# gsw_Nsquared_min

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

## 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`