Nonlinear Ekman Pumping Research Articles

Weakly Nonlinear Ekman Pumping in the Sri Lanka Dome and Southwest Monsoon Current

Abstract The Sri Lanka Dome is a cyclonic recirculation feature in the Southwest Monsoon Current system in the southern Bay of Bengal. Cooler sea surface temperature (SST) in the vicinity of this system is often denoted as the Bay of Bengal “Cold Pool.” Although the wind shadow of Sri Lanka creates a region of strong positive wind stress curl, both sea level height dynamics and the distribution of cool SST cannot be explained by wind stress curl alone via traditional Ekman pumping. Moreover, the Cold Pool region is often aligned with the eastern portion of the Sri Lanka Dome, as defined by sea surface height. Previous work has attributed the spatial SST pattern to lateral advection. In this analysis, we explore whether low-latitude weakly nonlinear “vorticity” Ekman pumping could be an explanation for both cooling and observed changes in sea level height in the southwest Bay of Bengal. We show that weakly nonlinear upwelling, calculated from ERA5 and AVISO geostrophic currents, collocates with changes in sea level height (and presumably isopycnals). While the SST signal is sensitive to several factors including the net surface flux, regional upwelling explains changes in AVISO sea level height if the nonlinear terms are included, in both the Sri Lanka Dome and the region of the Southwest Monsoon Current.

3D Structure of the Ras Al Hadd Oceanic Dipole

In the Arabian Sea, southeast of the Arabian peninsula, an oceanic dipole, named the Ras Al Hadd (RAH) dipole, is formed each year, lying near the Ras Al Hadd cape. The RAH dipole is the association of a cyclonic eddy (CE) to the northeast, with an anticyclonic eddy (AE) to the southwest. This dipole intensifies in the summer monsoon and disappears during the winter monsoon. This dipole has been described previously, but mostly for its surface expression, and for short time intervals. Here, we describe the 3D structure of this dipole over the 2000–2015 period, by combining colocalized ARGO float profiler data (a total of 7552 profiles inside and outside the RAH dipole) with angular momentum eddy detection and tracking algorithm (AMEDA) surface data. We show first the different water masses in and near the RAH dipole. The presence of the Persian Gulf water (PGW) below 200 m depth is confirmed in both eddies. Arabian Sea high salinity water (ASHSW) is found exclusively in the AE; a layer of fresh and cold water is observed above 100 m depth in both eddies. By analyzing the potential density structures, we show that the CE has a surface-intensified structure while the AE is subsurface-intensified. The sea level anomaly shows a 0.04 m elevation above the AE and a 0.2 m depression over the CE. The CE has a faster geostrophic velocity, (vertical velocity, respectively) 0.6 m s−1 than the AE, 0.15 m s−1 (respectively, 3 m day−1 for the CE and 0.6 m day−1 for the AE). After presenting the vertical structure of the dipole, we show the dominance of the nonlinear Ekman pumping in the CE over the linear pumping affecting the dipole. As a consequence, we explain the CE’s longer lifetime by its intensity and shallowness, and by its sensitivity to the interaction with the atmosphere (in particular the wind stress) and with neighboring eddies. We examined the possible (co)existence of symmetric, barotropic, and baroclinic instabilities in both eddies. These instabilities coexist near the surface in both eddies. They are intensified for the CE, which suggests that the CE is unstable and the AE is rather stable or may need a long time to be unstable.

Seasonal velocity variations over the entire Kuroshio path part II: dynamical interpretation for the current speed variation

The response of a jet to sudden winds was examined using a simple numerical regional model and an analytical model to investigate the mechanism underlying the local wind dynamics of seasonal velocity variations in the upper layer of the Kuroshio. The numerical model was used to simulate the distinct seasonal features in summer and autumn in the East China Sea and successfully reproduced the seasonal features in the velocity field under different sudden wind conditions. The current speed increased and decreased under summer and autumn wind conditions, respectively; and the current axis shifted to the offshore and inshore sides under summer and autumn wind conditions, respectively. We focused on the current speed variation and hypothesized that the current speed variation is forced by the thermocline variation due to nonlinear Ekman pumping. This hypothesis was examined using a rigid-lid reduced-gravity analytical model with Ekman layer dynamics. The analytical model results showed that the asymmetry of the jet profile has a marked effect on the current speed variation. With a higher wavenumber on the west side of a northward jet, the current speed increased and decreased under summer and autumn wind conditions, respectively. These findings can be used to explain the seasonal velocity variations in the upper layer in the East China Sea and over the entire Kuroshio path.

Interaction of Nonlinear Ekman Pumping, Near-Inertial Oscillations, and Geostrophic Turbulence in an Idealized Coupled Model

AbstractA new coupled model is developed to investigate interactions among geostrophic, Ekman, and near-inertial (NI) flows. The model couples a time-dependent nonlinear slab Ekman layer with a two-layer shallow water model. Wind stress forces the slab layer and horizontal divergence of slab-layer transport appears as a forcing in the continuity equation of the shallow water model. In one version of the slab model, self-advection of slab-layer momentum is retained and in another it is not. The most obvious impact of this explicit representation of the surface-layer dynamics is in the high-frequency part of the flow. For example, near-inertial oscillations are significantly stronger when self-advection of slab-layer momentum is retained, this being true both for the slab-layer flow itself and for the interior flow that it excites. In addition, retaining the self-advection terms leads to a new instability, which causes growth of slab-layer near-inertial oscillations in regions of anticyclonic forcing and decay in regions of cyclonic forcing. In contrast to inertial instability, it is the sign of the forcing, not that of the underlying vorticity, that determines stability. High-passed surface pressure fields are also examined and show the surface signature of unbalanced flow to differ substantially depending on whether a slab-layer model is used and, if so, whether self-advection of slab-layer momentum is retained.

Impact of Current‐Wind Interaction on Vertical Processes in the Southern Ocean

AbstractMomentum input from westerly winds blowing over the Southern Ocean can be modulated by mesoscale surface currents and result in changes in large‐scale ocean circulation. Here, using an eddy‐resolving 1/20 degree ocean model configured near Drake Passage, we evaluate the impact of current‐wind interaction on vertical processes. We find a reduction in momentum input from the wind, reduced eddy kinetic energy, and a modification of Ekman pumping rates. Wind stress curl resulting from current‐wind interaction leads to net upward motion, while the nonlinear Ekman pumping term associated with horizontal gradients of relative vorticity induces net downward motion. The spatially averaged mixed layer depth estimated using a density criteria is shoaled slightly by current‐wind interaction. Current‐wind interaction, on the other hand, enhances the stratification in the thermocline below the mixed layer. Such changes have the potential to alter biogeochemical processes including nutrient supply, biological productivity, and air‐sea carbon dioxide exchange.

The response of surface chlorophyll to mesoscale eddies generated in the eastern South China Sea

This study investigates the response of surface chlorophyll (CHL) to mesoscale eddies generated in the eastern South China Sea (ESCS) during their lifecycles based on global eddy dataset and chlorophyll data from January 2003 to December 2016. The results show that the responses of CHL anomalies to cyclones are stronger than anticyclones generated in the Luzon Strait (LS) and in the area off northwest Luzon Island (NWLI). CHL anomalies are higher when cyclones disappear than when they are generated in the LS and in the NWLI. Furthermore, impacts of different eddy dynamic mechanisms (eddy advection, eddy trapping, eddy pumping and eddy-induced Ekman pumping) on CHL anomalies are quantified during eddy lifecycles based on empirical orthogonal function (EOF) method. Our results reveal that CHL anomalies in cyclones generated in the NWLI are affected by eddy pumping and its strengthening effect enhanced until the middle stage of their lifecycles. CHL anomalies in cyclones generated in the LS are modulated by eddy advection and linear Ekman pumping. CHL anomalies in anticyclones generated in the LS are jointly induced by eddy trapping, nonlinear Ekman pumping and eddy pumping. This study helps us attribute surface CHL to specific mechanisms and understand the differences in the response of surface CHL to mesoscale eddies generated in the ESCS during their lifecycles, and thus gains a deeper understanding of the role of mesoscale eddies in regulating the marine primary production.

Ageostrophic Secondary Circulation in a Subtropical Intrathermocline Eddy

AbstractVertical motions play a key role in the enhancement of primary production within mesoscale eddies through the introduction of nutrients into the euphotic layer. However, the details of the vertical velocity field w driving these enhancements remain under discussion. For the first time the mesoscale w associated with an intrathermocline eddy is computed and analyzed using in situ high-resolution three-dimensional (3D) fields of density and horizontal velocity by resolving a generalized omega equation valid for high Rossby numbers. In the seasonal pycnocline the diagnosed w reveals a multipolar structure with upwelling and downwelling cells located at the eddy periphery. In the main pycnocline w is characterized by a dipolar structure with downwelling velocities upstream of the propagation path and upwelling velocities downstream. Maximum values of w reach 6.4 m day−1. An observed enhancement of chlorophyll-a at the eddy periphery coincides with the location of the upwelling and downwelling cells. Analysis of the forcing terms of the generalized omega equation indicates that the mechanisms behind the dipolar structure of the w field are a combination of horizontal deformation and advection of vertical relative vorticity by ageostrophic vertical shear. The wind during the eddy sampling was rather constant and uniform with a speed of 5 m s−1. Diagnosed nonlinear Ekman pumping leads to a dipolar pattern that mirrors the inferred w. Horizontal ageostrophic secondary circulation is dominated by centripetal acceleration and closes the dipole w structure. Vertical fluxes act to maintain the intrathermocline eddy structure.

Impact of submesoscale processes on dynamics of phytoplankton filaments

AbstractIn Monterey Bay, CA, during northwesterly, upwelling favorable winds, the development of a southward flowing cold jet along the entrance to the Bay is often observed. This dense cold jet separates warm waters of the anticyclonic circulation offshore from the water masses inside the Bay. Interactions between the cold jet and the offshore anticyclonic circulation generate ageostrophic secondary circulation (ASC) cells due to submesoscale processes as, for example, flow interaction with the development of surface frontogenesis and nonlinear Ekman pumping. Based on observations and modeling studies, we evaluate the impact of these submesoscale processes on the formation of chlorophyll a filaments during late spring‐earlier summer, and late summer time frames. We show that during the late summer time frame, ASC leads to the development of filaments with high values of chlorophyll a concentration along the edge of the cold jet–in contrast to the earlier summer time, when the ASC mixes phytoplankton much deeper to the area below of the euphotic depth, and chlorophyll a filaments are 3–4 times weaker.

Three-dimensional circulation in the NW Africa coastal transition zone

High-resolution data collected southeast of the Canary Islands during late winter 2006 are analyzed to describe the hydrography and three-dimensional circulation in the coastal transition zone off NW Africa. The data are optimally interpolated over a regular grid, the geostrophic velocity field is calculated and the Q-vector formulation of the omega equation is used to compute the quasi-geostrophic (QG) mesoscale vertical velocity. The coastal transition zone is divided into upwelling, frontal and offshore regions with distinct physical and dynamic characteristics. The upwelling region is characterized by cold and weakly stratified waters flowing towards the equator, with a poleward undercurrent of approximately 0.05 m s −1 over the continental slope. The frontal region exhibits a southwestward baroclinic jet associated with cross-shore raising isopycnals; the jet transport is close to 1 Sv, with maximum velocities of 0.18 m s −1 at surface decreasing to 0.05 m s −1 at 300 db. Vertical sections across the frontal region show the presence of deep eddies probably generated by the topographic blocking of the islands to the southward current, as well as much shallower eddies that likely have arisen as instabilities of the baroclinic upwelling jet. The QG mesoscale vertical velocity field is patchy, estimated to range from −18 to 12 m day −1, with the largest absolute values corresponding to an anticyclonic eddy located south of Fuerteventura Island. These values are significantly larger than estimates for other vertical velocities: diapycnal vertical velocities associated with mixing in the frontal region (a few meters per day), and wind-induced vertical velocities (non-linear Ekman pumping arising from the interaction between the wind stress and the background vorticity, maximum values of a few meters per day; linear Ekman pumping due to the divergence of Ekman transport, a fraction of a meter per day; or the coastal constraint in the upwelling region, about 0.7 m day −1). However, the patchiness in both the QG mesoscale vertical velocity and the non-linear Ekman pumping velocity cause their integrated vertical transports to be one order of magnitude smaller than either coastal Ekman transport (0.08 Sv), integrated linear Ekman pumping (−0.05 Sv) or diapycnal transfer (about 0.1–0.2 Sv). The pattern of the near-surface fluorescence field is a good indicator of these different contributions, with large homogeneous values in the coastal upwelling region and a patchy structure associated with the offshore mesoscale structures.

Transient upwelling hot spots in the oligotrophic North Pacific

Vertical exchange between deep, nutrient‐rich and nutrient‐depleted surface waters controls the physical supply of nutrients into the euphotic zone in the oligotrophic waters of the subtropical North Pacific Ocean. Sea surface temperature and ocean color satellite images are used in this study to show that submesoscale chlorophyll patches are locally intensified. These patches are associated with surface temperature fronts and regions of strong stretching of the eddying flow. The latter are identified by calculating the finite‐size Lyapunov exponents of the geostrophic flow derived from the sea surface height field from altimetry. Surface frontogenesis and nonlinear Ekman pumping (NLEP) arise as natural candidates for the sporadic generation of large vertical velocities that could favor the formation of these features. A high‐resolution regional numerical model simulation confirms that large vertical velocities are indeed associated with strong density fronts and gradients of relative vorticity. Using the Q vector divergence as a proxy for frontogenetically generated vertical velocities yields good agreement with the model vertical velocities, particularly in regions where they are large. The pattern and magnitude of NLEP suggests that it is also contributing to the strong vertical motions, although NLEP and model vertical velocities are not necessarily in phase. Surface frontogenesis and NLEP provide a possible explanation for the episodic injection of nutrients at the submesoscale, which are then horizontally stirred and modulated by the unstable manifolds of the flow field. Given that these surface‐intensified processes would be biogeochemically more effective when the pycnocline is shallow, they could also serve as one possible explanation for the late summer chlorophyll blooms that are known to occur in the region.

Baroclinic wave packets in an extended quasigeostrophic two‐layer model

An extended quasigeostrophic two‐layer model including nonlinear Ekman pumping and nonlinear interface perturbation is used to numerically study the formation and maintenance of baroclinic wave packets. With an initial zonal jet flow of north–south symmetry and small random initial perturbations wave packets of finite amplitude are produced and maintained with an equilibrated wave packet‐zonal flow system exhibiting simultaneously downstream‐upstream asymmetry and north–south asymmetry, the later of which has not been observed in the past simple quasigeostrophic two‐layer modeling studies. The northern upstream part of the wave packets is stronger than its southern upstream counterpart and therefore the peak of time‐and‐zonal‐average eddy kinetic energy associated with the wave packets is shifted poleward while the peak of the time‐mean zonal jet flow is shifted equatorward, which is in agreement with the observations.

비선형 Ekman 펌핑 모델의 개발

Developed in this study is a nonlinear Ekman pumping model to be used in simulating the rotating flows with quasi-three-dimensional Navier-Stokes equations. In this model, the Ekman pumping velocity is given from the solution of the Ekman boundary-layer equations for the region adjacent to the bottom wall of the flow domain; the boundary-layer equations are solved in the momentum-integral form. The developed model is then applied to rotating flows in a rectangular container receiving a time-periodic forcing. By comparing our results with the DNS and experimental data we have validated the developed model. We also compared our results with those given from the classical Ekman pumping model. It was found that our model can predict the rotating flows more precisely than the classical linear model.

An analysis of mechanisms for submesoscale vertical motion at ocean fronts

We analyze model simulations of a wind-forced upper ocean front to understand the generation of near-surface submesoscale, O(1 km), structures with intense vertical motion. The largest vertical velocities are in the downward direction; their maxima are situated at approximately 25 m depth and magnitudes exceed 1 mm/s or 100 m/day. They are correlated with high rates of lateral strain, large relative vorticity and the loss of geostrophic balance. We examine several mechanisms for the formation of submesoscale structure and vertical velocity in the upper ocean. These include: (i) frontogenesis, (ii) frictional effects at fronts, (iii) mixed layer instabilities, (iv) ageostrophic anticyclonic instability, and (v) nonlinear Ekman effects. We assess the role of these mechanisms in generating vertical motion within the nonlinear, three-dimensionally evolving flow field of the nonhydrostatic model. We find that the strong submesoscale down-welling in the model is explained by nonlinear Ekman pumping and is also consistent with the potential vorticity arguments that analogize down-front winds to buoyancy-forcing. Conditions also support the formation of ageostrophic anticyclonic instabilities, but the contribution of these is difficult to assess because the decomposition of the flow into balanced and unbalanced components via semigeostrophic analysis breaks down at O(1) Rossby numbers. Mixed layer instabilities do not dominate the structure, but shear and frontogenesis contribute to the relative vorticity and strain fields that generate ageostrophy.

A Comprehensive Analysis of Nonlinear Corrections to the Classical Ekman Pumping

The role of each nonlinear term in the vorticity and divergence equations derived from the primitive equations to the steady nonlinear Ekman pumping is examined for uni-directional flows with a small Rossby number comprehensively. For uni-directional flows with a constant horizontal shear, the perturbation analysis in the first order of a small Rossby number show that the contribution from the nonlinear divergence term in the vorticity equation to the Ekman pumping is the most dominant. That from the vertical advection term in the vorticity equation is the second dominant. The nonlinear terms from the divergence equation are less important for the nonlinear corrections to the classical Ekman pumping. In addition, the effect of the nonlinear divergence term to the Ekman pumping is opposite from that of the other nonlinear terms. The latter result also can be verified by qualitative discussions. Furthermore, the analytical solutions for constant horizontal shear flows can be utilized even for uni-directional flows with general horizontal shear. In this case, it is found that the contribution from the nonlinear divergence and horizontal advection terms in the vorticity equation to the Ekman pumping is the most dominant. That from the vertical advection and tilting terms in the vorticity equation is the second dominant. Some comments on the pre-existing approximate models of the nonlinear Ekman pumping are made.

Stable and Unstable Evolution of Modons Perturbed by Surface Term, Bottom Friction, and Bottom Topography Incorporating Nonlinear Ekman Pumping

The evolution, both stable and unstable, of contrarotating vortex pairs (“modons”) perturbed by upper-surface and bottom Ekman pumping is investigated using a homogeneous model with a variable free upper-surface and bottom topography. The Ekman pumping considered here differs from the classical Ekman pumping in that the divergence-vorticity term in the vorticity equation, nonlinear and omitted in previous studies, is explicitly included. Under the influence of both nonlinear Ekman pumping and the beta term, eastward- and westward-moving modons behave very differently. Eastward-moving modons are stable to the upper-surface perturbation but westward-moving modons are not. The latter move southwestward, triggering the tilt instability: the beta effect deepens the cyclones but weakens the anticyclone, and the vortex pair disperses into wave packets. Eastward-moving modons are stable to bottom friction in the sense that they diminish in time gradually at a rate independent of the signs of the vortices. Westward-moving modons behave differently depending on the strength of bottom friction. Cyclones decay faster than anticyclones, triggering the tilt instability in westward-moving modons, but only if the bottom friction is very weak. For sufficiently strong bottom friction, in contrast, modons decay monotonically: the cyclones still decay faster than anticyclones, but no wave packets formed before the modons completely dissipate. Westward-moving modons are always unstable to topographic forcing. Eastward-moving modons have varying behavior controlled by the height and width of the topography. Below a critical height, determined by the width, modons survive the topographic interaction: their trajectory meanders but the two contrarotating vortices always remain bound together after escaping the topography. Above the critical height, modons disassociate: the two vortices separate and disperse into wave packets. When the width of the topography is comparable to modon width, there exists a stable window within the unstable region of the topographic height in which the modons also survive the topographic encounter.

On dissipation of barotropic geostrophic motion on account of the nonlinear Ekman pumping

Abstract Presented is the theoretical investigation of dissipation of barotropic geostrophic motion with allowance for the divergence in the boundary layer with squared friction. Found are the analytical solutions of the relevant nonlinear problems for some limiting cases. In some respects, the solutions differ qualitatively from the classic case of “Ekman pumping”. In particular, (1) evolution rate of the geostrophic vortices depends on their amplitude; (2) the horizontal sizes of the initially localized disturbance grow as power function of time with the degree essentially lesser than in the classical model; and (3) the disturbances have the clearly expressed spatial boundary.