gsw_Nsquared

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

Contents

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   ---------------------------------
                        specvol_local x dP
Note. This routine uses rho 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)           [rad2 s-2 ]
p_mid  =  mid pressure between p grid      (M-1xN)              [ dbar ]
The units of N2 are radians2 s-2 however in may textbooks this is
 abreviated to s-2 as radians does not have a unit.  To convert the
 frequency to hertz, cycles sec-1, divide the frequency by 2π, ie N/(2π).

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 *
   0.060843209693499
   0.235723066151305
   0.216599928330380
   0.012941204313372
   0.008434782795209
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:

3.06.13 (4th August, 2021)

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