365 Days of Climate Awareness 111 – Rossby Waves

 

I’ve mentioned Rossby (planetary) waves in a number of posts. With each passing mention the realization grew in me that I need to explain—or attempt an explanation—of this very important global phenomenon. Every time you look at a weather map and see the jet stream snaking across Canada and the northern United States, you’re looking at Rossby waves rhythmically perturbing the air flow. They’re a complicated topic but I’ll give it a shot! (This will be another longer-than-usual post. But that’s okay because yesterday’s was really short. :P ).

Rossby waves, also known as planetary waves, are large-scale north-south fluctuations in the atmosphere and ocean. Their amplitude can be hundreds of miles, and one wavelength can be over a thousand. Waves are disturbances in a continuum—sound waves in the air, wind-driven waves on the ocean surface—where a restoring force acts to correct the disturbance. But the restoring force overcorrects, and pushes the medium in the opposite direction, creating the back-and-forth fluctuation. In sound waves, the restoring force is pressure—whether of air, water, or a solid (solids transmit sounds!). In wind-driven ocean waves, the restoring force is gravity. In Rossby waves, the restoring force  is (effectively) the Coriolis effect.

Schematic of a northern-hemisphere Rossby wave.

The Coriolis effect is a function of the vorticity within a fluid. Vorticity is, simply put, a measure of the angular momentum—the spin—at a given point in a fluid. Earth being a rotating sphere, vorticity varies from zero at the equator to its maximum value at the poles. Let’s assume some ocean water at a given latitude—50°N, for example—happened to be pushed to the north. The water moving to the north has negative vorticity—that is, less angular momentum—less spin--than the water around it. This negative vorticity manifests as the water from farther south being diverted to the right, in a clockwise motion.  This continual diversion to the right results in the water moving back to the south.

Likewise, if water from 50°N were pushed to the south, it would have greater vorticity (spin) than the more southerly water, resulting in its being diverted to the left, counterclockwise. The result is a wavelike motion, where water carried to the north or south, usually due to a pressure imbalance, begins to move in a curved path back toward its original latitude. Momentum then carries the parcel of water past its original latitude—into overshoot--and so the north-to-south wave motion is created.

Jet stream Rossby wave fluctuations.

This process is not limited to ocean water in the northern hemisphere. The same thing happens in the southern hemisphere: water moving south is diverted counterclockwise to the left, and water moving to the north is diverted clockwise to the right, again setting up the north-to-south Rossby wave motion. These waves occur in the atmosphere as well—in fact they’re named after the Swedish meteorologist, Carl-Gustaf Rossby, who discovered them.

The group velocity—how quickly the peaks and crests move—of a Rossby wave is slow. Atmospheric Rossby waves might take several weeks to travel across North America, while oceanic Rossby waves take months to cross a basin. Faster planetary waves have a westward group velocity, where the peaks and crests move to the west; slower wave crests travel to the east.

Meteorology, oceanography and even astrophysics share fluid dynamics. The same equations, with different numbers for variables like mass, velocity, and viscosity, are used to describe liquids, gases, and plasma. The rotational dynamics of the surface of the Sun and the outer layer of Jupiter are modeled in exactly the same way we do our own atmosphere.

As an aside: Carl’s son Tom was one of my grad school advisors. You’re not likely to find a gentler, kinder man. His Christmas glög parties were legendary, but he stopped throwing them because they lasted till dawn and he got too tired. Tom categorically refused to use the term “Rossby wave”—he insisted on the term planetary. He was modest enough to tell the story of how he flunked his first oral doctorate exam, but also loved tossing in a question on every final that had nothing whatsoever to do with his lectures—just to “see how we’d handle it.” He happens to be one of the most celebrated ocean researchers of the 20th century and is responsible for a good deal of our understanding of mid-ocean-depth dynamics.

Tomorrow: the North Atlantic Oscillation.

Be brave, and be well.