### Thermal Wind

Monday, August 8th, 2011Hi all,

we are trying to estimate the heat transportation along the SILBO path. To this end we are using essentially the thermal wind equations. Thermal wind is the most fundamental and significant dynamical balance controlling the large-scale circulation of the ocean. It is a consequence of hydrostatic and geostrophic balance, and appears as variations of geostrophic vertical velocity if density varies horizontally.

At first, in order to determine the scale at which processes take place, we took Rossby Radius as our reference (10 km in our case), so the processes will be on that scale. It's a good criteria to quantify all the mesoscale data. Every change in lower scales will be insignificance in our estimation.

After, we made an harmonic analysis, applying the Fourier Transform in order to estimate at which lengths (Δy) the changes of density gets more important for every range of depths (Δz = 10m, Figure 1). As we can see, most of the energy (90%, Figure 2) is concentrated above 100km (The red line indicates 100 km, and all the lengths at the left of this line are larger lengths). These analysis indicate that we are able to make different averaging among 10 and 100 kms in the direction of the glider path.

Finally, we applied the Thermal Wind equations with 10m as Δz and 10km as Δy (Figure 3). As we can see the variation of velocity gets higher while we get the surface. All these velocities are around 0 - 0.3 m/s in the surface along the glider path. These results seem to agree with real values.

Next step will be comparing these current velocities with the measured currents from the glider in order to check these results, before estimating the heat transportation combining these results with the measured temperature from glider.

Ruben & Alberto