Friday, April 12, 2013

Tilting Isopycnals (the simplified version)

Sunset over Cumberland Sound
One of the things I’m attempting to determine is if the Baffin Island Current*, which passes outside of the mouth of Cumberland Sound, bends into the sound. Last summer, we were able to conduct two rounds of CTD** casts at regular intervals across the sound's mouth. Unfortunately, I wasn’t actually there as I was too pregnant to be at sea. I doubt I would have fit in the bunk as the ship we used is a particularly cramped research vessel (picture here).

Even though it was cramped, the ship had a hull-mounted current meter. Unfortunately, the instrument wasn’t turned on. No one on board had the knowledge to fiddle with it, so I missed out on that data (that’s the way it goes sometimes). Without measured currents, how does one infer water flow from CTD data?

The Baffin Island Current is geostrophic, that is, the pressure gradient force is balanced by the Coriolis force. In this case, friction and tides become unimportant and can be ignored when calculating current flows.

The pressure gradient force is the weight of water as the sea surface height is not at the same everywhere. This force is always directed from areas with high pressure to areas of low pressure. Without a balancing force, a parcel of water will move from the area of high pressure to the low one. But, there is another force out there to balance with - the Coriolis force.

Actually, the Coriolis force isn’t a real force; instead it is like an imaginary friend that shows up to solve a problem. It pops up when we treat our rotating planet as though it’s an inertial frame of reference to use Newton’s laws. Newton's laws form the base of ocean physics - and most other things that aren't moving too fast or are too small. Now, we’ll move on to pretending the Coriolis force is real. This force acts in different directions depending on the hemisphere, since I work in the northern hemisphere, I’ll take it as acting to the right.

As soon as the parcel of water from above starts to move because of the pressure gradient force, it will be acted upon by the Coriolis force and deflected to the right. The result will be a current that flows along an isobar (line of constant pressure) - a geostrophic flow.

In the ocean, pressure is difficult to measure. Fortunately, pressure is related to density and density depends on salinity and temperature which I measured. In the Arctic, where Cumberland Sound is, density depends mostly on the salinity, however, since I measured both I used both. I’ve calculated density and plotted up lines of constant density, which are called isopycnals. From plotting a cross-section of density, isopycnal slopes tell us if water flows in or out of the section, which is exactly what I’m looking for (note: isobars and isopycnals have opposite slopes).

From isopycnal slopes, a relative velocity can be calculated as currents move faster where the isopycnal slopes are steeper. Actual velocities would have been nice to get, leaving me wishing I had been on the ship to turn on the current meter. However, relative velocities still answer my question of whether the Baffin Island Current bends into my site. The answer is yes it does.

*The Baffin Island Current is the official name of this current which passes along the coast of Baffin Island (a nice diagram showing it can be found in this paper). Many currents have assigned names, the Gulf Stream and Kuroshio are perhaps more familiar examples. 

**CTD stands for Conductivity Temperature Depth. From conductivity, salinity is calculated. This instrument samples the water as it descends directly down from the ship resulting in profiles of these properties with depth.

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