Why are the waves so much higher with 'wind against tide'?

Or more precisely, how can wave size be increased so much by even a weak counter-current?

The effect can clearly be seen in river mouths and straits where an ocean swell encounters a counter current. It also happens in deep water, such as when the Gulf Stream encounters head seas. There need not be any wind.

The often given reasons (increased apparent wind speed, shallow waters, steepening of the waves, etc.) cannot account for the strength of the effect. Formulas might elucidate it, but my mind is more visual. In 1992 my eureka moment came one day while heading east on a motor yacht through the Current Rock passage in the Virgin Islands where I had a birds-eye view of whole effect clearly displayed in front of me.

Although many factors influence wave size, my explanation of this particular effect is the difference in speed of forward motion of the wave-train inside the area of counter-current versus outside. For clarity, the illustrations show waves in a regular and parallel pattern which would be unlikely in our messy real world.

 

 

Figure 1

A counter-current will cause a distortion in the wave-train, as the waves in the center of the current move slightly slower than those on either side. This bending of the wave-train causes the waves on the sides to slowly converge towards the center, increasing the energy and height near the center at C.

 

 

Figure 2

Even a very weak counter-current could have a noticeable effect as a modest convergence will eventually concentrate the wave energy given enough distance.

 

 

Figure 3

The opposite effect is also true: if the current were to run in the direction of the waves, the wave height at the center would be reduced by divergence of the wave-train (see river example below).
When waves curve towards the shore in shallower water it's mostly by refraction (e.g. around a round island or behind a headland).

 

Figure 4

When wind blows parallel to a river that has no current, the waves are fairly uniform in size across the width (disregarding a slight reduction near the shore from reduced wind speed and refraction in shallow depth).

River with wind but no current

 

Figure 5

The current (black/white arrows) in a river is usually strongest in the deeper center. When the wind is blowing with the current, the wave-train is bent by the stronger current in the center, causing divergence (red arrows) and a reduction in wave height.

River wind with current

 

Figure 6

When the current flows against the wind, the wave-train also bends but now the waves converge (red arrows) towards the center where their energy piles up into noticeably higher waves. Near the river banks, the waves are reduced.

River with current against wind

Figure 7

Divergence is sometimes used to great effect in harbours exposed to large ocean seas. After a narrow entrance at A, the jetties curve away from each other, causing waves to spread. This reduces the height of the waves that reach the harbour proper at B.

Leo, Oct 24, 2015

Comments are appreciated.

 

© Leo Lindstrand. All rights reserved.