In 1893, during the Fram expedition, Fridtjof Nansen and his crew encountered a phenomenon where the velocity of the ship was reduced significantly, even though the engine was working at full speed. Nansen described this phenomenon as “dead water” (Brady, 2014). This dead water effect can happen when the ship creates an internal wave as it moves through water. The water must be stratified, meaning that the top layer is less dense than the bottom layer. At the same time, the draught of the ship must have the same depth as the top layer. The internal wave produces a drag, reducing the velocity of the ship. The speed of the wave is only dependent of densities and depth of the layers, not the velocity of the ship. (Grue, 2018).
We performed an experiment (as seen in the video) where we recreated the ocean conditions and created an internal wave. Then we explored how and when the internal wave could influence the velocity of the ship. To simulate the conditions Nansen experienced, a wooden boat was pulled with constant force across a tank filled with water. The water had two layers, one fresh layer on top (clear), and one saline underneath (purple). The depth of the saline layer must be much greater than the depth of the fresh layer.
The experiment was performed several times with the boat being pulled with constant, but different, force. We expect that if the speed of the boat is larger than the speed of the internal wave, the boat will not feel the wave because it moves faster than the internal wave. If the speed of the boat is smaller than the speed of the internal wave (as seen in the video), the wave will catch up with the boat, and the speed of the boat will be much reduced.
In order to observe Lee Waves and their related phenomenon, an experiment was conducted in a large water tank with a stratified two layer system. The two layer system was constructed with fresh water sitting atop colder salt water. The fresh water had a salinity of about 0‰, with a density of 1000 kg/m3 while the pink-dyed salt water had a salinity of about 35‰, and a density of 1028 kg/m3. In order to force Lee Waves to propagate, a mountain was moved along the bottom at two different speeds, fast and slow. While conducting an experiment to visualize Lee Waves, the phenomenon of the hydraulic jump can be observed. This event can be visualized when water flows over rocks or even in one’s kitchen sink. This occurs when water flowing over a surface goes from subcritical to supercritical, which is calculated through the Froude number. To calculate this, the velocity of the flow is divided by the phase speed of the shallow water gravity waves. The square root of this fraction is then taken to provide a unitless value called the Froude number. The result is either greater than one (supercritical) or less than one (subcritical). Supercritical Froude numbers indicate that waves cannot propagate upstream. This can physically be visualized when the flow over the observed surface goes from smooth and rather thin, to turbulent and rough. As we pushed the mountains through the stratified water, the denser saltwater (shown with pink dye) was forced up and over the mountain, resulting in turbulent motion just behind the surface anomaly. As the thinner flowing water moved from the downhill slope of the mountain to just downstream and onto the bottom of the tank, the flow went from smooth to rather chaotic. The interface where the flow becomes turbulent is the hydraulic jump. The smoother water flowing over the mountain is supercritical while the more mixed water just downstream is the subcritical flow. When the mountain was moved at the faster speed, this hydraulic jump was shifted accordingly. Instead of the hydraulic jump occurring just behind the mountain, the waves seemed to lag with the more turbulent flow occurring farther downstream than with the slower mountain speed.
(by: Jori Neteland-Kyte, Sara Elisabeth Holen Sælen , Susanne Moen Olsen)
Lee waves are a type of internal gravity waves, which is generated as fluid moves over an obstacle. The fluid needs to be stably stratified for this to occur. These waves can occur in both the atmosphere and in the ocean. (Cushman-Roisin and Beckers, 2011, page 412) To show this phenomenon it is convenient to perform a simple experiment, where a long tank is used. The tank is filled with stratified water, the bottom layer is denser than the layer above. A purple color is added to the denser water at the bottom layer, as seen in Figure 1. This is done to distinguish between the two layers. The tank is also equipped with a moving obstacle which is possible to move at different constant velocities across the bottom of the tank.
When the obstacle is moved across the tank, waves are generated in the interface between the layers as seen in the figure 2.
Figure 3. displays how the Lee waves propagates, with the positions for the supercritical area, the hydraulic jump and subcritical area marked by the arrows. The supercritical area is positioned directly above the moving obstacle, which appears as one smooth wave. In the transition between the supercritical and the subcritical area, the hydraulic jump is found. This occurs at the end of the descending side of the moving obstacle. Following behind the
hydraulic jump is the subcritical area, this is where a train of waves are generated. These waves decays with time.
There hasn’t been much happening on this blog lately, since I’ve been busy, busy, busy teaching geophysical fluid dynamics to the third year bachelor students here at GFI. My job description as an associate professor at UiB includes 50% teaching – however giving the (somewhat equation heavy) course for the first time it felt more like 150%… but now the last lecture is given, the students are happily (?) preparing for the exam, and I finally have time to do some science… and to update the blog!
First I’ll have the students tell and show you what they did with Mirjam when she was visiting the Bjerknes centre and Bergen in October. One flight of stairs down from my office, in the basement of GFI, there is a 6 m long tank. It is not round and it is not rotating (like the tank in Grenoble), but it can move mountains! Or rather, it holds a mountain that can be moved. Why would one want to move a mountain in a tank? Well, as Arne Foldvik, the professor emiritus who built the tank a few decades ago realized, if you want to study flow over topography in the lab, then it is easier to have the fluid move beneath the fluid than to make the fluid move over the mountain… and the physics are the same.
Arne (who later left the lab and became on of the Norwegian pioneers in Antarctic oceanography) spent years with the tank – my student only spent an hour but they did some really nice stuff! Thank you again Mirjam for setting it all up – and thanks to the students for handing in the (non-compluslory) assignments that you’ll be able to read (and watch) in the days to come!
Below you see Arne Foldvik showing off his results – and inspecting his old tank.