Gibbs Seawater (GSW) Oceanographic Toolbox of TEOS–10
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Thermodynamically Consistent Semi-Compressible Fluids: A
Thermodynamically consistent semi-compressible fluids: a variational perspective Christopher Eldred [email protected] Org 01446 (Computational Science), Sandia National Laboratories Fran¸coisGay-Balmaz [email protected] CNRS, Ecole Normale Sup´erieurede Paris, LMD Abstract This paper presents (Lagrangian) variational formulations for single and multicompo- nent semi-compressible fluids with both reversible (entropy-conserving) and irreversible (entropy-generating) processes. Semi-compressible fluids are useful in describing low-Mach dynamics, since they are soundproof. These models find wide use in many areas of fluid dynamics, including both geophysical and astrophysical fluid dynamics. Specifically, the Boussinesq, anelastic and pseudoincompressible equations are developed through a uni- fied treatment valid for arbitrary Riemannian manifolds, thermodynamic potentials and geopotentials. By design, these formulations obey the 1st and 2nd laws of thermody- namics, ensuring their thermodynamic consistency. This general approach extends and unifies existing work, and helps clarify the thermodynamics of semi-compressible fluids. To further this goal, evolution equations are presented for a wide range of thermodynamic variables: entropy density s, specific entropy η, buoyancy b, temperature T , potential temperature θ and a generic entropic variable χ; along with a general definition of buoy- ancy valid for all three semicompressible models and arbitrary geopotentials. Finally, the elliptic equation is developed for all three equation sets in the case of reversible dy- namics, and for the Boussinesq/anelastic equations in the case of irreversible dynamics; and some discussion is given of the difficulty in formulating the elliptic equation for the pseudoincompressible equations with irreversible dynamics. arXiv:2102.08293v1 [physics.flu-dyn] 16 Feb 2021 1 Introduction Many important situations in fluid dynamics, especially astrophysical and geophysical fluids, have fluid velocities significant less than the speed of sound. -
Notes on the Function Gsw Stabilise SA Const T (SA,CT,P)
Notes on the function gsw_stabilise_SA_const_t (SA,CT,p) Stabilisation of hydrographic profiles 1. Introduction The vertical stability of a water column is described by the square of the buoyancy frequency ( N 2 ). In this paper we follow the N 2 definition similar to that used in Jackett and McDougall (1995), now defined in terms of the vertical gradients of Absolute Salinity and Conservative Temperature (these being the salinity and temperature variables of TEOS-10, IOC et al. (2010)) αβΘΘ∂Θ ∂S gN−22=−+A , (1) vP∂∂xy, v Pxy, where the vertical derivatives are taken at constant latitude and longitude with respect to absolute pressure P . The gravitational acceleration is given the symbol g and v is the specific volume of seawater, being the reciprocal of in situ density ρ , and the thermal expansion and haline contraction coefficients defined with respect to Absolute Salinity SA and Conservative Temperature Θ are given by 1 ∂v 1 ∂v α Θ = and β Θ = − . (2) v ∂Θ vS∂ SpA , A Θ, p There are many ways to evaluate N 2 and McDougall and Barker (2014) list six of the most commonly used definitions and they show that they are all equivalent. In this paper we will also use the expression for N 2 written in terms of the vertical gradient of in situ temperature, namely αβtt∂T ∂S gN−22= − −Γ + A , (3) ∂∂ v Pxy, vPxy, where Γ is the adiabatic lapse rate, and the thermal expansion and haline contraction coefficients defined with respect to Absolute Salinity SA and in situ temperature are given by 1 ∂v 1 ∂v α t = and β t = − . -
GSW Toolbox List
Page 1. GSW version 3.06.12 Gibbs SeaWater (GSW) Oceanographic Toolbox of TEOS–10 Practical Salinity (SP), PSS-78 specific volume, density and enthalpy gsw_SP_from_C Practical Salinity from conductivity, C (incl. for SP < 2) gsw_specvol specific volume gsw_C_from_SP conductivity, C, from Practical Salinity (incl. for SP < 2) gsw_alpha thermal expansion coefficient with respect to CT gsw_SP_from_R Practical Salinity from conductivity ratio, R (incl. for SP < 2) gsw_beta saline contraction coefficient at constant CT gsw_R_from_SP conductivity ratio, R, from Practical Salinity (incl. for SP < 2) gsw_alpha_on_beta alpha divided by beta gsw_SP_salinometer Practical Salinity from a laboratory salinometer (incl. for SP < 2) gsw_specvol_alpha_beta specific volume, thermal expansion and saline contraction coefficients gsw_SP_from_SK Practical Salinity from Knudsen Salinity gsw_specvol_first_derivatives first derivatives of specific volume gsw_specvol_second_derivatives second derivatives of specific volume Absolute Salinity (SA), Preformed Salinity (Sstar) and Conservative Temperature (CT) gsw_specvol_first_derivatives_wrt_enthalpy first derivatives of specific volume with respect to enthalpy gsw_specvol_second_derivatives_wrt_enthalpy second derivatives of specific volume with respect to enthalpy gsw_SA_from_SP Absolute Salinity from Practical Salinity gsw_specvol_anom specific volume anomaly gsw_Sstar_from_SP Preformed Salinity from Practical Salinity gsw_specvol_anom_standard specific volume anomaly realtive to SSO & 0°C gsw_CT_from_t Conservative -
Thermal Properties for the Thermal-Hydraulics Analyses of the BR2 Maximum Nominal Heat Flux
ANL/RERTR/TM-11-20 Rev. 1 Thermal Properties for the Thermal-Hydraulics Analyses of the BR2 Maximum Nominal Heat Flux Rev. 1 Nuclear Engineering Division About Argonne National Laboratory Argonne is a U.S. Department of Energy laboratory managed by UChicago Argonne, LLC under contract DE-AC02-06CH11357. The Laboratory’s main facility is outside Chicago, at 9700 South Cass Avenue, Argonne, Illinois 60439. For information about Argonne and its pioneering science and technology programs, see www.anl.gov. DOCUMENT AVAILABILITY Online Access: U.S. Department of Energy (DOE) reports produced after 1991 and a growing number of pre-1991 documents are available free via DOE’s SciTech Connect (http://www.osti.gov/scitech/) Reports not in digital format may be purchased by the public from the National Technical Information Service (NTIS): U.S. Department of Commerce National Technical Information Service 5301 Shawnee Rd Alexandria, VA 22312 www.ntis.gov Phone: (800) 553-NTIS (6847) or (703) 605-6000 Fax: (703) 605-6900 Email: [email protected] Reports not in digital format are available to DOE and DOE contractors from the Office of Scientific and Technical Information (OSTI): U.S. Department of Energy Office of Scientific and Technical Information P. O. B o x 6 2 Oak Ridge, TN 37831-0062 www.osti.gov Phone: (865) 576-8401 Fax: (865) 576-5728 Email: [email protected] Disclaimer This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor UChicago Argonne, LLC, nor any of their employees or officers, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. -
Chapter 2 Approximate Thermodynamics
Chapter 2 Approximate Thermodynamics 2.1 Atmosphere Various texts (Byers 1965, Wallace and Hobbs 2006) provide elementary treatments of at- mospheric thermodynamics, while Iribarne and Godson (1981) and Emanuel (1994) present more advanced treatments. We provide only an approximate treatment which is accept- able for idealized calculations, but must be replaced by a more accurate representation if quantitative comparisons with the real world are desired. 2.1.1 Dry entropy In an atmosphere without moisture the ideal gas law for dry air is p = R T (2.1) ρ d where p is the pressure, ρ is the air density, T is the absolute temperature, and Rd = R/md, R being the universal gas constant and md the molecular weight of dry air. If moisture is present there are minor modications to this equation, which we ignore here. The dry entropy per unit mass of air is sd = Cp ln(T/TR) − Rd ln(p/pR) (2.2) where Cp is the mass (not molar) specic heat of dry air at constant pressure, TR is a constant reference temperature (say 300 K), and pR is a constant reference pressure (say 1000 hPa). Recall that the specic heats at constant pressure and volume (Cv) are related to the gas constant by Cp − Cv = Rd. (2.3) A variable related to the dry entropy is the potential temperature θ, which is dened Rd/Cp θ = TR exp(sd/Cp) = T (pR/p) . (2.4) The potential temperature is the temperature air would have if it were compressed or ex- panded (without condensation of water) in a reversible adiabatic fashion to the reference pressure pR. -
Spiciness Theory Revisited, with New Views on Neutral Density, Orthogonality, and Passiveness
Ocean Sci., 17, 203–219, 2021 https://doi.org/10.5194/os-17-203-2021 © Author(s) 2021. This work is distributed under the Creative Commons Attribution 4.0 License. Spiciness theory revisited, with new views on neutral density, orthogonality, and passiveness Rémi Tailleux Dept. of Meteorology, University of Reading, Earley Gate, RG6 6ET Reading, United Kingdom Correspondence: Rémi Tailleux ([email protected]) Received: 26 April 2020 – Discussion started: 20 May 2020 Revised: 8 December 2020 – Accepted: 9 December 2020 – Published: 28 January 2021 Abstract. This paper clarifies the theoretical basis for con- 1 Introduction structing spiciness variables optimal for characterising ocean water masses. Three essential ingredients are identified: (1) a As is well known, three independent variables are needed to material density variable γ that is as neutral as feasible, (2) a fully characterise the thermodynamic state of a fluid parcel in material state function ξ independent of γ but otherwise ar- the standard approximation of seawater as a binary fluid. The bitrary, and (3) an empirically determined reference function standard description usually relies on the use of a tempera- ξr(γ / of γ representing the imagined behaviour of ξ in a ture variable (such as potential temperature θ, in situ temper- notional spiceless ocean. Ingredient (1) is required because ature T , or Conservative Temperature 2), a salinity variable contrary to what is often assumed, it is not the properties im- (such as reference composition salinity S or Absolute Salin- posed on ξ (such as orthogonality) that determine its dynam- ity SA), and pressure p. -
Equations of Motion Using Thermodynamic Coordinates
2814 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 30 Equations of Motion Using Thermodynamic Coordinates ROLAND A. DE SZOEKE College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, Oregon (Manuscript received 21 October 1998, in ®nal form 30 December 1999) ABSTRACT The forms of the primitive equations of motion and continuity are obtained when an arbitrary thermodynamic state variableÐrestricted only to be vertically monotonicÐis used as the vertical coordinate. Natural general- izations of the Montgomery and Exner functions suggest themselves. For a multicomponent ¯uid like seawater the dependence of the coordinate on salinity, coupled with the thermobaric effect, generates contributions to the momentum balance from the salinity gradient, multiplied by a thermodynamic coef®cient that can be com- pletely described given the coordinate variable and the equation of state. In the vorticity balance this term produces a contribution identi®ed with the baroclinicity vector. Only when the coordinate variable is a function only of pressure and in situ speci®c volume does the coef®cient of salinity gradient vanish and the baroclinicity vector disappear. This coef®cient is explicitly calculated and displayed for potential speci®c volume as thermodynamic coor- dinate, and for patched potential speci®c volume, where different reference pressures are used in various pressure subranges. Except within a few hundred decibars of the reference pressures, the salinity-gradient coef®cient is not negligible and ought to be taken into account in ocean circulation models. 1. Introduction perature surfaces is a potential for the acceleration ®eld, Potential temperature, the temperature a ¯uid parcel when friction is negligible. Because the gradient of this would have if removed adiabatically and reversibly from function gives the geostrophic ¯ow when it balances ambient pressure to a reference pressure, is a valuable Coriolis force, it is also called the geostrophic stream- concept in the study of the atmosphere and oceans. -
Recovery of Temperature, Salinity, and Potential Density from Ocean
PUBLICATIONS Journal of Geophysical Research: Oceans RESEARCH ARTICLE Recovery of temperature, salinity, and potential density from 10.1002/2013JC009662 ocean reflectivity Key Points: Berta Biescas1,2, Barry R. Ruddick1, Mladen R. Nedimovic3,4,5, Valentı Sallare`s2, Guillermo Bornstein2, Recovery of oceanic T, S, and and Jhon F. Mojica2 potential density from acoustic reflectivity data 1Department of Oceanography, Dalhousie University, Halifax, Nova Scotia, Canada, 2Department of Marine Geology, Thermal anomalies observations at 3 the Mediterranean tongue level Institut de Cie`ncies del Mar ICM-CSIC, Barcelona, Spain, Department of Earth’s Sciences, Dalhousie University, Halifax, 4 5 Comparison between acoustic Nova Scotia, Canada, Lamont-Doherty Earth Observatory of Columbia University, Palisades, New York, USA, University of reflectors in the ocean and isopycnals Texas Institute for Geophysics, Austin, Texas, USA Supporting Information: Methods Abstract This work explores a method to recover temperature, salinity, and potential density of the Supporting figures ocean using acoustic reflectivity data and time and space coincident expendable bathythermographs (XBT). The acoustically derived (vertical frequency >10 Hz) and the XBT-derived (vertical frequency <10 Hz) impe- Correspondence to: dances are summed in the time domain to form impedance profiles. Temperature (T) and salinity (S) are B. Biescas, then calculated from impedance using the international thermodynamics equations of seawater (GSW [email protected] TEOS-10) and an empirical T-S relation derived with neural networks; and finally potential density (q) is cal- culated from T and S. The main difference between this method and previous inversion works done from Citation: Biescas, B., B. R. Ruddick, M. R. real multichannel seismic reflection (MCS) data recorded in the ocean, is that it inverts density and it does Nedimovic, V. -
W.R.Young 2010. Dynamic Enthalpy, Conservative Temperature, and The
394 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 40 Dynamic Enthalpy, Conservative Temperature, and the Seawater Boussinesq Approximation WILLIAM R. YOUNG Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California (Manuscript received 8 June 2009, in final form 27 August 2009) ABSTRACT A new seawater Boussinesq system is introduced, and it is shown that this approximation to the equations of motion of a compressible binary solution has an energy conservation law that is a consistent approximation to the Bernoulli equation of the full system. The seawater Boussinesq approximation simplifies the mass con- servation equation to $ Á u 5 0, employs the nonlinear equation of state of seawater to obtain the buoyancy force, and uses the conservative temperature introduced by McDougall as a thermal variable. The conserved energy consists of the kinetic energy plus the Boussinesq dynamic enthalpy hz, which is the integral of the buoyancy with respect to geopotential height Z at a fixed conservative temperature and salinity. In the Boussinesq approximation, the full specific enthalpy h is the sum of four terms: McDougall’s potential en- z thalpy, minus the geopotential g0Z, plus the Boussinesq dynamic enthalpy h , and plus the dynamic pressure. The seawater Boussinesq approximation removes the large and dynamically inert contributions to h, and it reveals the important conversions between kinetic energy and hz. 1. Introduction Boussinesq approximation in which thermodynamic re- lations are simplified by linearizing the EOS (Spiegel This note demonstrates that the Boussinesq approxi- and Veronis 1960). The extra complexity of the seawater mation used in physical oceanography has an energy Boussinesq approximation is required to capture ocean- conservation law that consistently approximates en- ographic processes, such as cabbeling and the thermo- ergy conservation in the full equations of motion. -
Observational and Energetics Constraints on the Non-Conservation of Potential/Conservative Temperature and Implications for Ocean Modelling
Observational and energetics constraints on the non-conservation of potential/conservative temperature and implications for ocean modelling R´emi Tailleux Department of Meteorology, University of Reading, Earley Gate, PO Box 243, Reading, RG6 6BB, United Kingdom. Email: [email protected], Telephone: +44(0)1183788328. Fax: +44(0)1183788316. Abstract This paper elucidates the nature of heat non conservation by showing that the nonconservative production/destruction of po- tential temperature and entropy is related to the production/destruction by surface buoyancy fluxes, while the non conservation of potential enthalpy/conservative temperature is a direct measure of the compressible work of expansion/contraction. These results are used to show how to estimate the nonconservative production of potential temperature, entropy and conservative temperature from observations and from numerical ocean model estimates of the ocean energy cycle. The results suggest that the non conser- vation of potential temperature could be easily accounted for in numerical ocean models with a simple modification of existing codes, providing a potential alternative option to TEOS10 recommendation of switching from potential temperature to conservative temperature. Keywords: ocean modelling, conservation equations, heat non-conservation, energy conservation, potential temperature, conservative temperature 1. Introduction θ in coarse-grained primitive hydrostatic Boussinesq models. Specifically, the method works as follows. Starting from the The issue of -
Numerical Implementation and Oceanographic Application of the Gibbs Thermodynamic Potential of Seawater R
Numerical implementation and oceanographic application of the Gibbs thermodynamic potential of seawater R. Feistel To cite this version: R. Feistel. Numerical implementation and oceanographic application of the Gibbs thermodynamic po- tential of seawater. Ocean Science, European Geosciences Union, 2005, 1 (1), pp.9-16. hal-00298266 HAL Id: hal-00298266 https://hal.archives-ouvertes.fr/hal-00298266 Submitted on 12 Apr 2005 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Ocean Science, 1, 9–16, 2005 www.ocean-science.net/os/1/9/ Ocean Science SRef-ID: 1812-0792/os/2005-1-9 European Geosciences Union Numerical implementation and oceanographic application of the Gibbs thermodynamic potential of seawater R. Feistel Baltic Sea Research Institute, Seestrasse 15, 18119 Warnemunde,¨ Germany Received: 11 November 2004 – Published in Ocean Science Discussions: 17 November 2004 Revised: 27 January 2005 – Accepted: 18 March 2005 – Published: 12 April 2005 Abstract. The 2003 Gibbs thermodynamic potential func- structure was chosen for its simplicity in analytical partial tion represents a very accurate, compact, consistent and com- derivatives and its numerical implementation, as discussed prehensive formulation of equilibrium properties of seawater. in Feistel (1993). -
Numerical Implementation and Oceanographic Application of the Gibbs Thermodynamic Potential of Seawater R
Numerical implementation and oceanographic application of the Gibbs thermodynamic potential of seawater R. Feistel To cite this version: R. Feistel. Numerical implementation and oceanographic application of the Gibbs thermodynamic potential of seawater. Ocean Science Discussions, European Geosciences Union, 2004, 1 (1), pp.1-19. hal-00298363 HAL Id: hal-00298363 https://hal.archives-ouvertes.fr/hal-00298363 Submitted on 17 Nov 2004 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Ocean Science Discussions, 1, 1–19, 2004 Ocean Science OSD www.ocean-science.net/osd/1/1/ Discussions SRef-ID: 1812-0822/osd/2004-1-1 1, 1–19, 2004 European Geosciences Union Numerical implementation and oceanographic application R. Feistel Numerical implementation and oceanographic application of the Gibbs Title Page thermodynamic potential of seawater Abstract Introduction Conclusions References R. Feistel Tables Figures Baltic Sea Research Institute, Seestraße 15, D-18119 Warnemunde,¨ Germany Received: 11 November 2004 – Accepted: 16 November 2004 – Published: 17 November J I 2004 J I Correspondence to: R. Feistel ([email protected]) Back Close © 2004 Author(s). This work is licensed under a Creative Commons License. Full Screen / Esc Print Version Interactive Discussion EGU 1 Abstract OSD The 2003 Gibbs thermodynamic potential function represents a very accurate, com- 1, 1–19, 2004 pact, consistent and comprehensive formulation of equilibrium properties of seawater.