gsw_internal_energy_second_derivatives

second derivatives of internal energy (75-term equation)

Contents

USAGE:

[u_SA_SA, u_SA_CT, u_CT_CT, u_SA_P, u_CT_P] = ...
                       gsw_internal_energy_second_derivatives(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 the 75-term equation has been fitted in a restricted range of 
parameter space, and is most accurate inside the "oceanographic funnel" 
described in  McDougall et al. (2003).  The GSW library function 
"gsw_infunnel(SA,CT,p)" is avaialble to be used if one wants to test if 
some of one's data lies outside this "funnel". 

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(SA,CT,p)
u_SA_SA =
   1.0e-04 *
  -0.819630879789472
  -0.815991440934607
  -0.829998881000640
  -0.850454751660842
  -0.275191185099451
   0.935521724807209
u_SA_CT =
   1.0e-03 *
  -0.131647989755567
  -0.131253260179302
  -0.143764305018288
  -0.175089006292492
   0.044242679479252
   0.582715895326373
u_CT_CT =
  -0.000723349499915
  -0.000720061216325
  -0.000745410281876
  -0.000733890626293
   0.000470364582417
   0.003405297338392
u_SA_P =
   1.0e-07 *
  -0.002844346969485
  -0.008509204835375
  -0.019897886928086
  -0.042812697313995
  -0.102544848040703
  -0.171670276420447
u_CT_P =
   1.0e-07 *
  -0.001722190998963
  -0.005214908835889
  -0.015155996668111
  -0.048975118096772
  -0.129113528684486
  -0.230925961569104

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.
McDougall, T.J., D.R. Jackett, D.G. Wright and R. Feistel, 2003: 
 Accurate and computationally efficient algorithms for potential 
 temperature and density of seawater.  J. Atmosph. Ocean. Tech., 20,
 pp. 730-741.
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