# gsw_Nsquared_CT25

    buoyancy (Brunt-Vaisala) frequency squared  (N2) (25-term equation)

## Contents

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

## USAGE:

    [n2, p_mid, in_funnel] = gsw_Nsquared_CT25(SA,CT,p,{lat})

## DESCRIPTION:

    Calculates the buoyancy frequency squared (N2)(i.e. the Brunt-Vaisala
    frequency squared) at the mid pressure from the equation,

                            d(rho_local)
           N2   =  g2   x  --------------
                               d(p)

    Note. This routine uses rho from "gsw_rho_CT25", which is the
      computationally-efficient 25-term expression for density in terms of
      SA, CT and p.
    Note also that the pressure increment, dP, in the above formula is in
      Pa, so that it is 104 times the pressure incerment dp in dbar.

    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 ]
           (ie. 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 ]
    p_mid      =  Mid pressure between p grid      (M-1xN)          [ dbar ]
    in_funnel  =  0, if SA, CT and p are outside the "funnel"
               =  1, if SA, CT and p are inside the "funnel"
    Note. The term "funnel" describes the range of SA, CT and p over which
      the error in the fit of the computationally-efficient 25-term
      expression for density was calculated (McDougall et al., 2010).

## 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, p_mid, in_funnel] = gsw_Nsquared_CT25(SA,CT,p,lat)

    n2 =

    1.0e-003 *

     0.060813236592168
     0.235575235293653
     0.215788878338715
     0.012919578124467
     0.008414868047304

    p_mid =

    1.0e+002 *

     0.300000000000000
     0.875000000000000
     1.875000000000000
     4.250000000000000
     8.000000000000000

    in_funnel =

       1
       1
       1
       1
       1
       1

## AUTHOR:

    Trevor McDougall and Paul Barker.  [ help_gsw@csiro.au ]

## VERSION NUMBER:

    2.0 (22nd July, 2010)

## 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, P. M. Barker, C. Roberts-Thomson, R.
     Feistel and R. W. Hallberg, 2010:  A computationally efficient 25-term
     expression for the density of seawater in terms of Conservative
     Temperature, and related properties of seawater.  To be submitted
     to Ocean Science Discussions.

     The software is available from http://www.TEOS-10.org