gsw_Nsquared_min

minimum buoyancy (Brunt-Vaisala) frequency squared (N2) 
(75-term equation)

Contents

USAGE:

[N2, N2_p, N2_specvol, N2_alpha, N2_beta, dSA, dCT, dp] = ...
                                       gsw_Nsquared_min(SA,CT,p,{lat})

DESCRIPTION:

Calculates the minimum buoyancy frequency squared (N2)(i.e. the 
Brunt-Vaisala frequency squared) at the mid pressure from the equation,
                 ( beta x d(SA) - alpha x d(CT) )
   N2  =  g2  x  ---------------------------------
                        specvol_local x dP
Note. This routine uses specvol from "gsw_specvol", which is the 
computationally efficient 75-term expression for specific volume in 
terms of SA, CT and p (Roquet et al., 2015).
Note also that the pressure increment, dP, in the above formula is in
Pa, so that it is 104 times the pressure increment dp in dbar.
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". 
TEOS-10
Click for a more detailed description of buoyancy 
(Brunt-Vaisala) frequency squared (N2).

INPUT:

SA  =  Absolute Salinity                                        [ g/kg ]
CT  =  Conservative Temperature                                [ deg C ]
p   =  sea pressure                                             [ dbar ]
       ( i.e. absolute pressure - 10.1325 dbar )
OPTIONAL:
lat  =  latitude in decimal degrees north                [ -90 ... +90 ]
  Note. If lat is not supplied, a default gravitational acceleration 
     of 9.7963 m/s2 (Griffies, 2004) will be applied.
SA & CT need to have the same dimensions.
p & lat may have dimensions 1x1 or Mx1 or 1xN or MxN, where SA & CT
are MxN.

OUTPUT:

N2         =  Brunt-Vaisala Frequency squared  (M-1xN)           [ s-2 ]
N2_p       =  pressure of minimum N2                            [ dbar ]
N2_specvol =  specific volume at the minimum N2               [ kg m-3 ]
N2_alpha   =  thermal expansion coefficient with respect         [ K-1 ]
              to Conservative Temperature at the minimum N2
N2_beta    =  saline contraction coefficient at constant      [ kg g-1 ]
              Conservative Temperature at the minimum N2
dSA        =  difference in salinity between bottles          [ g kg-1 ]
dCT        =  difference in Conservative Temperature between   [ deg C ]
              bottles
dp         =  difference in pressure between bottles            [ dbar ]

EXAMPLE:

SA  = [34.7118; 34.8915; 35.0256; 34.8472; 34.7366; 34.7324;]
CT  = [28.8099; 28.4392; 22.7862; 10.2262;  6.8272;  4.3236;]
p   = [     10;      50;     125;     250;     600;    1000;]
lat = 4;
[N2, N2_p, N2_specvol, N2_alpha, N2_beta, dSA, dCT, dp] = ...
                                     gsw_Nsquared_min(SA,CT,p,lat)
N2 =
1.0e-003 *
    0.0608
    0.2204
    0.1606
    0.0116
    0.0079
N2_p =
        50
       125
       250
       600
      1000
N2_specvol =
   1.0e-03 *
    0.9782
    0.9762
    0.9730
    0.9710
    0.9690
N2_alpha =
   1.0e-03 *
    0.3227
    0.2811
    0.1732
    0.1463
    0.1294
N2_beta =
   1.0e-03 *
    0.7176
    0.7262
    0.7505
    0.7551
    0.7571
dSA =
    0.1797
    0.1341
   -0.1784
   -0.1106
   -0.0042
dCT =
   -0.3707
   -5.6530
  -12.5600
   -3.3990
   -2.5036
dp =
        40
        75
       125
       350
       400

AUTHOR:

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

VERSION NUMBER:

3.05.5 (3rd June, 2016)

REFERENCES:

Griffies, S. M., 2004: Fundamentals of Ocean Climate Models. Princeton,
 NJ: Princeton University Press, 518 pp + xxxiv.
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 section 3.10 and Eqn. (3.10.2) of this TEOS-10 Manual.
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
 The software is available from http://www.TEOS-10.org