Waves 101 (Part 2)

I owe you one more background post on wave physics. Hopefully this, along with the last post, will help you make some sense of why we’re making the measurements I’ll be describing later on in the cruise. The two main topics of this post are the frequency spectrum and the Radiative Transfer Equation. These topics are both related to the wave energy: how it’s distributed in the waves and how it’s transferred between the waves, atmosphere, and ocean.

Waves contain energy. If I drop a stone in a lake, some of the energy of that falling stone is converted into wave energy in the outward propagating waves. Wave energy is equally distributed between potential energy (from the deformation of the surface above the resting state) and kinetic energy (from the orbital motion of the water). The wave energy is proportional to the square of the wave height, so the bigger the waves, the more energy they contain.

I mentioned before that waves are described by their frequency. It’s nice to imagine waves as a single amplitude and frequency, but the reality is that the sea surface is an irregular mix of frequencies interacting and interfering with each other. We use a spectrum to describe this distribution, which basically shows how much wave energy is present at each frequency. Calculating the frequency spectrum isn’t trivial, but it can be done by measuring a the sea surface at a point over a sufficient amount of time, which we do with with buoys (as I’ll describe soon). Throw in a little math and you’ve got yourself a spectrum.

The Radiative Transfer Equation (RTE) governs how the spectrum evolves. It’s a form of conservation of energy; It says that the change in wave energy is equal to the net difference between energy sources and losses. The input of energy comes from friction from the wind acting on the sea surface. Most of the loss of energy is due to wave breaking (this is the term in the energy balance we’re trying to better understand with this cruise). All wave forecast models use the Radiative Transfer Equation to predict the change in waves, so if you’re looking at surf report on your vacation, you have the RTE to thank for that. To keep track of all the terms in the RTE, we need good measurements of the wind, waves, and wave breaking. All of the instruments that we deploy are aimed at making one (or more) of these measurements.

You might be surprised by how many unknowns remain in these topics. For a number of reasons (more computing power, better remote instruments including satellites and HD digital video) some fundamental questions are now within reach. And yet, humans have been successfully sailing across the oceans for centuries now. This disconnect between practical knowledge and scientific discovery is one of the things I find so interesting about waves and the ocean. But that’s all for now, stay tuned for more day-to-day commentary of the cruise.

– Mike

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