gsw_enthalpy_second_derivatives

second derivatives of enthalpy

Contents

USAGE:

[h_SA_SA, h_SA_CT, h_CT_CT] = gsw_enthalpy_2nd_derivatives(SA,CT,p)

DESCRIPTION:

Calculates the following three second-order derivatives of specific
enthalpy (h),
 (1) h_SA_SA, second order derivative with respect to Absolute Salinity
     at constant CT & p.
 (2) h_SA_CT, second order derivative with respect to SA & CT at
     constant p.
 (3) h_CT_CT, second order derivative with respect to CT at constant
     SA & p.
TEOS-10
Click for a more detailed description of the second
derivatives of specific enthalpy.

INPUT:

SA  =  Absolute Salinity                                        [ g/kg ]
CT  =  Conservative Temperature                                [ deg C ]
p   =  sea pressure                                             [ dbar ]
       (i.e. absolute pressure - 10.1325 dbar)
SA & CT need to have the same dimensions.
p may have dimensions 1x1 or Mx1 or 1xN or MxN, where SA & CT are MxN.

OUTPUT:

h_SA_SA  =  The second derivative of specific enthalpy with respect to
            Absolute Salinity at constant CT & p.    [ J/(kg (g/kg)^2) ]
h_SA_CT  =  The second derivative of specific enthalpy with respect to
            SA and CT at constant p.                  [ J/(kg K(g/kg)) ]
h_CT_CT  =  The second derivative of specific enthalpy with respect to
            CT at constant SA and p.                      [ J/(kg K^2) ]

EXAMPLE:

SA = [34.7118; 34.8915; 35.0256; 34.8472; 34.7366; 34.7324;]
t =  [28.7856; 28.4329; 22.8103; 10.2600;  6.8863;  4.4036;]
p =  [     10;      50;     125;     250;     600;    1000;]
[h_SA_SA, h_SA_CT, h_CT_CT] = gsw_enthalpy_second_derivatives(SA,CT,p)
h_SA_SA =
  0.000082752219662
  0.000414449264358
  0.001089849221923
  0.002473058502734
  0.006107254340947
  0.010388021033928
  
 h_SA_CT =
 
  0.000130254397677
  0.000654928172110
  0.001880402010403
  0.005474186056408
  0.014339376841409
  0.025245467907619
  
 h_CT_CT =

  0.000714090119067
  0.003584609310758
  0.009736868475975
  0.024061418823850
  0.061537073639407
  0.107564288175526

AUTHOR:

Trevor McDougall and Paul Barker.  [ help_gsw@csiro.au ]

VERSION NUMBER:

2.0 (26th August, 2010)

REFERENCES:

IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of
 seawater - 2010: Calculation and use of thermodynamic properties.
 Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
 UNESCO (English), 196 pp.  Available from the TEOS-10 web site.
  See Notes on the first and second order isobaric derivatives of
  specific enthalpy.
McDougall T. J., D. R. Jackett, P. M. Barker, C. Roberts-Thomson, R.
 Feistel and R. W. Hallberg, 2010:  A computationally efficient 25-term
 expression for the density of seawater in terms of Conservative
 Temperature, and related properties of seawater.  To be submitted
 to Ocean Science Discussions.
This software is available from http://www.TEOS-10.org