Soon after we started deploying isopycnal floats in the Gulf Stream one of my students, Arthur Mariano, insisted that we should deploy floats in pairs or clusters to study how they initially disperse – or equivalently for how long will they stay close. I was reluctant to do this as this meant using twice as many instruments for the basic objective of tracing out fluid pathways in the Gulf Stream. I’d rather use them to get independent realizations. But Arthur was insistent, so as our confidence in the new float technology grew and could send them on longer missions, I relented and began deploying floats in pairs knowing that they would eventually part ways and become independent tracers of fluid motion. The results were striking to say the least.
Pairs of isopycnal floats would stay within a few km of each other even as they traveled 100s of km. This was especially true if the floats settled out on the same isopycnal surface. Incredibly, one pair stayed within 10 km as they drifted north over 700 km in the north Atlantic Current over a two-month period. In a later study Dave Hebert released pairs and triplets of floats in the Gulf Stream. One triplet stayed tightly together passing through a meander trough just as it was splitting off a cold core ring. One of the floats got trapped in it while the other two continued as a pair in the Gulf Stream for another 1000 km. Common to those that stay tightly together is that they were very nearly on the same isopycnal: their temperatures were the same to within a tenth of a degree centigrade, which given a typical stratification of 1°C over 40 m means within 5 m of the same isopycnal surface.
In 2003 Dave led a major study to study isopycnal dispersion over a wide range of scales (from km to 100s km); he coined it LIDEX for ‘Lagrangian Isopycnal Dispersion Experiment’. At each of five sites in the eastern tropical North Atlantic 9 floats were released, 5 on an isopycnal near 500 m depth and 4 near 800 m depth (the 27.1 and 27.3 kg/m3 surfaces, both in the main thermocline). Under the watchful eye of Jim Fontaine extreme care had been taken to ballast the floats to those two isopycnal surfaces, and the effort paid off. In one analysis of the float data, we picked out all those pairs or triplets that settled at the same temperature to within 0.1°C after release. With an initial separation of less than 1 km (they were deployed within minutes of each other) they moved together tracing out beautiful inertial oscillations such that their average separation had only increased to about ~5 km over 30 days or equivalently ~2 mm/s. Floats that were not within 0.1°C would separate more rapidly. Why was this?
The main thermocline is highly stratified, which means that one layer can slide around in the horizontal relative to another with little contact or mixing in the vertical. Floats on neighboring isopycnal surfaces will reveal slightly different patterns of motion reflecting the ‘slipperiness’ of adjacent layers. But if floats are on the same isopycnal, their world is effectively 2-dimensional, there is no slip resulting in little relative motion at these small separations. Internal waves are weak, and tidal motions are coherent on much larger scales. Inertial oscillations are energetic, but their scales of coherence are evidently much larger than the separation between floats and thus inefficient at scattering the floats. Indeed, neighboring floats loop through their inertial oscillations in tight pirouettes like members of a Corps de ballet. What remains at the km scale is the strain associated with the mesoscale eddy field, and that is not very large. In such a 2-dimensional non-divergent world the rate of separation of particles will depend upon their separation. Thus, dispersion is weak when pairs are close but will increase with separation due to the background mesoscale strain. Given that the rate of pair separation depends upon their separation dispersion will have an exponential character. But as their separation grows subsequent dispersion will no longer be local but governed by the mesoscale eddy field. At that point being on the same isopycnal surface no longer matters.
This is useful to know. It is quite challenging to target floats to precisely the same isopycnal. In the previous blog I noted that we could determine the weight of a float to within a few parts in ten to the 5th power! But given that the coefficient of thermal expansion is ~1 part in ten to the 4th power, that means we can’t target to better than a few 10ths of a °C. So unless one is specifically interested in studying the initial rate of separation of particle pairs on the same isopycnal surface - what might be called ‘iso-isopycnal dispersion’ - it’s nice to know that it isn’t crucial to require and expect that level of ballasting accuracy.