23 cm/s


Katabatic wind: a usually gentle wind of cool air that drains down the mountain slope overnight. When the sun warms the slope and the air above it, a katabatic wind usually stops.

Yestermorn, I was watching the languid drift of steam fog as it was carried offshore by a gentle katabatic wind. On other occasions, I had seen ripples on the water caused by the passage of a katabatic wind, but on this occasion, although there were tiny waves flowing towards the shore from off the Lake, the katabatic wind passed over the water without leaving a trace. If the drifting steam fog hadn’t revealed its passage, I wouldn’t have known there was a wind at all. How can a wind travel over the water without disturbing it? (Continued below the first picture.)

Even though a wind was carrying steam fog across the water, no water waves revealed its passage.


Suddenly, the lightbulb went on. I knew that everything that moves across the surface of water makes waves — well, everything that moves faster than 23 centimetres per second. I already knew that if a bug, such as a whirligig beetle or a water strider, moves very slowly across the water it makes no waves and so avoids both wave resistance and revealing itself to prey through spreading waves. Now, it seems, I can add a gentle katabatic wind to the things that can move over a water surface and neither make waves nor encounter wave resistance.

For there to be a water wave, there must be a force that restores the position of the water that has been disturbed by, say, wind, boat, or swimming animal. If the wavelengths are longer than 1.7 cm, the dominant restoring force is gravity; less than 1.7 cm, it is the surface tension of water. These really short waves are sometimes called capillary waves, but more often they get the name ripples.

The odd thing is that the two types of waves behave differently: the fastest ripples are the shortest ones; the fastest gravity waves are the longest ones. A wavelength of 1.7 cm has a wave speed of 23 cm/s, which is both the slowest ripple and the slowest (gravity) wave. All other waves move faster than 23 cm/s. So a bug or wind moving across the water at a lower speed cannot excite waves.

Gentle breeze: If 23 cm/s (0.23 m/s, 0.8 km/hr, or .5 mph) is the transition speed, just how slow is it? It is about a quarter or a fifth of a typical adult walking speed — a baby crawl.

This seemingly esoteric and curious fact has easily observable consequences, as will be seen.

As a katabatic wind flows down the mountain slope, it is slowed at the surface by the friction of passing over trees and rocks. Assuming it is moving at less than 23 cm/s when it reaches the Lake, it does not disturb the water. However, this lack of wave resistance also means that the drainage wind now begins to accelerate. A short distance offshore, the wind is moving faster than 23 cm/s and now it begins to make waves.

There are katabatic winds on the Lake in this sunrise scene taken a month and a half ago. Disturbed water can be seen in the image below. Katabatic winds have descended the slope on the shady (cool) left side of the picture and have spread over the water. They are also apparent on portions of the right side still in shade, but where the sun has warmed the slope, the winds have ceased. On the left side there is often a gap between the shore and the disturbed water. While there is a wind there, the air is moving at less than 23 cm/s. However, the lack of resistance to the flow allows it to accelerate above the transition speed and start disturbing the water farther offshore with waves.

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2 Responses to 23 cm/s

  1. John Hart says:

    Nice observations! I would imagine that there is a lot of local complexity to the patterns you are observing. The descending slightly cooler air mass coming down the hill side will likely experience local inversions with the warmer moist air (that accounts for the mist) that prevent the wind from disturbing the surface. Could local mixing account for the somewhat random patterns of moving air affecting the water surface? It would interesting to see the same image as a timelapse series during the early morning hours.

    • Alistair says:

      John, to be clear, there is steam fog in the first picture, but not in the second one. In that overview of the Lake, the disturbance on the water is the result of waves formed when the katabatic wind accelerates to more than 23 cm/s. The steam fog in the first picture is the result of cold most air flowing over the warm water. This is not a fog that formed as a result of the cooling of vapour (such as what happens with a wave cloud or cumulus). Rather, the condensation results from vapour mixing (no net cooling is involved). Warm vapour that has evaporated from the lake, mixes with the cooler vapour in the katabatic flow and condensation results. This is the same condensation process that occurs in a contrail and when you see your breath on a cold day. And, a time-lapse movie would, indeed, be fun. However, none of this lasts long. When the sun is down, there isn’t much light to see things and soon after it gets up and warms the slopes, the flow stops.

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