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

Lectures on Thermodynamics and Ocean Mixing (September 2018)

Course Outline The aim of these lectures is to present the fundamentals of thermodynamics in the context of fluid flow and mixing in the ocean and the interaction of seawater and ice. The course will develop thermodynamic concepts that are needed to account for the flow of heat in the coupled atmosphere-ocean-ice system of planet earth. The thermophysical quantities in the ocean are functions of three variables, namely salinity, temperature and pressure, and this functional dependence complicates what is even meant by seemingly simple concepts such as "specific volume", "specific heat" and "heat content per unit mass". For example, what is a meaningful definition of an “isopycnal surface”? The ocean and atmosphere are in a continuous state of turbulent motion, and the course will derive the appropriate theoretical framework in which these time varying motions should be examined. This course introduces the conservation laws that govern the fluid dynamics the ocean, in particular concentrating on what variables should be carried in ocean models given that the ocean is subject to turbulent fluxes rather than simply molecular fluxes of heat and salt. The distinctions between variables that are conservative versus those that are non-conservative are emphasized. Several new results on the interaction of seawater and ice, and particularly of frazil ice, will be introduced. These results add thermodynamic rigor to existing practices. This rigor is now possible because the thermodynamic properties of seawater, ice and humid air have been redefined in 2010, as adopted by the Intergovernmental Oceanographic Commission. Frazil ice is the name used when small crystals of ice form in cold seawater such as occurs at the underside of ice shelves near the poles. The course will explore some of the implications of this thermodynamic knowledge for how oceanic data should be analyzed. For example, it is possible to developed a closed expression for the mean absolute velocity in the ocean, but it seems to depend on the local value “neutral helicity” of the ocean; a property that is normally understood as being the course of the mathematically ill-defined nature of neutral density surfaces in the ocean. Results such as this are at the edge of our oceanographic understanding and need further research. We now know that diapycnal mixing in the deep ocean is stronger near the sea floor. The course will discuss the dynamical implications of this bottom-intensification of diapycnal mixing. We will find that the net diapycnal upwelling of Bottom Water is actually the net GEOMAR Thermodynamics and Ocean Mixing Lectures, Sep. 2018 result of a larger upwelling across density surfaces in the bottom boundary layer partially offset by diapycnal sinking motion in the ocean interior

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

Constraints on developing organic poultry production OF0128T

This study aimed to provide MAFF with an assessment of the potential for organic poultry production in England and Wales and, in particular, to identify likely constraints on the development of organic poultry production enterprises, including physical, financial and market factors. The study will e composed of 3 specific objectives outlines as follows, together with ways in which they might be achieved: 1. Definition of the physical production parameters for alternative poultry production to organic standards, with particular emphasis on free range and perchery systems and their respective input requirements and output potential. A detailed literature review will be conducted and consultations will be made with existing organic poultry producers. Direct experience with conventional free range and perchery production systems at the National Institute of Poultry Husbandry and other published information will be utilised to identify potential areas for improvement and/or future research; 2. Investigation of market opportunities for organic poulry meat and egg production in England and Wales, through an examination of the existing market structure and an appraisal of existing and potential marketing strategies. The market for organic poultry meat and eggs will be analysed for shape, size and future potential. Alternative marketing approaches for this sector will be considered and a desk study will be conducted involving a review of trade journals and poultry sector business reports, together with consultation with key players in the sector; and 3.Formulation of an appropriate farm business plan to illustrate the relative profitability of alternative systems of organic poultry production, including the projection of cash flows under given assumptions and the application of sensitivity analyses to key variables influencing profitability. The business plan will cover a wide range of areas, including: industry and market size; producer strategy; capital requirements,; marketing strategy; projected funds; and building, labour and statutory requirements

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

OMIP contribution to CMIP6: experimental and diagnostic protocol for the physical component of the Ocean Model Intercomparison Project

The Ocean Model Intercomparison Project (OMIP) is an endorsed project in the Coupled Model Intercomparison Project Phase 6 (CMIP6). OMIP addresses CMIP6 science questions, investigating the origins and consequences of systematic model biases. It does so by providing a framework for evaluating (including assessment of systematic biases), understanding, and improving ocean, sea-ice, tracer, and biogeochemical components of climate and earth system models contributing to CMIP6. Among the WCRP Grand Challenges in climate science (GCs), OMIP primarily contributes to the regional sea level change and near-term (climate/decadal) prediction GCs. OMIP provides (a) an experimental protocol for global ocean/sea-ice models run with a prescribed atmospheric forcing; and (b) a protocol for ocean diagnostics to be saved as part of CMIP6. We focus here on the physical component of OMIP, with a companion paper (Orr et al., 2016) detailing methods for the inert chemistry and interactive biogeochemistry. The physical portion of the OMIP experimental protocol follows the interannual Coordinated Ocean-ice Reference Experiments (CORE-II). Since 2009, CORE-I (Normal Year Forcing) and CORE-II (Interannual Forcing) have become the standard methods to evaluate global ocean/sea-ice simulations and to examine mechanisms for forced ocean climate variability. The OMIP diagnostic protocol is relevant for any ocean model component of CMIP6, including the DECK (Diagnostic, Evaluation and Characterization of Klima experiments), historical simulations, FAFMIP (Flux Anomaly Forced MIP), C4MIP (Coupled Carbon Cycle Climate MIP), DAMIP (Detection and Attribution MIP), DCPP (Decadal Climate Prediction Project), ScenarioMIP, HighResMIP (High Resolution MIP), as well as the ocean/sea-ice OMIP simulations