAO and GSF indices covary on the decadal time scale but only during 1972–2018. A secondary peak in the NAO–GSF covariability emerges on multiannual time scales but only during 2005–15. The nonstationarity in the decadal NAO–GSF covariability is also manifested in variations in their lead–lag relationship. Indeed, the NAO tends to lead the GSF shifts by 3 years during 1972–90 and by 2 years during 1990–2018. The response of the GSF to the NAO at the decadal time scale can be interpreted as the joint effect of the fast response of wind-driven oceanic circulation, the response of deep oceanic circulation, and the propagation of Rossby waves. However, there is evidence of Rossby wave propagation only during 1972–90. Here it is suggested that the nonstationarity of Rossby wave propagation caused the time lag between the NAO and the GSF shifts on the decadal time scale to differ between the two time periods.

Historical changes in wind-driven ocean circulation drive pattern of Pacific warming

The tropical Pacific warming pattern since the 1950s exhibits two warming centers in the western Pacific (WP) and eastern Pacific (EP), encompassing an equatorial central Pacific (CP) cooling and a hemispheric asymmetry in the subtropical EP. The underlying mechanisms of this warming pattern remain debated. Here, we conduct ocean heat decompositions of two coupled model large ensembles to unfold the role of wind-driven ocean circulation. When wind changes are suppressed, historical radiative forcing induces a subtropical northeastern Pacific warming, thus causing a hemispheric asymmetry that extends toward the tropical WP. The tropical EP warming is instead induced by the cross-equatorial winds associated with the hemispheric asymmetry, and its driving mechanism is southward warm Ekman advection due to the off-equatorial westerly wind anomalies around 5°N, not vertical thermocline adjustment. Climate models fail to capture the observed CP cooling, suggesting an urgent need to better simulate equatorial oceanic processes and thermal structures.

Response of the tropical Pacific Ocean to wind changes related to global warming from simulations with an ocean general circulation model

A suite of numerical experiments is implemented with an ocean general circulation model (OGCM) to ex-amine the roles of wind stress and wind speed for oceanic changes in the tropical Pacific under global warming. In particular, we turned off the changes of wind stress and/or wind speed in the model to identify the effects of wind-driven ocean circulation and air-sea latent heat flux (i.e., its portion through the wind speed influence on the efficiency of latent heat flux). Results show that 1) the wind stress change appears to be a key forcing mechanism for weakening the tropical surface currents as well as for the oceanic changes in the equatorial thermocline, while it only contributes secondarily to the sea surface temperature (SST) pattern formation in the tropics; 2) the wind speed change is the leading cause for the minimum warming over the southeast subtropics and for a stronger surface warming in the northern hemisphere than in the southern hemisphere; and 3) the enhanced surface warming along the equator is mainly due to the effect of warming in the absence of wind stress and wind speed changes, and this effect also plays a significant role for changing the equatorial thermocline.

Boundary Layer Formation in the Quasigeostrophic Model Near Nonperiodic Rough Coasts

We study the so-called homogeneous model of wind-driven ocean circulation or the 2D quasigeostrophic model. Our attention focuses on performing a complete asymptotic analysis that highlights boundary layer formation along the coastal line. We assume rough coasts without any particular structure, resulting in the study of a nonlinear PDE system for the western boundary layer in an infinite domain. As a consequence, we look for the solution in nonlocalized Sobolev spaces. Under this hypothesis, the eastern boundary layer exhibits a singular behavior at low frequencies far from the rough boundary, leading to issues with convergence. The problem is tackled by imposing ergodicity properties. We establish the well-posedness of the governing boundary layer equations and the asymptotic solution. Our results generalize the ones in Bresch and Gérard-Varet (Commun Math Phys 253(1):81–119, 2005) for periodic irregularities.

A Morley-type virtual element approximation for a wind-driven ocean circulation model on polygonal meshes

In this work, we propose and analyze a Morley-type virtual element method to approximate the Stommel–Munk model in stream-function form. The discretization is based on the fully nonconforming virtual element approach presented in Antonietti et al., (2018) and Zhao et al., (2018). The analysis restricts to simply connected polygonal domains, not necessarily convex. Under standard assumptions on the computational domain we derive some inverse estimates, norm equivalence and approximation properties for an enriching operatorEh defined from the nonconforming space into its H2-conforming counterpart. With the help of these tools we prove optimal error estimates for the stream-function in broken H2-, H1- and L2-norms under minimal regularity condition on the weak solution. Employing postprocessing formulas and adequate polynomial projections we compute from the discrete stream-function further fields of interest, such as: the velocity and vorticity. Moreover, for these postprocessed variables we establish error estimates. Finally, we report practical numerical experiments on different families of polygonal meshes.

Effects of mesoscale turbulence on the wind-driven circulation in a closed basin with topography

This paper studies the effects of time-dependent, mesoscale turbulence on the wind-driven ocean circulation in a closed basin with variable topography. Numerical simulations of a single-layer fluid with finite topography at the sloping boundaries are performed. The flow is forced by a suitable combination of a steady, basin-scale wind that generates the classical western-intensified anticyclonic gyre, plus a shorter, time-dependent forcing that injects energy at a narrow range of scales. Two contrasting situations are considered. First, in the absence of the large-scale forcing, the turbulence generates a cyclonic flow that follows the geostrophic contours around the basin. Second, the resulting mean circulation is studied when the large and small-scale forcing terms are considered together. In particular, it is discussed that the alteration of the anticyclonic gyre may be due to the turbulent-induced cyclonic circulation.

A C1 virtual element method for the stationary quasi-geostrophic equations of the ocean

In this present paper, we propose and analyze a C1-conforming virtual element method to solve the so-called one-layer stationary quasi-geostrophic equations (QGE) with applications in the large scale wind-driven ocean circulation, formulated in terms of the stream-function. This problem corresponds to a nonlinear fourth order partial differential equation. The C1 virtual space and the discrete scheme are built in a straightforward way due to the flexibility of the virtual approach. Under the assumption of small data, we prove well-posedness of the discrete problem by using a fixed-point strategy and under standard assumptions on the computational domain, we establish error estimates in H2-norm for the stream-function. Finally, we report four numerical experiments that illustrate the behavior of the proposed scheme and confirm our theoretical results on different families of polygonal meshes.

On the role of domain aspect ratio in the westward intensification of wind-driven surface ocean circulation

Abstract. The two seminal studies on westward intensification, carried out by Stommel and Munk over 70 years ago, are revisited to elucidate the role of the domain aspect ratio (i.e., meridional to zonal extents of the basin) in determining the transport of the western boundary current (WBC). We examine the general mathematical properties of the two models by transforming them to differential problems that contain only two parameters – the domain aspect ratio and the non-dimensional damping (viscous) coefficient. Explicit analytical expressions are obtained from solutions of the non-dimensional vorticity equations and verified by long-term numerical simulations of the corresponding time-dependent equations. The analytical expressions as well as the simulations imply that in Stommel's model both the domain aspect ratio and the damping parameter contribute to the non-dimensional transport of the WBC. However, the transport increases as a cubic power of the aspect ratio and decreases linearly with the damping coefficient. On the other hand, in Munk's model the WBC's transport increases linearly with the domain aspect ratio, while the damping coefficient plays a minor role only. This finding is employed to explain the weak WBC in the South Pacific. The decrease in transport of the WBC for small-domain aspect ratio results from the decrease in Sverdrup transport in the basin's interior because the meridional shear of the zonal velocity cannot be neglected as an additional vorticity term.

Reduced Order Models for the Quasi-Geostrophic Equations: A Brief Survey

Reduced order models (ROMs) are computational models whose dimension is significantly lower than those obtained through classical numerical discretizations (e.g., finite element, finite difference, finite volume, or spectral methods). Thus, ROMs have been used to accelerate numerical simulations of many query problems, e.g., uncertainty quantification, control, and shape optimization. Projection-based ROMs have been particularly successful in the numerical simulation of fluid flows. In this brief survey, we summarize some recent ROM developments for the quasi-geostrophic equations (QGE) (also known as the barotropic vorticity equations), which are a simplified model for geophysical flows in which rotation plays a central role, such as wind-driven ocean circulation in mid-latitude ocean basins. Since the QGE represent a practical compromise between efficient numerical simulations of ocean flows and accurate representations of large scale ocean dynamics, these equations have often been used in the testing of new numerical methods for ocean flows. ROMs have also been tested on the QGE for various settings in order to understand their potential in efficient numerical simulations of ocean flows. In this paper, we survey the ROMs developed for the QGE in order to understand their potential in efficient numerical simulations of more complex ocean flows: We explain how classical numerical methods for the QGE are used to generate the ROM basis functions, we outline the main steps in the construction of projection-based ROMs (with a particular focus on the under-resolved regime, when the closure problem needs to be addressed), we illustrate the ROMs in the numerical simulation of the QGE for various settings, and we present several potential future research avenues in the ROM exploration of the QGE and more complex models of geophysical flows.

A posteriori analysis of a B-spline based finite-element method for the stationary quasi-geostrophic equations of the ocean

We provide a posteriori error analysis of a B-spline based finite-element method for the streamfunction formulation of the stationary quasi-geostrophic equations to model the large scale wind-driven ocean circulation. The analysis gives rise to a posteriori error estimator for more efficient and accurate modeling of a strong western boundary layer via adaptive local refinement of the computational geometries. To verify the capability of the error estimator, we use hierarchical B-splines in conjunction with Dörfler marking strategy. Numerical studies are performed for several benchmark examples on rectangular and L-shape ocean geometries.

Simple numerical tests for ocean tidal models

There is a growing interest in tidal effects on the global wind-driven oceanic circulation. Tidal models used in such investigations have been verified by comparison with satellite and tide gauge data, but synthetic tests have not been published. In this paper we present three numerical tests in spherical geometry, which are suitable for testing the tidal component of global ocean models. The first test is a tsunami-like propagation of an initial Gaussian depression with no external forcing. The other two tests examine the tidal response of an ocean with an undulating bottom with four Gaussian ridges and an ocean with a flat bottom with a realistic land mask. We provide the results from six model configurations, which differ in the time-stepping scheme and computational grid used. Most of them are implemented in present-day global ocean models. Although the proposed numerical tests are simple compared to realistic simulations, their analytic solutions are not available. We thus check the conservation of time invariants to ensure that the solutions are physically meaningful. We also compare the time evolution of certain physical quantities and the differences in sea surface heights at particular time instants with respect to a reference solution. All tested time stepping schemes are suitable for tidal studies except for the Euler implicit time stepping scheme. Model configurations based on the Arakawa grids B/E use smoothing to suppress the grid-scale noise which results in an energy leakage of around 5%. The B/E-grid energy leakage is probably acceptable if we consider that tuned diffusive terms are used in real-world configurations. The C-grid and B/E-grid solutions differ in the vicinity of solid boundaries as a consequence of different boundary conditions. The B-grid and E-grid solutions are similar, unless the shape of the solid boundaries is complex due to the different shapes of the respective grid cells.

Towards understanding potential atmospheric contributions to abrupt climate changes: characterizing changes to the North Atlantic eddy-driven jet over the last deglaciation

Abstract. Abrupt climate shifts of large amplitudes were common features of the Earth's climate as it transitioned into and out of the last full glacial state approximately 20 000 years ago, but their causes are not yet established. Midlatitude atmospheric dynamics may have played an important role in these climate variations through their effects on heat and precipitation distributions, sea ice extent, and wind-driven ocean circulation patterns. This study characterizes deglacial winter wind changes over the North Atlantic (NAtl) in a suite of transient deglacial simulations using the PlaSim Earth system model (run at T42 resolution) and the TraCE-21ka (T31) simulation. Though driven with yearly updates in surface elevation, we detect multiple instances of NAtl jet transitions in the PlaSim simulations that occur within 10 simulation years and a sensitivity of the jet to background climate conditions. Thus, we suggest that changes to the NAtl jet may play an important role in abrupt glacial climate changes. We identify two types of simulated wind changes over the last deglaciation. Firstly, the latitude of the NAtl eddy-driven jet shifts northward over the deglaciation in a sequence of distinct steps. Secondly, the variability in the NAtl jet gradually shifts from a Last Glacial Maximum (LGM) state with a strongly preferred jet latitude and a restricted latitudinal range to one with no single preferred latitude and a range that is at least 11∘ broader. These changes can significantly affect ocean circulation. Changes to the position of the NAtl jet alter the location of the wind forcing driving oceanic surface gyres and the limits of sea ice extent, whereas a shift to a more variable jet reduces the effectiveness of the wind forcing at driving surface ocean transports. The processes controlling these two types of changes differ on the upstream and downstream ends of the NAtl eddy-driven jet. On the upstream side over eastern North America, the elevated ice sheet margin acts as a barrier to the winds in both the PlaSim simulations and the TraCE-21ka experiment. This constrains both the position and the latitudinal variability in the jet at LGM, so the jet shifts in sync with ice sheet margin changes. In contrast, the downstream side over the eastern NAtl is more sensitive to the thermal state of the background climate. Our results suggest that the presence of an elevated ice sheet margin in the south-eastern sector of the North American ice complex strongly constrains the deglacial position of the jet over eastern North America and the western North Atlantic as well as its variability.

Strong form-based meshfree collocation method for wind-driven ocean circulation

A meshfree point collocation method for modeling large scale wind-driven ocean circulation is proposed. A distinct feature of the method is its ability to represent derivative operators via moving least-square approximation of the Taylor expansion through point-wise computations at collocation points. The method directly discretizes strong forms using the precomputed derivative operators at each collocation point. Numerical studies with three benchmark problems are performed to demonstrate the accuracy and robustness of the method. Along with these studies, an examination is presented regarding the effect of numerical parameters on the error behavior of the proposed method. Finally, wind-driven ocean circulation in the Mediterranean Sea is examined to test the method’s ability to model realistic oceanic flow with arbitrary shaped coastal lines.

Hopf bifurcation and transition of three-dimensional wind-driven ocean circulation problem

The purpose of this article is three-fold. The first is to investigate the linear stability of the basic flow governed by the three-dimensional (3D) quasi-geostrophic (QG) equation with a steady wind force. We show that the basic flow will become unstable as the Reynolds number crosses a critical value. The second is to study the dynamic transition associated with the instability of the basic flow at the critical Reynolds number. It is proved that the type of the phase transition is determined by a parameter called transition number which is mainly determined by the Reynolds number and the aspect ratio. More precisely, the negative (positive) sign of the real part of the transition number corresponds to the continuous (catastrophic) transition. The last objective is to apply numerical experiments to examine the specific transition type for specified control parameters. We show that the real part of the transition number is always negative, leading to only the continuous transition.

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.

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.

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.

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.

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.

[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.