# Will tsunami waves travel forever if there was no land?

If there was no land for tsunami waves to collide with, can the waves travel around the globe for forever?

• You seem to be asking whether there's such a thing as a perpetual motion machine. – Dawood ibn Kareem Apr 27 '19 at 23:38
• Thanks, now I have "Mountains" by Hans Zimmer stuck in my head (the track that played in Interstellar on the planet with the gigantic tidal waves). – Fabian Röling Apr 28 '19 at 18:58
• What would happen on a hypothetical Earth with no land? – billpg Apr 29 '19 at 9:27

The waves will not travel forever.

Water particles moving against and around each other will have friction, and the friction will cause motion energy to be converted to heat (which will dissipate throughout the water and air). The wave will eventually cease to exist unless energy is added.

• The real question is, what effects would such conditions create, like the wave wrapping around the globe and crossing itself. – RudolfJelin Apr 29 '19 at 11:27
• @RudolfJelin: They already do that, no need for a hypothetical. The oceans are interconnected around Antartica. – MSalters Apr 29 '19 at 14:21

To answer this, I would appeal to the general principle which we call the 2nd law of thermodynamics. One way of expressing it is that the entropy of an isolated system cannot decrease. This means that in order to keep going for ever, a wave motion would have to involve no entropy increase. But almost all processes involve some increase of entropy, and in the case of water waves this is certainly going to happen, because of viscosity and turbulence in the water. Therefore the wave will gradually dissipate its energy and eventually die down.

• Maybe I didn't drink enough coffee in order to follow your logic but I feel some information is missing. What is the system you're talking about? Is it really isolated? Why couldn't a wave keep going forever after some entropy increase? – Eric Duminil Apr 27 '19 at 13:14
• If your {Earth + Atmosphere + Ocean} system really were isolated, there would be no wave to begin with, would it? – Eric Duminil Apr 27 '19 at 13:51
• @EricDuminil The waves going on "forever" (my comment under the OP notwithstanding) because earth is not an isolated system are called tides ;-). – Peter - Reinstate Monica Apr 27 '19 at 14:15
• I will say the one reason I could think this might not be true would be if the thermal energy from the sun were somehow keeping this going. I don't know if it would be possible, but the tsunami might have some way of reaching a sort of resonance with the heating and cooling cycles to keep it's energy. That seems unlikely enough that it's probably more confusing to add it to the answer (perhaps even physically impossible still, but that would take some simulations). – JMac Apr 27 '19 at 14:28
• "Forever" is never going to happen : the sun will explode in a few billion years anyway. Still, the Great Red Spot on Jupiter has been observed for 350 years, so your argument doesn't seem to be enough to rule out a wave being maintained by an anticyclonic storm for a few years, for example. – Eric Duminil Apr 27 '19 at 18:17

Of course, no. Tsunamis are a series of pressure waves with a longitudinal mode and have much higher wavelengths, speed, and period than the normal ones. Normal ocean waves only involve motion of the uppermost layer of the water, but Tsunami waves involve the movement of the entire water column from surface to seafloor.

However, they are still akin to normal waves when it comes to dissipative forces such as friction between layers (or viscosity), just that it takes longer due to the sheer amount of energy density they carry. The mass of water getting displaced is particularly high, and due to high inertia, they tend to keep moving until resistance offered by the shape of the shoreline and other dissipative forces take over. Conservation of energy ensures the dissipation through heat, sound (which ultimately decays to thermal energy of the medium).

Tsunami waves have much longer periods ranging from 10 minutes to 2 hours, wavelengths of 100-500 km, and travel at speeds of 800-1000 km per hour[1]. Near the shore, the killer waves slow to between 10 to 20 mph (16 to 32 km/h) and gain enormous height. In reality, Tsunamis can travel as far as 10 miles (16 km) inland, depending on the shape and slope of the shoreline [2].

# Waves keep going forever, in a way

As others pointed out already, waves tend to lose energy.

However, what will (theoretically) happen is that at any point in time the wave will lose a fraction of its energy, but never truely 100%. So though you will soon reach a point where random noise will make it practically impossible to detect a wave, the effect of the wave will never truely be gone.

So, while you will not notice it and definitely won't call it a tsunami, the wave can be seen as going on forever!

• Quantum Mechanics would like to have a word, though. The exponential decay model you imply here is purely a classical effect. – MSalters Apr 29 '19 at 14:23
• Haha, yes but as the question asks about a simplified reality (world without land) I feel like this answer still belongs here – Dennis Jaheruddin Apr 29 '19 at 16:36