# Why are waves higher in the Gulf Stream?

To the editor: Anyone who listens to a NOAA weather broadcast in the Florida Keys hears the warning repeated in the usual computer dialect many times each hour whenever the wind is from the north: “Seas x to y feet – except higher in the Gulf Stream.”

I suspect everyone assumes this is the way it should be. Many have actually experienced these higher seas in the Gulf Stream. Even those who have not enjoyed this experience can reasonably accept it should be rougher out there in the stream. But do we really know why the rough waves are produced?

Years ago, when I first experienced these unusually rough seas in the Gulf Stream, I reasoned the waves were higher because wave heights depended on the wind velocity relative to the water, not the true wind velocity. If, for example, the water is moving north at 3 knots and the true wind is from the north at 20 knots, then the waves are those of, say, the apparent or relative wind of 23 knots instead of the true wind of 20 knots.

I easily understood this bit of basic physics. But I had a problem. In the 1950s I spent significant time on a submarine operating in the seas produced by the trade winds in the Hawaiian Islands. Steady winds, beautiful waves. I got to know the orderly relationship of wind and wave.

In the ’70s through the ’90s, I spent considerable time on ocean racing sailboats. Wind and seas were crucial to this sport. Therefore, eventually I became even better calibrated on what wave conditions were associated with what wind speeds. From my calibration, I was certain the high waves and overall roughness of the seas in the Gulf Stream with a northerly wind were greater than could be explained by merely adding the approximately 3 to 4 knots of current to the true wind speed.

Of course 3 to 4 knots is nominal. Often the stream flows 4.5 knots in the center, and I have seen it often as fast as 5.1 knots. Also, the actual velocity distribution in the Gulf Stream is not simple and changes with time. Sometimes the maximum velocity is 4.2 knots, while other times it is 5.1 knots. Sometimes the boundary of the stream is very close to shore, while other times the flow is well offshore. The only constant I have observed in many crossings is the general northerly flow higher near or slightly east of the center.

Also, there was another puzzle: exceptionally smooth water. With a southerly wind (and with the Gulf Stream flowing northerly), I had seen the converse of the rough water phenomenon: unusually smooth seas. Simple physics says the 3-knot northerly current should be subtracted from, say, a 15-knot southerly wind to find that the apparent wind is only 12 knots. The wave heights, however, were much smaller than they should have been, by my calibration.

I concluded there must be something I was overlooking. Over the years, and in the absence of explanation from others, I developed my own second-order explanation. It seems time that I expose it to scrutiny. The second order seems straightforward to me. However, my seagoing friends seem surprised when I explain it to them, never having heard of it. My physicist friends have found no specific error – but there was some skepticism because I have not created a proper math model, and until recently I had not found supporting technical papers.

In the Straits of Florida, the essential element of the second-order explanation is the nonuniform distribution of stream velocity. The velocity varies from the high-velocity center of the stream to the lower velocity away from the center. This velocity gradient is caused, I believe, primarily by the fact that the water is deep in the middle and gradually shoals toward either shore. Thus, the water flow experiences more drag away from the center than it does in the center.

The essential phenomenon is that the nonuniform velocity distribution causes a focusing to create rough seas with a north wind, and a defocusing to create smooth seas with a south wind.

The Gulf Stream in the Florida Straits has a depth of roughly 2,000 feet near the center. The depth is many times greater than the wave height, so the deep-water approximation to wave formation can be used. That is, the bottom does not directly affect wave formation. Moreover, the waves have no awareness that they are moving relative to the bottom. Toward the edges of the stream, the depth is still great enough that the main effect of the bottom is to provide increasing drag, which slows the water, as noted. This slowing creates the lateral velocity gradient, which, as we shall see, ultimately results in increased (or decreased) wave heights.

To explain why the velocity gradient affects the wave heights, I find it easier to explain, first, the case of wind blowing in the same direction as the current, i.e., southerly wind and current flowing northerly to produce smoother seas.

We know a wind initially produces waves with crests (wave fronts) parallel to each other and perpendicular to the wind direction. This would be the case of either zero current or, equivalently, a current of uniform velocity (zero gradient) across the current stream.

Now we must consider the nonuniform velocity distribution of the actual Gulf Stream current. The Gulf Stream, as mentioned, has its maximum speed approximately in the center and minimum speed near either shore boundary. The waves in the middle of the Gulf Stream are moving faster over the bottom than are the waves nearer shore. Therefore, the wave front becomes curved as it proceeds north.

The consequence of the curvature of the wave front is that the waves, and their energy, begin moving toward either shore. So that is the crux of the situation: The wave energy in the center of the stream is now traveling toward shore, where it will begin to dissipate. In the case of the Gulf Stream in the Straits of Florida, the wave energy will eventually reach shore and dissipate fully. And, I assert, that is why the sea is so smooth with a south wind.

Now let’s turn to the northerly wind situation. As noted, the apparent wind, which determines wave height, is greater than the true wind speed – higher by the stream velocity northward. But the extraordinary roughness of the seas in a north wind results from the effect of the nonuniform current acting in the reverse manner of the southerly wind. Now the wave fronts are curved inward, so the wave energy is focused in the center of the stream, and not dissipated on the shore. Hence, we have extremely rough seas; seas far angrier than predicted by a mere 3- or 4-knot current increase in wind speed.

This concept of focusing (or defocusing) wave energy may be thought of in terms of an analogy. Consider rays of light passing through an eyeglass or other lens. The basic characteristic of a lens is that light moves more slowly through glass than through air. Thus, the light rays that traverse the thicker part of the lens are slowed relative to those that traverse the thinner part. This leads to either focusing or defocusing, depending on the shape of the lens.

Similarly, the waves that must traverse the high-speed center of the Gulf Stream are either slowed (in the case of a northerly wind) or accelerated (in the case of a southerly wind) relative to the waves that traverse the slower water at the sides of the stream. Just as in the case of a lens, this relative change in speed results in either focusing or defocusing.

What are the consequences of either focusing or defocusing the waves? In the case of defocusing, with a southerly wind, the waves are turned away from the center of the stream and move out of the stream. The energy is dissipated.

With a northerly wind and focusing of wave energy, the waves move toward the center of the stream. The wave energy, instead of being dissipated, is concentrated and continues to increase in the center of the stream. Thus, the waves build into abnormally rough and often dangerous seas.

– Nils Muench is an ex-submarine officer and former director of research for GM. He has raced extensively on the Great Lakes and in Florida, and has crossed the Gulf Stream 40 times.