# gsw_Nsquared_min

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

## Contents

- USAGE:
- DESCRIPTION:
- INPUT:
- OUTPUT:
- EXAMPLE:
- AUTHOR:
- VERSION NUMBER:
- REFERENCES:

## 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".

    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