13.8: Wind Stress- A Transfer of Energy

As we learned in Chapter 15, winds—movements of air—are caused by differences in air pressure at different locations in the atmosphere. Air, of course, is a mixture of gases, including nitrogen (N₂), oxygen (O₂), water vapor (H₂O), argon, carbon dioxide, and others. So when we talk about air molecules, we are talking about these molecules collectively.

Wind represents molecules of air in motion. These moving molecules contain a form of energy known as kinetic energy—energy in motion. Lots of things have kinetic energy: the air around you, winds, a flying insect, a hurled rock, an automobile speeding down the highway, or people at a rave, for example. The ripples that you notice when the wind interacts with the ocean surface result from collisions between air molecules and water molecules. Literally, an air molecule bangs into a water molecule.

The transfer of energy from the wind to the ocean surface along the horizontal plane of the ocean (parallel to the ocean surface) is known as surface wind stress (e.g., Jones et al. 2001). It’s the surface wind stress that sets the ocean in motion. Most of the energy transferred by surface wind stress makes waves, but a small amount of it causes currents (movements of water, the ocean analog of wind). Some energy is also dissipated as heat.

The banging of molecules transfers energy from the moving molecule to the unmoving molecule. The energy transfer sets the previously unmoving molecule in motion. The amount of energy transferred from the moving molecule to the unmoving molecule depends on momentum—the product of a molecule’s mass and its velocity. The larger a molecule (the greater its mass), the greater its momentum. Alternatively, or additionally, the faster a molecule (the greater its velocity), the greater its momentum. A good way to think about momentum is to think about the difference between an insect hitting your windshield at 75 mph or a rock hitting your windshield at that speed. The insect, with little mass, makes a splat, but no harm done other than a dirty windshield. A rock, on the other hand, with a larger mass and greater momentum, can put a crack in your windshield. If the rock is a meteorite, fuhgeddaboudit! (Your car is toast.)

When a moving molecule of air bangs into an unmoving molecule of water, a transfer of momentum occurs from the moving molecule to the unmoving molecule—an act of physics known as momentum transfer. The formerly unmoving molecule gains kinetic energy and begins to move. Of course, the now-energized water molecule is going to transfer momentum to surrounding water molecules because there will be collisions and transfers of kinetic energy from moving water molecules to other water molecules. So kinetic energy is passed from molecule to molecule within the upper ocean.

At the same time, some of the energy transferred through momentum causes vertical displacement of water molecules. The lifting or lowering of water molecules at the surface will change their potential energy, which is energy contained in an object or system due to its position or placement. When raised above the resting sea level, such as at the crest of a wave, a water particle gains potential energy in proportion to its height above the resting level. When that water particle moves downward, it releases that potential energy as kinetic energy. The same is true when lowering a water particle below the resting state. At the trough of a wave, the buoyancy of the water beneath the water particle will force it upward. As it moves, it will release potential energy.

In general, about half the energy in a wave is in the form of kinetic energy, and the other half is in the form of potential energy. Because the orbital motions of water particles represent kinetic energy, and the height of a wave determines the diameter (and circumference) of the wave orbital, and because the height of a wave determines the potential energy in a wave (the displacement of a water particle above or below the resting level), the total energy in a wave—kinetic plus potential—can be described in terms of the wave height (e.g., Knauss and Garfield 2017), as:

E = 1/8 × ρ × g × H²

(Eq. 19.4)

Total energy in a wave equals 1/8 times the water density (ρ, pronounced rho) times acceleration due to gravity (g, which is 9.8 meters per second squared ) times the height of the wave squared (H²).

The take-home message here is that a 6-foot wave has four times the energy of a 3-foot wave. A 12-foot wave has 16 times the energy of a 3-foot wave. Waves are extremely powerful, and now you know why.