Ensemble inequivalence, bicritical points and azeotropy for generalized Fofonoff flows

We present a theoretical description for the equilibrium states of a large class of models of two-dimensional and geophysical flows, in arbitrary domains. We account for the existence of ensemble inequivalence and negative specific heat in those models, for the first time using explicit computations. We give exact theoretical computation of a criteria to determine phase transition location and type. Strikingly, this criteria does not depend on the model, but only on the domain geometry. We report the first example of bicritical points and second order azeotropy in the context of systems with long range interactions.Comment: 4 pages, submitted to Phys. Rev. Let

Available potential energy for mode eddies

Also published as: Journal of Physical Oceanography 11 (1981): 30-47Available potential energy (APE) is defined as the difference between total potential plus internal energy of a fluid in a gravity field and a corresponding reference field in which the fluid is redistributed (leveled) adiabatically to have constant stably-stratified densities along geopotential surfaces. Potential energy changes result from local shifts of flu id mass relative to geopotential surfaces that are accompanied by local changes of enthalpy and internal energy and global shifts of mass (because volumes of fluid elements are not conserved) that do not change enthalpy or internal energy. The potential energy changes are examined separately by computing available gravitational potential energy (GPE) per unit mass and total GPE (TGPE) per unit area. A technique for estimating GPE in the ocean is developed by introducirtg a reference density field (or an equivalent specific volume anomaly field) that is a function of pressure only and is connected to the observed field by adiabatic vertical displacements. The full empirical equation of state for seawater is used in the computational algorithm. The accuracy of the estimate is limited by the data and sampling and not by the algorithm itself, which can be made as precise as desired. The reference density field defined locally for an ocean region allows redefinition of dynamic height ΔD (potential energy per unit mass) relative to the reference field. TGPE per unit area becomes simply the horizontal average of dynamic height integrated over depth in the region considered. The reference density surfaces provide a precise approximation to material surfaces for tracing conservative variables such as salinity and potential temperature and for estimating vortex stretching between surfaces. The procedure is applied to the MODE density data collected in 1973. For each group of stations within five 2-week time windows (designated Groups A-E) the estimated GPE is compared with the net APE based on the Boussinesq approximation and to the low-frequency kinetic energy measured from moored buoys. Changes of potential energy of the reference field from one time window to the next are large compared with the GPE within each window, indicating the presence of scales larger than the station grid. An analysis of errors has been made to show the sensitivity of the estimates to data accuracy and sampling frequency.Prepared for the Office of Naval Research under Contract N00014-76-C-0197

Vertical coherence of short-periodic current variations

A study is described which attempts to obtain information about the vertical correlation of ocean currents at frequencies higher than inertial. Current velocity and temperature data for sensor separations of 4–12 m were taken with a mooring at ‘Site D’. The coherence and phase spectra for velocity component pairs reveals that motions are rotational at low frequencies. A cut-off frequency exists above which coherence drops to low values. The limiting frequency coincides with the minimum Väisälä frequency of the total water column. These cross-spectral properties support the assumption that the motion in this frequency range is governed by internal wave dynamics. The coherence and phase spectra of temperature pairs indicate that a field of temperature structure is superimposed on the mean field which is weakly correlated to the field of motion

Consistency Relations for Internal Waves

A complete set of linearly independent relationships among the different cross spectral components obtained from pairs of moored instruments is derived which can be utilized to test whether or not the observed fluctuations within the internal wave frequency band represent a field of propagating internal waves. A further complete set of relationships is derived which enables to test whether or not the internal wave field is horizontally isotropic and (or) vertically symmetric. These relations are compared with corresponding relations for alternative models (standing internal wave modes, three-dimensional isotropic turbulence) and their capability to discriminate between the various models is investigated. The tests are applied to a set of data for which it is found that the observed fluctuations are consistent with both propagating and standing internal waves whereas isotropic turbulence must be rejected for the most part of the internal wave frequency band

Characterizing horizontal variability and energy spectra in the Arctic Ocean halocline

Energy transfer from the atmosphere into the upper Arctic Ocean is expected to become more efficient as summer sea-ice coverage decreases and multiyear ice thins due to recent atmospheric warming. However, relatively little is known about how energy is transferred within the ocean by turbulent processes from large to small scales in the presence of ice and how these pathways might change in future. This study characterises horizontal variability in several regions of the Eurasian Arctic Ocean under differing sea-ice conditions. Historic along track CTD data collected by a Royal Navy submarine during summer 1996 allows a unique examination of horizontal variability and associated wavenumber spectra within the Arctic Ocean halocline. Spectral analysis indicates that potential energy variance under perennial sea-ice in the Amundsen Basin is O(100) less than within the Marginal Ice Zone (MIZ) of Fram Strait. Spectra from all regions show a transition in scaling at wavelengths of approximately 5 to 7 km. At scales greater than the transition wavelength to 50 km, energy spectra are consistent with a k-3 scaling (where k is wavenumber) and interior quasi-geostrophic dynamics. The scaling of spectra at these scales is extremely similar between regions suggesting similar dynamics and energy exchange pathways. The k-3 scaling is steeper than typically found in regions of mid latitude open ocean. At scales below the transition wavelength to 300 m, spectra are close to a k-5/3 scaling or flatter, indicating a change in dynamics, which is potentially due to internal waves dominating variability at small scales

On the Origin of the Azores Current

The Azores Current, south of the Azores Archipelago, is part of the subtropical North Atlantic gyre. Using an international hydrographic data set, we analyze mean and seasonal geostrophic transport fields in the upper 800 m of the ocean in order to determine the origin of the Azores Current in the western basin and seasonal changes in the related flow. Geostrophic currents are obtained by using the method applied by Stramma (1984) in the eastern basin. The Azores Current is found to originate in the area of the Southwest Newfoundland Rise (Figure 10). In winter an almost uniform current connects this region of origin with the Azores Current, while a branching into two current bands is observed in summer, with the southern band forming a marked cyclonic loop. Within the upper 800 m, all of the transport in the northern band and about 70% of the transport in the southern band recirculates in the eastern basin. Additionally, expendable bathythermograph data from the Azores Current region indicate an increase of eddy potential energy from winter to summer

Thermobaric control of gravitational potential energy generation by diapycnal mixing in the deep ocean

Sources and sinks of gravitational potential energy (GPE) play a rate-limiting role in the large scale ocean circulation. A key source is turbulent diapycnal mixing, whereby irre- versible mixing across isoneutral surfaces is enhanced by turbulent straining of these surfaces. This has motivated international observational efforts to map diapycnal mixing in the global ocean. However, in order to accurately relate the GPE supplied to the large scale circulation by diapycnal mixing to the mixing energy source, it is first necessary to determine the ratio, ξ , of the GPE generation rate to the available potential energy dissipation rate associated with turbulent mixing. Here, the link between GPE and hydro- static pressure is used to derive the GPE budget for a com- pressible ocean with a nonlinear equation of state. The role of diapycnal mixing is isolated and from this a global cli- matological distribution of ξ is calculated. It is shown that, for a given source of mixing energy, typically three times as much GPE is generated if the mixing takes place in bottom waters rather than in the pycnocline. This is due to GPE destruction by cabbelling in the pycnocline, as opposed to thermobaric enhancement of GPE generation by diapycnal mixing in the deep ocean

Classic Article: Steady flow in a frictionless homogenous ocean

A mathematical model is developed to study the free (frictionless) steady horizontal flow which can occur in a homogeneous ocean of constant depth. The flow satisfies the dynamic constraint that the vertical component of absolute vorticity is constant along a streamline. The conclusion is reached that in an enclosed ocean a free steady circulation cannot have any slow broad eastward currents. The eastward currents must occur as narrow streams of high velocity and high relative vorticity. Intensified currents are present along the eastern and western coasts. The theory which is developed for the homogeneous ocean of constant depth can be applied to the two-layer ocean if the horizontal divergence of flow is negligible. If the horizontal divergence is not negligible, then the intensification of poleward currents is more pronounced and that of equatorward currents less pronounced as compared with the homogeneous ocean

Nonlinear limits to ocean thermal structure

The nonlinear volume changes associated with diffusion and mixing of different seawater types produce significant conversions of gravitational potential energy to kinetic energy to maintain and enhance mixing processes and to limit the magnitudes of temperature gradients that can persist in the ocean. Several examples are given to illustrate these critical temperature gradients beyond which conversion exceeds local energy consumption by mixing. The vertical temperature gradients in the Gulf Stream reduce downstream from Cape Hatteras to the critical limit found in the North Atlantic thermocline. The limiting gradients are also seen in surface thermoclines and in staircase structures. Although the theoretical interpretation of the nonlinear limiting processes is still incomplete, the observational evidence is compelling for further study of these mechanisms

Steady flow in a frictionless homogeneous ocean

A mathematical model is developed to study the free (frictionless) steady horizontal flow which can occur in a homogeneous ocean of constant depth. The flow satisfies the dynamic constraint that the vertical component of absolute vorticity is constant along a streamline...