# gsw_Turner_Rsubrho

Turner angle & Rsubrho (75-term equation)

## Contents

## 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