Göran Broström

The Thermohaline Circulation and Vertical Mixing: Does Weaker Density Stratification Give Stronger Overturning?

The possibility that a decreased equator-to-Pole surface density difference could imply stronger rather than weaker thermohaline circulation (THC) is explored theoretically as well as with the aid of numerical simulations. The idea builds on the classical thermocline scaling, stating that the THC should increase with density difference as well as with vertical diffusivity. To explore possible changes in vertical diffusivity that would follow a change in the oceanic density difference, simple models of internal wave mixing are considered. For reasonable assumptions concerning the energy supply to vertical mixing, the overall diffusivity tends to increase with decreasing density difference. This enhancement of the vertical diffusivity acts to deepen the thermocline, an effect that can cause the THC to amplify despite that the surface density difference is reduced. This remarkable state of affairs is illustrated with simulations from a one-hemisphere ocean circulation model. In the simulations, two stratification-dependent diffusivity representations are investigated, which both imply that a weaker density difference will be associated with a stronger THC. The more common mixing representation, where the diffusivity is taken to be fixed, yields the opposite and well-known result: a weaker density difference will be associated with a weaker THC.

Observation-based evaluation of surface wave effects on currents and trajectory forecasts

Knowledge of upper ocean currents is needed for trajectory forecasts and is essential for search and rescue operations and oil spill mitigation. This paper addresses effects of surface waves on ocean currents and drifter trajectories using in situ observations. The data set includes colocated measurements of directional wave spectra from a wave rider buoy, ocean currents measured by acoustic Doppler current profilers (ADCPs), as well as data from two types of tracking buoys that sample the currents at two different depths. The ADCP measures the Eulerian current at one point, as modelled by an ocean general circulation model, while the tracking buoys are advected by the Lagrangian current that includes the wave-induced Stokes drift. Based on our observations, we assess the importance of two different wave effects: (a) forcing of the ocean current by wave-induced surface fluxes and the Coriolis–Stokes force, and (b) advection of surface drifters by wave motion, that is the Stokes drift. Recent theoretical developments provide a framework for including these wave effects in ocean model systems. The order of magnitude of the Stokes drift is the same as the Eulerian current judging from the available data. The wave-induced momentum and turbulent kinetic energy fluxes are estimated and shown to be significant. Similarly, the wave-induced Coriolis–Stokes force is significant over time scales related to the inertial period. Surface drifter trajectories were analysed and could be reproduced using the observations of currents, waves and wind. Waves were found to have a significant contribution to the trajectories, and we conclude that adding wave effects in ocean model systems is likely to increase predictability of surface drifter trajectories. The relative importance of the Stokes drift was twice as large as the direct wind drag for the used surface drifter.

Thermodynamic analysis of ocean circulation

Abstract Calculating a streamfunction as function of depth and density is proposed as a new way of analyzing the thermodynamic character of the overturning circulation in the global ocean. The sign of an overturning cell in this streamfunction directly shows whether it is driven mechanically by large-scale wind stress or thermally by heat conduction and small-scale mixing. It is also shown that the integral of this streamfunction gives the thermodynamic work performed by the fluid. The analysis is also valid for the Boussinesq equations, although formally there is no thermodynamic work in an incompressible fluid. The proposed method is applied both to an idealized coarse-resolution three-dimensional numerical ocean model, and to the realistic high-resolution Ocean Circulation and Climate Advanced Model (OCCAM). It is shown that the overturning circulation in OCCAM between the 200- and 1000-m depth is dominated by a thermally indirect cell of 24 Sverdrups (1 Sv ≡ 106 m3 s−1), forced by Ekman pumping. In th...

Baroclinic boundary currents with downstream decreasing buoyancy: A study of an idealized Nordic Seas system

The dynamics of a baroclinic boundary current losing buoyancy along its path is analyzed both theoretically and using a numerical ocean-circulation model. A fundamental ingredient in our analysis is that the side boundaries of the ocean basin are sloping gently down to the deep ocean. Theoretically we find that the coastal boundary current develops two branches: one seaward baroclinic jetstream and one barotropic current, which is confined to the continental slope. The baroclinic jetstream decreases its transport as the buoyancy is lost from the surface layer. This decrease in transport is compensated by an increase in the barotropic flow on the slope. When the buoyancy is lost altogether, the entire volume transport occurs in the barotropic slope current. In our numerical experiments we focus on the penetration of warm water over a sill into a cold semi-enclosed basin. The flow enters as a baroclinic current with a thickness approximately equal to the sill depth and proceeds around the basin on essentially the same depth while being transformed to a barotropic slope current which leaves the basin over the sill. It should be noted that the circulation does not involve any renewal of the deep water in the cold basin, except in the initial spin up of the system. We suggest that our results can illuminate some basic aspects of the dynamics in the Nordic Seas, which are invaded by North Atlantic surface water over the Greenland-Scotland Ridge. One striking example; is the observations reported by Orvik et al. (2001), which show that the flow of Atlantic water along the Norwegian coast has two branches: A baroclinic jetstream and a shelf-bound barotropic current. The existence of this double-flow structure is to be expected from our theoretical considerations and numerical simulations.

Eulerian versus Lagrangian Approaches to the Wave-Induced Transport in the Upper Ocean

Abstract It is demonstrated that the Eulerian and the Lagrangian descriptions of fluid motion yield the same form for the mean wave-induced volume fluxes in the surface layer of a viscous rotating ocean. In the Eulerian case, the volume fluxes are obtained in the familiar way by integrating the horizontal components of the Navier–Stokes equation in the vertical direction, as seen, for example, in the book by Phillips. In the direct Lagrangian approach, the perturbation equations for the second-order mean drift are integrated in the vertical direction. This yields the advantage that the form drag, which is a source term for the wave-induced transports, can be related to the virtual wave stress that acts to transfer dissipated mean wave momentum into mean currents. In particular, for waves that are periodic in space and time, comparisons between empirical and theoretical relations for the form drag yield an estimate for the wave-induced bulk turbulent eddy viscosity in the surface layer. A simplistic approa...

Comparison of HF radar measurements with Eulerian and Lagrangian surface currents

High-frequency (HF) radar-derived ocean currents are compared with in situ measurements to conclude if the radar observations include effects of surface waves that are of second order in the wave amplitude. Eulerian current measurements from a high-resolution acoustic Doppler current profiler and Lagrangian measurements from surface drifters are used as references. Directional wave spectra are obtained from a combination of pressure sensor data and a wave model. Our analysis shows that the wave-induced Stokes drift is not included in the HF radar-derived currents, that is, HF radars measure the Eulerian current. A disputed nonlinear correction to the phase velocity of surface gravity waves, which may affect HF radar signals, has a magnitude of about half the Stokes drift at the surface. In our case, this contribution by nonlinear dispersion would be smaller than the accuracy of the HF radar currents, hence no conclusion can be made. Finally, the analysis confirms that the HF radar data represent an exponentially weighted vertical average where the decay scale is proportional to the wavelength of the transmitted signal.

A Quasi-Eulerian, Quasi-Lagrangian View of Surface-Wave-Induced Flow in the Ocean

Abstract In this study the influence of surface waves on the mean flow in an ocean of arbitrary depth is examined. The wave-induced forcing on the mean flow is obtained by integrating the Eulerian equations for mass and momentum balance from the bottom to an undulating material surface within the water column. By using the mean position of the material surface as the vertical coordinate, the authors obtain the depth dependence of the mean flow and the wave-induced forcing. Substitution of the vertical coordinate makes the model Lagrangian in the vertical direction. The model is Eulerian in the horizontal direction, allowing one to model the effects of a spatially nonuniform wave field or varying depth in a straightforward way.

Thermohaline circulation induced by bottom friction in sloping-boundary basins

We show that a velocity field in geostrophic and hydrostatic balance on the f-plane can be diagnosed from an arbitrarily prescribed distribution of buoyancy in a basin with closed depth contours. We emphasize the steady-state circulation associated with a large-scale horizontal buoyancy gradient, attained in the absence of wind forcing. For inviscid motion, the diagnosed field contains a free barotropic along-isobath flow which can be chosen arbitrarily, e.g. in such a way that the buoyant “southern” pool of surface water essentially recirculates. Including bottom friction, we show that steady motion requires that the net Ekman transport across closed depth contours must vanish. This constraint determines the free barotropic motion and thereby the entire velocity field, which proves to be independent of the strength of the bottom friction. The barotropic flow component serves to create a “thermohaline” circulation, i.e. a circulation which tends to spread the buoyant water horizontally. Analytical solutions and results from a numerical experiment are presented to illustrate the steady flow resulting in a basin where the upper-ocean density increases across the basin.

Observations of Turbulence Caused by a Combination of Tides and Mean Baroclinic Flow over a Fjord Sill

Thisstudyinvestigates thedissipation ratesandflow conditionsattheDrobakSillinthe Oslofjord.Thearea was transected 13 times with a free-falling microstructure shear probe during 4 days in June 2011. At the same time, an ADCP was deployed inside the sill. During most tidal cycles, internal hydraulic jumps with high dissipation rates were foundon the downstreamside of the sill. However, the internal responsevariedstrongly betweendifferenttidal cycleswith similar barotropicforcing.In the beginning of the observational period,ebb tides had no hydraulic jumps, and in the end one of the flood tides did not have a hydraulic jump. During the same period, the mean baroclinic exchange flow changed from inflow to outflow in the bottom layer. The authors conclude that the conditions at the sill are on the edge of forming hydraulic jumps and that the mean baroclinic exchange may push the flow above or below the limit of a hydraulic jump depending on the situation. This conclusion is supported by two-layer hydraulic theory. The volume-integrated dissipation rates within 500m from the sill crest compare well with estimates of energy loss in the lower layer calculated from the Bernoulli drop under the assumption of no energy loss in the upper layer. Finally, the mean dissipation rateatthesillwascomparedwiththeradiationofinternaltidalenergyawayfromthesill,anditwasfoundthat about 60%‐90% of the total energy loss was dissipated locally.

Note on Coriolis-Stokes force and energy

In this study, we consider the origin of the Coriolis-Stokes (CS) force in the wave-averaged momentum and energy equations and make a short analysis of possible energy input to the ocean circulation (i.e., Eulerian mean velocity) from the CS force. Essentially, we find that the CS force appears naturally when considering vertically integrated quantities and that the CS force will not provide any energy input into the system for this case. However, by including the “Hasselmann force”, we show some inconsistencies regarding the vertical structure of the CS force in the Eulerian framework and find that there is a distinct vertical structure of the energy input and that the net input strongly depends on whether the wave zone is included in the analysis or not. We therefore question the introduction of the “Hasselmann force” into the system of equations, as the CS force appears naturally in the vertically integrated equations or when Lagrangian vertical coordinates are used.