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Tamay M. Özgökmen and Fulvio Crisciani

Abstract

The dynamics of zonal recirculating flows (β plumes) driven by a source of potential vorticity, or a sink of mass, located at the eastern boundary of an ocean basin are investigated using analytical solutions of the barotropic, linear, steady quasigeostrophic equation with bottom and lateral friction.

By scaling the ratio of the strength of the recirculation to that of the sink by that from the inviscid solution, the regimes are identified in which friction becomes a dominant factor. The primary new finding of this study is that the recirculating flow component disappears due to frictional effects when the meridional extent of the sink becomes small. Unlike for the zonal extent of the sink, which affects the recirculating component only if it is on the order of the frictional boundary layer scale, the deviation of the recirculating flow strength from that given by the inviscid solution is apparent for meridional sink scales, which are much larger than the frictional boundary layer scale. Also, location of the maximum recirculation and westward penetration distance of the plumes are quantified. Finally, a stability analysis is conducted to determine the parameter regime in which the β plumes are candidates for instability.

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Anne Molcard, Annalisa Griffa, and Tamay M. Özgökmen

Abstract

Because of the increases in the realism of OGCMs and in the coverage of Lagrangian datasets in most of the world's oceans, assimilation of Lagrangian data in OGCMs emerges as a natural avenue to improve ocean state forecast with many potential practical applications, such as environmental pollutant transport, biological, and naval-related problems.

In this study, a Lagrangian data assimilation method, which was introduced in prior studies in the context of single-layer quasigeostrophic and primitive equation models, is extended for use in multilayer OGCMs using statistical correlation coefficients between velocity fields in order to project the information from the data-containing layer to the other model layers. The efficiency of the assimilation scheme is tested using a set of twin experiments with a three-layer model, as a function of the layer in which the floats are launched and of the assimilation sampling period normalized by the Lagrangian time scale of motion.

It is found that the assimilation scheme is effective provided that the correlation coefficient between the layer that contains the data and the others is high, and the data sampling period Δt is smaller than the Lagrangian time scale TL. When the assimilated data are taken in the first layer, which is the most energetic and is characterized by the fastest time scale, the assimilation is very efficient and gives relatively low errors also in the other layers (≈ 40% in the first 120 days) provided that Δt is small enough, Δt << TL. The assimilation is also efficient for data released in the third layer (errors < 60%), while the dependence on Δt is distinctively less marked for the same range of values, since the time scales of the deeper layer are significantly longer. Results for the intermediate layer show a similar insensitivity to Δt, but the errors are higher (exceeding 70%), because of the lower correlation with the other layers. These results suggest that the assimilation of deep-layer data with low energetics can be very effective, but it is strongly dependent on layer correlation. The methodology also remains quite robust to large deviations from geostrophy.

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Tamay M. Özgökmen and Eric P. Chassignet

Abstract

The emergence of Fofonoff-like flows over a wide range of dissipative parameter regimes is explored in a wind-driven two-layer quasigeostrophic model. Two regimes are found in which Fofonoff-like circulations emerge as a direct consequence of the baroclinic nature of the system, since the wind forcing used in these experiments has been shown to inhibit the formation of Fofonoff flows in the barotropic case. The first regime is one in which the magnitudes of the frictional coefficients (viscosity and bottom dissipation) are extremely small. The experiments clearly illustrate the transition of the numerical solution from a conventional wind-driven circulation to an inertial Fofonoff-like regime. The latter circulation first appears in the lower layer and then spreads throughout the water column via barotropization. The second regime, surprisingly, is obtained with very high bottom friction. This result indicates that entropy can be maximized independently in each layer, depending on the distribution of forcing and dissipation. This sheds a new perspective on the common assumption that forcing and dissipation are disruptive effects that prevent the system from displaying a Fofonoff state.

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Tamay M. Özgökmen and Eric P. Chassignet

Abstract

In light of previous numerical studies demonstrating a strong sensitivity of the strength of thermohaline circulation to the representation of overflows in ocean general circulation models, the dynamics of bottom gravity currents are investigated using a two-dimensional, nonhydrostatic numerical model. The model explicitly resolves the Kelvin–Helmholtz instability, the main mechanism of mixing in nonrotating bottom gravity currents.

A series of experiments were conducted to explore the impact of density difference and slope angle on the dynamics of bottom gravity currents in a nonrotating and homogeneous environment. The features of the simulated currents; that is, a characteristic head at the leading edge and lumped vortices in the trailing fluid, agree qualitatively well with those observed in laboratory experiments. Quantitative comparisons of speed of descent indicate that laboratory results remain valid at geophysical scales.

Two distinct regimes of entrainment of ambient fluid into bottom gravity currents are identified: (i) the laminar entrainment regime is associated with the initial growth of the characteristic head due to the drag exerted by the fresh fluid in front and (ii) the turbulent entrainment is associated with the Kelvin–Helmholtz instabilities. The turbulent entrainment is found to be much stronger than the laminar entrainment, and entrainment in the turbulent regime is less sensitive to the slope angle than that in the laminar regime. The entrainment is quantified as a function of basic parameters of the system, the buoyancy flux and the slope angle, for the purpose of parameterizing the mixing induced by bottom gravity currents.

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Tamay M. Özgökmen, Paul F. Fischer, Jinqiao Duan, and Traian Iliescu

Abstract

Overflows are bottom gravity currents that supply dense water masses generated in high-latitude and marginal seas into the general circulation. Oceanic observations have revealed that mixing of overflows with ambient water masses takes place over small spatial and time scales. Studies with ocean general circulation models indicate that the strength of the thermohaline circulation is strongly sensitive to representation of overflows in these models. In light of these results, overflow-induced mixing emerges as one of the prominent oceanic processes. In this study, as a continuation of an effort to develop appropriate process models for overflows, nonhydrostatic 3D simulations of bottom gravity are carried out that would complement analysis of dedicated observations and large-scale ocean modeling. A parallel high-order spectral-element Navier–Stokes solver is used as the basis of the simulations. Numerical experiments are conducted in an idealized setting focusing on the startup phase of a dense water mass released at the top of a sloping wedge. Results from 3D experiments are compared with results from 2D experiments and laboratory experiments, based on propagation speed of the density front, growth rate of the characteristic head at the leading edge, turbulent overturning length scales, and entrainment parameters. Results from 3D experiments are found to be in general agreement with those from laboratory tank experiments. In 2D simulations, the propagation speed is approximately 20% slower than that of the 3D experiments and the head growth rate is 3 times as large, Thorpe scales are 1.3–1.5 times as large, and the entrainment parameter is up to 2 times as large as those in the 3D experiments. The differences between 2D and 3D simulations are entirely due to internal factors associated with the truncation of the Navier–Stokes equations for 2D approximation.

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Toshio M. Chin, Tamay M. Özgökmen, and Arthur J. Mariano

Abstract

A recipe for a cubic B-spline-based solution for multivariate variational formulation of a data analysis and assimilation problem is provided. To represent a signal whose smallest wavelength is L, the spline scale must be at most L/2, or approximately the Nyquist wavelength. This spline scale defines the computational grid, which tends to be coarser than the typical grid required for finite-difference discretization and hence offers a significant advantage in computational efficiency. The geostrophy–thin-plate model is introduced and applied to a set of analysis problems to demonstrate the effectiveness of the solution technique.

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Yeon S. Chang, Tamay M. Özgökmen, Hartmut Peters, and Xiaobiao Xu

Abstract

The outflow of warm, salty, and dense water from the Red Sea into the western Gulf of Aden is numerically simulated using the Hybrid Coordinate Ocean Model (HYCOM). The pathways of the modeled overflow, temperature, salinity, velocity profiles from stations and across sections, and transport estimates are compared to those observed during the 2001 Red Sea Outflow Experiment. As in nature, the simulated outflow is funneled into two narrow channels along the seafloor. The results from the three-dimensional simulations show a favorable agreement with the observed temperature and salinity profiles along the channels. The volume transport of the modeled overflow increases with the increasing distance from the southern exit of the Bab el Mandeb Strait due to entrainment of ambient fluid, such that the modeled transport shows a reasonable agreement with that estimated from the observations. The initial propagation speed of the outflow is found to be smaller than the estimated interfacial wave speed. The slow propagation is shown to result from the roughness of the bottom topography characterized by a number of depressions that take time to be filled with outflow water. Sensitivities of the results to the horizontal grid spacing, different entrainment parameterizations, and forcing at the source location are investigated. Because of the narrow widths of the approximately 5 km of the outflow channels, a horizontal grid spacing of 1 km or less is required for model simulations to achieve a reasonable agreement with the observations. Comparison of two entrainment parameterizations, namely, TPX and K-profile parameterization (KPP), show that similar results are obtained at 1-km resolution. Overall, the simulation of the Red Sea outflow appears to be more strongly affected by the details of bottom topography and grid spacing needed to adequately resolve them than by parameterizations of diapycnal mixing.

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Tamay M. Özgökmen, William E. Johns, Hartmut Peters, and Silvia Matt

Abstract

Given the motivation that overflow processes, which supply source waters for most of the deep and intermediate water masses in the ocean, pose significant numerical and dynamical challenges for ocean general circulation models, an intercomparison study is conducted between field data collected in the Red Sea overflow and a high-resolution, nonhydrostatic process model. The investigation is focused on the part of the outflow that flows along a long narrow channel, referred to as the “northern channel,” that naturally restricts motion in the lateral direction such that the use of a two-dimensional model provides a reasonable approximation to the dynamics. This channel carries about two-thirds of the total Red Sea overflow transport, after the overflow splits into two branches in the western Gulf of Aden. The evolution of the overflow in the numerical simulations can be characterized in two phases: the first phase is highly time dependent, during which the density front associated with the overflow propagates along the channel. The second phase corresponds to that of a statistically steady state. The primary accomplishment of this study is that the model adequately captures the general characteristics of the system: (i) the gradual thickening of the overflow with downstream distance, (ii) the advection of high salinity and temperature signals at the bottom along the channel with little dilution, and (iii) ambient water masses sandwiched between the overflow and surface mixed layer. To quantify mixing of the overflow with the ambient water masses, an entrainment parameter is determined from the transport increase along the slope and is expressed explicitly as a function of mean slope angle. Bulk Richardson numbers are estimated both from data and model and are related to the entrainment parameter. The range of entrainment parameter and its functional dependence on bulk Richardson number in this study are found to be in reasonable agreement with those reported from various laboratory experiments and that based on measurements of the Mediterranean overflow. The results reveal a complex dynamical interaction between shear-induced mixing and internal waves and illustrate the high computational and modeling requirements for numerical simulation of overflows to capture (at least in part) turbulent transports explicitly.

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Tamay M. Özgökmen, Eric P. Chassignet, and Claes G. H. Rooth

Abstract

As the salty and dense Mediteranean overflow exits the Strait of Gibraltar and descends rapidly in the Gulf of Cadiz, it entrains the fresher overlying subtropical Atlantic Water. A minimal model is put forth in this study to show that the entrainment process associated with the Mediterranean outflow in the Gulf of Cadiz can impact the upper-ocean circulation in the subtropical North Atlantic Ocean and can be a fundamental factor in the establishment of the Azores Current. Two key simplifications are applied in the interest of producing an economical model that captures the dominant effects. The first is to recognize that in a vertically asymmetric two-layer system, a relatively shallow upper layer can be dynamically approximated as a single-layer reduced-gravity controlled barotropic system, and the second is to apply quasigeostrophic dynamics such that the volume flux divergence effect associated with the entrainment is represented as a source of potential vorticity.

Two sets of computations are presented within the 1½-layer framework. A primitive-equation-based computation, which includes the divergent flow effects, is first compared with the equivalent quasigeostrophic formulation. The upper-ocean cyclonic eddy generated by the loss of mass over a localized area elongates westward under the influence of the β effect until the flow encounters the western boundary. In the steady state, the circulation pattern consists of bidirectional zonal flows with a limited meridional extent: eastward to the south of the sink and westward to the north of the sink. The localized sink drives a horizontal circulation in the interior ocean whose strength is approximately an order of magnitude greater than the sink’s strength. It is demonstrated that the induced circulation in the far field from a localized sink is insensitive to the neglect of the divergent flow component.

A set of parameter sensitivity experiments is then undertaken with the quasigeostrophic model for an idealized midlatitude circulation, driven both by wind forcing and “thermohaline” flow through the open southern and northern boundaries. When a sink near the eastern boundary is superimposed on the idealized midlatitude circulation, it is shown to alter significantly the upper-ocean flow and induce an eastward zonal current, which resembles the Azores Current in location and transport. This mechanism also generates a westward current to the north of the sink location, which could be associated with the Azores Countercurrent. An extensive series of sensitivity experiments is conducted to determine the response of this current system to changes in the boundary layer processes, sink strength, sink distribution, model resolution, and wind forcing. The magnitude of the current transports is found to be sensitive to the sink intensity and to its distance from the coastline.

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Mine Çağlar, Tamay M. Özgökmen, and Leonid I. Piterbarg

Abstract

In light of the recent high-resolution radar data of surface velocity, which have revealed submesoscale eddies between the Florida Current and the coast, an objective method of detecting eddies and estimating their parameters such as center coordinates, size, and intensity is suggested. The obtained statistics are used to parametrically represent the birth–death process of eddies filling up the observation area via a model stochastic velocity field known as Çinlar flow. It appears that the suggested approach leads to a reasonable parameterization of this process for potential future use in OGCMs or coastal models.

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