gsw_internal_energy_second_derivatives_CT_exact

Contents

USAGE:

[u_SA_SA, u_SA_CT, u_CT_CT, u_SA_P, u_CT_P] = ...
               gsw_internal_energy_second_derivatives_CT_exact(SA,CT,p)

DESCRIPTION:

Calculates the following five second-order derivatives of 
  internal energy,
 (1) u_SA_SA, second order derivative with respect to Absolute Salinity
     at constant CT & p.
 (2) u_SA_CT, second order derivative with respect to SA & CT at
     constant p.
 (3) u_CT_CT, second order derivative with respect to CT at constant
     SA & p.
 (4) u_SA_P, second-order derivative with respect to SA & P at 
     constant CT. 
 (5) u_CT_P, second-order derivative with respect to CT & P at 
     constant SA     

Note that this function uses the full Gibbs function.  There is an 
alternative to calling this function, namely 
gsw_internal_energy_second_derivatives(SA,CT,p), which uses the 
computationally efficient 75-term expression for specific volume in 
terms of SA, CT and p (Roquet et al., 2015).

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:

u_SA_SA  =  The second derivative of internal energy with respect to
            Absolute Salinity at constant CT & p.   [ (J/kg)(g/kg)^-2 ]
u_SA_CT  =  The second derivative of internal energy with respect to
            SA & CT at constant p.              [ (J/kg)(g/kg)^-1 K^-1]
u_CT_CT  =  The second derivative of internal energy with respect to
            CT at constant SA and p.                    [ (J/kg) K^-2 ]
u_SA_P   =  The second derivative of internal energy with respect to
            SA & P at constant CT.            [ (J/kg)(g/kg)^-1 Pa^-1 ]
u_CT_P   =  The second derivative of internal energy with respect to
            CT & P at constant SA.                [ (J/kg) K^-1 Pa^-1 ]

EXAMPLE:

SA = [34.7118; 34.8915; 35.0256; 34.8472; 34.7366; 34.7324;]
CT = [28.7856; 28.4329; 22.8103; 10.2600;  6.8863;  4.4036;]
p =  [     10;      50;     125;     250;     600;    1000;]

[u_SA_SA, u_SA_CT, u_CT_CT, u_SA_P, u_CT_P] = ...
                       gsw_internal_energy_second_derivatives_CT_exact(SA,CT,p)

u_SA_SA =

   1.0e-04 *

  -0.083825343496748
  -0.083416792635045
  -0.084948480848605
  -0.085554093346234
  -0.014989876934701
   0.151822855467358

u_SA_CT =

   1.0e-03 *

  -0.131960094412962
  -0.131426154575457
  -0.143661243353954
  -0.176542994620612
   0.038873103109403
   0.578487406867507

u_CT_CT =

  -0.000723400187344
  -0.000719998992295
  -0.000745814518760
  -0.000736301199729
   0.000456106079104
   0.003383686798365

u_SA_P =

   1.0e-07 *

  -0.002355222222595
  -0.007035025555756
  -0.016468311540362
  -0.035407474852142
  -0.084808691842265
  -0.141942939648594

u_CT_P =

   1.0e-07 *

  -0.001718583707015
  -0.005204387424044
  -0.015207379618322
  -0.049042313140502
  -0.129085760730138
  -0.230817132562563

AUTHOR:

Trevor McDougall and Paul Barker.          [ help@teos-10.org ]

VERSION NUMBER:

3.05 (16th February, 2015)

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.

Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate
 polynomial expressions for the density and specifc volume of seawater
 using the TEOS-10 standard. Ocean Modelling.

This software is available from http://www.TEOS-10.org