# gsw_Nsquared_min

minimum buoyancy (Brunt-Vaisala) frequency squared (N^{2}) (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 (N^{2})(i.e. the Brunt-Vaisala frequency squared) at the mid pressure from the equation,

( beta x d(SA) - alpha x d(CT) ) N^{2}= g^{2}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 10^{4}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 (N |

## 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/s^{2}(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) [rad^{2}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 ]

The units of N^{2}are radians^{2}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, 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:

3.06.13 (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