# gsw_Nsquared

    buoyancy (Brunt-Vaisala) frequency squared (N2) (48-term equation)

## Contents

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

## USAGE:

    [N2, p_mid] = gsw_Nsquared(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,

                                 ( beta x d(SA) - alpha x d(CT) )
       N2  =  g2 x rho_local x  ---------------------------------
                                              dP

    Note. This routine uses rho from "gsw_rho", which is the computationally
      efficient 48-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 increment dp in dbar.

    Note that the 48-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. (2013).  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 ]
    p_mid  =  mid pressure between p grid      (M-1xN)              [ 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, p_mid] = gsw_Nsquared(SA,CT,p,lat)

    N2 =

    1.0e-003 *

       0.060846990523477
       0.235607737824943
       0.215533939997650
       0.012924024206854
       0.008425873682231

    p_mid =

    1.0e+002 *

       0.300000000000000
       0.875000000000000
       1.875000000000000
       4.250000000000000
       8.000000000000000

## AUTHOR:

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

## VERSION NUMBER:

    3.02 (17th November, 2012)

## 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., P.M. Barker, R. Feistel and D.R. Jackett, 2013:  A
     computationally efficient 48-term expression for the density of
     seawater in terms of Conservative Temperature, and related properties
     of seawater.  To be submitted to J. Atm. Ocean. Technol., xx, yyy-zzz.

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