Tuesday, March 28, 2017

Looking at Data, Episode 4 (round and round we go!)

We have all likely had the experience in a classroom where we were expected to take something on faith; someone else discovered it and provided evidence, and that had to be good enough. In science, many of these ideas challenge our innate perception of the world, and it becomes hard to fully integrate them into how we perceive the world without coming up with the evidence ourselves. Newton’s Laws of Motion are a popular target for rote memorization in physical science classes, something so many can repeat and yet so few fundamentally embrace. Aristotle may not have grasped all the intricacies of physics, but he certainly had a solid handle on how humans see things.
The path through which the buoy has drifted over the last several days provides indirect evidence of inertial motions in the mixed layer of the ocean. It does not move in a perfectly repeatable circle because there are always other effects super-imposed on top, such as a mean current.

The study of fluids (like the ocean) is different from the study of individual particles (you, me, a car, a tennis ball) in many ways. The basic laws still apply: applying forces affects the motion of the water, mass can’t appear or disappear, and all the energy that enters and leaves the system must be accounted for. However, the standard fare of tennis balls and ramps doesn’t work as well in a continuous fluid. True, fluids will flow downhill under the force of gravity, but while they do so they can be influenced by the topography of their path and interactions with the rest of the environment (heating/cooling, evaporation, etc). When we look at the ocean, we are not only dealing with a fluid, but also have to consider the fact that the Earth is rotating. Oftentimes, there are so many simultaneous processes going on in the ocean that it is hard to pick out the ones you have been taught to expect theoretically in the classroom.

The core of Newton’s laws is the concept of inertia: unbalanced forces are required to change the motion of an object. It makes sense that you have to push on something to make it speed up, but it is often challenging to grasp that things are only slowing down because forces are acting on them, not because they have some inherent property that makes them want to slow down and be at rest. Without friction, you could roll something across the floor and it would continue indefinitely. Weird.
A "progressive vector diagram" showing the expected path of a parcel of water if it had the observed velocity. This is more direct evidence of inertial motions, since it is based on direct measurements of the velocity. (Figure credit: John Mickett)

In a fluid ocean, when you factor in the rotation of the Earth, it gets even weirder. Imagine you have a strong gust of wind that pushes on the surface of the ocean and makes it start moving. In a non-rotating model, if we were to ignore friction, that chunk of water would keep moving along in a straight line. On and on and on. However, because the ocean is on a curved and rotating surface, this is not what happens. Once a particle is in motion, if that motion persists long enough, it should follow a curved path, clockwise in the northern hemisphere and counterclockwise in the southern hemisphere (assuming the same perspective). This behavior is attributed to the Coriolis force, although in reality this is a way to explain the motion of a particle on a rotating platform from a stationary perspective. Ultimately, the water is merely conserving its momentum, traveling the path that maintains a constant momentum at all times in the absence of forces. This is perfectly analogous to the tennis ball rolling across the frictionless floor in a straight line indefinitely, once we incorporate rotation into the picture.
Although this figure can be a bit difficult to decipher, it shows that the "u" (east-west) and "v" (north-south) velocities are each switching direction twice a day, as one would expect for a particle moving in a circle. This is indicated by the shift from bluer shades to yellower shades that occurs regularly in the top 60 meters. This figure is based directly on ADCP current data. (Figure credit: John Mickett)
In real life, this can be hard to observe. The optimal conditions for producing these “inertial motions” are a strong wind-gust followed by a period of calm (persistent wind will continuously force the water to change its motion). In addition, the platform you use to observe the motions must travel with the mixed layer, which we sometimes treat as a “slab” or uniform chunk for approximations, since the surface ocean is what is being directly forced by the wind. You need to know the position of the object regularly enough to trace out a reasonable path. Finally, you must be able to observe over a considerable length of time, because these motions take close to a day to complete a rotation at our latitude.

In this case, we don’t just have to believe it because the textbooks claim it happens. Both our buoy (which we have following the mixed layer right now with the positioning of the drag elements) and the floats appear to be following largely inertial motions, collectively following very similar curved paths roughly once a day. The signature also shows up in our ADCP current data that we are measuring directly from the ship. Without any additional forcing, these motions would die out due to friction, but for the past few days, we have been able to observe a set of wonderfully predictable oscillations. Physics works!
Close-up view of the sea surface temperature in our region from the infrared satellite image. As you can see from the range of colors, we are right in the middle of a region with substantial variations in temperature. Although the image may look grainy, the resolution is actually quite impressive for satellite data, and is incredibly valuable in getting an overview of the region.

1 comment:

  1. Very well written! You make these topics easy for the lay person to understand.