Streamfunctions for the lateral velocity vector in a compressible ocean

Streamfunctions are known in (i) geopotential surfaces, (ii) isobaric surfaces, (iii) surfaces of constant in situ density, ρ, and (iv) surfaces of constant steric anomaly, δ. lt is desirable to map a streamfunction in a surface in which most of the mixing and movement of water-masses occurs so that the streamlines obtained in two dimensions will approximate the flow paths of the full three-dimensional flow field. These surfaces are believed to be neutral surfaces, but while a streamfunction exists in a neutral surface, we do not as yet have a closed expression for it in terms of a vertical integral of hydrographic quantities, and quite possibly we never will. An error analysis performed on the use of the Montgomery function (acceleration potential) in a neutral surface shows that the typical error at a depth of 1000 m is about 2 mm/s. To reduce the velocity error below 0.5 mm/s at 1000 m, one would need to map the Montgomery function in a surface that differed in slope from a steric anomaly surface by less than 5 × 10–6. An error analysis is also performed on the approximate Bernoulli function that is found by integrating gzi∂ρ/∂z in the vertical, showing that errors in this Bernoulli function over a depth range of 1000 m are equivalent to a lateral velocity error of 3 mm/s. These examples demonstrate that great care must be taken in calculating a streamfunction in any surface in which an exact expression is unknown. Expressions for the relative slopes of several surfaces (surfaces of constant pressure, steric anomaly surfaces and neutral surfaces) are also derived

Flux measurements across a finger interface at low values of the stability ratio

We present the results of laboratory experiments across a sharp finger interface using heat and salt as the properties which contribute to density. Values of the stability ratio Rp as low as 1.2 were achieved so the results approach the range of Rp which is of interest in the ocean. The buoyancy flux ratio, corrected for vertical heat conduction, Rf* was found to depend on Rp, but at Rp = 1.2, Rf* is still only 0.65 ± 0.1. Values of Stern\u27s number A = βFs(l – Rf)/ν(αTz – βSz) were found to depend on the magnitude of the step in salinity across the interface as well as on Rp. Most of our experiments were performed with small contrasts in salinity between the layers and Stern\u27s number was found to increase as this salinity difference decreased. On the basis of our measurements of A, we believe that pure vertical heat conduction will not be significant in the ocean

Spiciness

We define and present algorithms for spiciness, which is an oceanographic variable whose isopycnal variations reflect isopycnal water-mass contrasts in density units. Discussion of spiciness in the oceanographic literature has often concentrated on its supposed orthogonality to isopycnals on the salinity-temperature diagram and how this orthogonal nature means that spiciness is a “passive” thermodynamic variable. Here we show that this “orthogonal” property is devoid of physical meaning. Moreover, it is emphasized that the notion of “orthogonality” on the salinity-temperature diagram does not give rise to a passive thermodynamic variable. Rather, the passive nature of variations of any thermodynamic variable is gained by evaluating those variations along isopycnals so that, for example, the isopycnal variations of both Absolute Salinity and Conservative Temperature are passive. The advantage of using isopycnal variations of our definition of spiciness is that this measures the passive spatial variations of water-mass properties in density units. The spiciness variables presented here have been derived using the equation of state from the International Thermodynamic Equation of Seawater – 2010

The material derivative of neutral density

An expression for the rate of change of neutral density following a fluid parcel (the material derivative) is derived and checked numerically. This expression can be used to quantify the degree to which neutral density varies even under purely adiabatic and isohaline motions. We also present an approximate form of neutral density, namely a rational function of only two variables, either salinity and conservative temperature or salinity and potential temperature

Does the nonlinearity of the equation of state impose an upper bound on the buoyancy frequency?

Mixing in the ocean is usually accompanied by a net reduction in volume caused by the nonlinear nature of the equation of state. This contraction-on-mixing at a certain depth implies that the whole water column above this depth slumps a little and so suffers a reduction in gravitational potential energy. Under certain circumstances the gravitational potential energy of the entire water column can decrease as a consequence of mixing activity at a certain depth. We examine Fofonoff\u27s hypothesis that in these circumstances the net reduction of gravitational potential energy of the whole water column causes a local increase in the turbulent mixing activity at the location of the original mixing. Fofonoff proposed that this increased local mixing diffuses the local property gradients until the criterion for positive feedback is no longer satisfied, so providing an upper bound for the vertical stratification in the ocean. Bearing in mind the relatively inefficient nature of turbulent mixing at causing diapycnal fluxes (the majority of the turbulent kinetic energy goes directly into internal energy), we find that the criterion for positive feedback is a factor of approximately seven more difficult to achieve than has been realized to date. An examination of oceanic data shows that while Fofonoff\u27s original criterion for positive feedback is often exceeded, the more appropriate criterion is almost never approached. The positive feedback hypothesis assumes that the reduction in the gravitational potential energy of the whole water column appears at the location of the original mixing as an increase in the turbulent mixing activity. We show that this very focused oceanic response is extremely difficult to justify. For example there is no such feedback in a strictly one-dimensional water column; rather all of the reduction in gravitational potential energy appears as an increase in internal energy at the depth of the original mixing and there is no possibility of any positive feedback to increase the turbulent mixing. As the positive feedback hypothesis is lacking a convincing theoretical basis and is not supported by oceanic data, we do not believe that it acts as an effective upper bound on oceanic stratification

IAPSO: tales from the ocean frontier

Our 21st century perspective on the oceans is due to the realization that knowledge of them and specifically their role in earth's climate are central to determining the future health of our planet. This present knowledge of the oceans builds on the farsighted work of people who, over the past century, worked to address seemingly intractable problems. The International Association for the Physical Sciences of the Oceans (IAPSO) has, over that long time span, promoted and supported the international approach that is now commonplace and has championed the provision of cross-cutting activities, the value of which we now fully recognize. This paper describes the key events in IAPSO's history and the roles played by the scientists involved

Basalts erupted along the Tongan fore-arc during subduction initiation: evidence from geochronology of dredged rocks from the Tonga fore-arc and trench

A wide variety of different rock types were dredged from the Tonga fore arc and trench between 8000 and 3000 m water depths by the 1996 Boomerang voyage. 40Ar-39Ar whole rock and U-Pb zircon dating suggest that these fore arc rocks were erupted episodically from the Cretaceous to the Pliocene (102 to 2 Ma). The geochemistry suggests that MOR-type basalts and dolerites were erupted in the Cretaceous, that island arc tholeiites were erupted in the Eocene and that back arc basin and island arc tholeiite and boninite were erupted episodically after this time. The ages generally become younger northward suggesting that fore arc crust was created in the south at around 48–52 Ma and was extended northward between 35 and 28 Ma, between 9 and 15 Ma and continuing to the present-day. The episodic formation of the fore arc crust suggested by this data is very different to existing models for fore arc formation based on the Bonin-Marianas arc. The Bonin-Marianas based models postulate that the basaltic fore arc rocks were created between 52 and 49 Ma at the beginning of subduction above a rapidly foundering west-dipping slab. Instead a model where the 52 Ma basalts that are presently in a fore arc position were created in the arc-back arc transition behind the 57–35 Ma Loyalty-Three Kings arc and placed into a fore arc setting after arc reversal following the start of collision with New Caledonia is proposed for the oldest rocks in Tonga. This is followed by growth of the fore arc northward with continued eruption of back arc and boninitic magmas after that time

Water-mass transformations in a neutral density framework and the key role of light penetration

A new formulation is proposed for the evaluation of the dianeutral transport in the ocean. The method represents an extension of the classical diagnostic approach for estimating the water-mass formation from the buoyancy balance. The inclusion of internal sources such as the penetrative solar shortwave radiation (i.e., depth-dependent heat transfer) in the estimate of surface buoyancy fluxes has a significant impact in several oceanic regions, and the former simplified formulation can lead to a 100% error in the estimate of water-mass formation due to surface buoyancy fluxes. Furthermore, internal mixing can also be overestimated in inversions of in situ data when the shortwave radiation is not allowed to be penetrative.The method examines the evolution equation of neutral density via the tendencies of potential temperature and salinity. The neutral density framework does not require the choice of a reference pressure and thus, unlike previous approaches that consider potential density, it is well suited for examining the whole open-ocean water column.The methodology is easy to implement, particularly for ocean numerical models. The authors present here its application to a long simulation made with an ice–ocean global model, which allowed the method to be validated.<br/