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 *
-0.002353268094506
-0.007029334357723
-0.016418681747556
-0.035380276284246
-0.084822481842961
-0.142006349667287
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:
3.06.16 (28th September, 2022)
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 and P.M. Barker, 2015: Accurate
polynomial expressions for the density and specific volume of seawater
using the TEOS-10 standard. Ocean Modelling, 90, pp. 29-43.
http://dx.doi.org/10.1016/j.ocemod.2015.04.002
This software is available from http://www.TEOS-10.org