gsw_enthalpy_second_derivatives_CT_exact

second derivatives of enthalpy

Contents

USAGE:

[h_SA_SA, h_SA_CT, h_CT_CT] = gsw_enthalpy_second_derivatives_CT_exact(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.
Note that this function uses the full Gibbs function.  There is an 
alternative to calling this function, namely 
gsw_enthalpy_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).
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;]
CT =  [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_CT_exact(SA,CT,p)
h_SA_SA =
   0.000082767011576
   0.000414469343141
   0.001089580017293
   0.002472193425998
   0.006103171596320
   0.010377465312463
  
 h_SA_CT =
 
   0.000130320164426
   0.000655016236924
   0.001879127443985
   0.005468695168037
   0.014315709000526
   0.025192691262061
  
 h_CT_CT =

   0.000714365642428
   0.003584965089168
   0.009733337653703
   0.024044402143825
   0.061449390733344
   0.107333638394904

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.
  See Notes on the first and second order isobaric derivatives of
  specific enthalpy.
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