# gsw_Turner_Rsubrho

`Turner angle & Rsubrho (75-term equation)`

## USAGE:

`[Tu, Rsubrho, p_mid] = gsw_Turner_Rsubrho(SA,CT,p)`

## DESCRIPTION:

```Calculates the Turner angle and the Rsubrho as a function of pressure
down a vertical water column.  These quantities express the relative
contributions of the vertical gradients of Conservative Temperature and
Absolute Salinity to the vertical stability (the square of the
Brunt-Vaisala Frequency squared, N^2).  Tu and Rsubrho are evaluated at
the mid pressure between the individual data points in the vertical.
This function uses computationally-efficient 75-term expression for
specific volume in terms of SA, CT and p (Roquet et al., 2015).```
```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 the Turner angle & Rsubrho.```

## INPUT:

```SA  =  Absolute Salinity                                        [ g/kg ]
CT  =  Conservative Temperature                                [ deg C ]
p   =  sea pressure                                             [ dbar ]
( i.e. absolute pressure - 10.1325 dbar )```
```SA & CT need to have the same dimensions,
p may have dimensions 1x1 or Mx1 or 1xN or MxN, where SA & CT are MxN.```

## OUTPUT:

```Tu       =  Turner angle, on the same (M-1)xN grid as p_mid.
Turner angle has units of:           [ degrees of rotation ]
Rsubrho  =  Stability Ratio, on the same (M-1)xN grid as p_mid.
Rsubrho is dimensionless.                       [ unitless ]
p_mid    =  mid pressure between the indivual points of the p grid.
That is, p_mid is on a (M-1)xN grid in the vertical.
p_mid has units of:                                 [ 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;]```
`[Tu, Rsubrho, p_mid] = gsw_Turner_Rsubrho(SA,CT,p)`
`Tu =`
```  -2.063858905281147
41.758435216784427
47.606966981687535
53.710351151706369
45.527063858211527```
`Rsubrho =`
` 1.0e+002 *`
```  -0.009304335069039
-0.176564834348709
0.219627771740757
0.065271424662002
1.087044054679743```
`p_mid =`
` 1.0e+002 *`
```   0.300000000000000
0.875000000000000
1.875000000000000
4.250000000000000
8.000000000000000```

## AUTHOR:

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

## VERSION NUMBER:

`3.05 (16th February, 2015)`

## REFERENCES:

```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 Eqns. (3.15.1) and (3.16.1) 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, P.M. Barker, 2015: Accurate
polynomial expressions for the density and specifc volume of seawater
using the TEOS-10 standard. Ocean Modelling.```
` The software is available from http://www.TEOS-10.org`