# How do I maximize a planet's wave height (on average)?

## Premise

I am in the formation phase of a fictional world. I would like one of its notable characteristics to be extremely large waves. On Earth, most of our large waves are triggered by earthquakes, landslides and things to that effect. Here is an example from 2005:

The graph makes the Earth tsunami look impressive, however this is more of an outlier. Most waves on Earth are much smaller. I would like to make my fictional world's waves to be triggered differently. Instead of sparse, infrequent natural disasters, I want something more dependable to allow for extremely large waves. This way the average wave height will be higher.

## Question

How can I maximize the wave height on my planet such that the waves average a very high number? Here I mean each wave is very large. I'm not so interested in occasional giant waves that raise the average, unless there is no other way.

Waves, indeed weather in general, are examples of highly stochastic outcomes; there is a lot of randomness and there are so many variables that come into play. This is what makes this situation very difficult but very interesting at the same time.

Further Clarifications

Below are clarifications to account for some of those variables. It is my no means an exhaustive list, but it's all that my knowledge base allows for, and is hopefully enough to frame the scope to be within reason.

• Desired wave height: I don't know what's a realistic expectation here, I'd like to say the higher the better
• Land/ocean ratio: configurable. I'm not sure, but I'd imagine this to be an important factor in the calculations. As a general guide, we should assume oceans account for anywhere between 25%-75% of the planet.
• Number of moons: configurable
• Planet climate: to have liquid water, it would be in the "Goldilocks zone", other details can be configured
• Air currents/streams: configurable, I know in certain circumstances, the way currents interact is one of the leading explanations for rogue waves here on Earth, but I'm not sure if air currents are too sporadic for my goal of consistent very high waves
• Do you want frequent monster waves that raise the average? Or really big all the time? – Bob Jacobsen Jun 19 '18 at 16:21
• @BobJacobsen I mean big all the time. I'll try to edit for clarity; I forgot that when Bill Gates moves into your neighborhood, everyone becomes a millionaire. That's how averages work. – Arash Howaida Jun 19 '18 at 16:24
• Have you ever seen Interstellar? – ScienceKeanu Jun 19 '18 at 18:46
• I came here to upvote tthis question, and what I see? I already uopvoted it... – Mołot Jun 21 '18 at 22:00

For waves that have small heights relative to the water depth ($H\ll a$), we can use Airy wave theory. This works well for waves that are far out at sea, and can include tsunamis, in deep water. I wrote about this in more detail here, but to make a long story short, the height of a wave is given by $$H=\sqrt{\frac{16E_w}{\rho g}}\to H\propto\frac{1}{\sqrt{g}}$$ where $\rho$ is the density of the water and $E_w$ is the energy imparted to it. Therefore, on a planet with lower surface gravity, the waves will, in general, be higher, as wave height is inversely proportional to $\sqrt{g}$. Honestly, the same thing should apply even with Airy wave theory isn't appropriate, because the higher the wave, the more potential energy it has, and potential energy depends on $g$. In fact, gravity is the restoring force for all but the smallest waves (with frequencies of at least 10 Hz); at those tiny regimes, surface tension is more important.

Surface gravity can be written as $$g\propto \rho_\oplus R_\oplus$$ where $\rho_\oplus$ and $R_\oplus$ are the radius and density of the planet. Decreasing either will lead to lower surface gravities, and larger waves.

There are some additional - local, not large-scale - climatic factors that need to be considered for wind waves (not tsunamis):

• The wind should, ideally, be moving faster than the wave. It turns out this is easier on a low-gravity planet, since for the wave speed $c$, $c\propto\sqrt{g}$. Thus, the waves will, on average, move slower, and it will be easier for wind to transfer energy to them.
• We need constant wind, moving in the same direction (rather than rapidly changing direction). Kamino, the watery planet from Star Wars, is an interesting example; rapid winds drive waves constantly. That said, the atmospheric currents there seem chaotic, which might limit wave height.

As an aside, ScienceKeanu mentioned the large "waves" featured in Interstellar, where a planet orbits a black hole; the gravitational pull of the black holes causes time dilation and extreme conditions on the planet. I should just point out that these aren't actually waves; rather, they're the planet's extreme tidal bores, which occur regularly. Furthermore, they don't change the median wave height on the planet; the true waves shown seem to be fairly normal.

• Your dichotomy of large-scale vs local factors is very informative. I appreciate the formula too, thanks! – Arash Howaida Jun 19 '18 at 16:51
• On the note of constant, less chaotic wind: this could lead to the interesting consequence of the planet being an example of the Hairy Ball Theorem, in that the winds would need to have at least one place that's either super chaotic or where there isn't wind (depending on what story you want to tell, or possibly more math than I'm ready or able to do) – Delioth Jun 19 '18 at 19:46
• @delioth one place (at least) where there is no wind. The “fixed point in the wind” must always exist. It would be interesting if that were a fixed point on the planet. Not sure if that’s possible or not. Certainly it could linger stably for a long time, like the eye of Jupiter’s Great Red Spot which is just now spinning down after centuries. – SRM Jun 19 '18 at 21:25

Ocean waves (normally) get their energy from wind.

Consistent, large swells on Earth come from the trade winds: strong winds over a long distance with consistent direction.

To increase those, you should have a lot of solar energy, a short day (higher rotation), thicker atmosphere and/or large east/west extents to your oceans.

Large cyclonic storms also make waves. The conditions for trade winds also help make lots of those. Because trade winds tend to only produce waves in certain areas, storm waves are important for the rest of the planet. California surfers, for example, study them relentlessly.

• That's fascinating! Especially the concept of east/west extents. I wonder about the north/south extents, but if we go too far we could be faced with frozen polar caps. – Arash Howaida Jun 19 '18 at 16:46
• Trades are driven by north/south temperature difference & the Coriolanus force: they’re basically planet-sized storms. So a hot equator and cold poles will drive bigger winds & waves. – Bob Jacobsen Jun 19 '18 at 16:51
• @BobJacobsen: "Coriolis" force. Coriolanus was a (semi-legendary) 5th century BCE Roman general and traitor, and the titular character of a famous play. Gaspard-Gustave de Coriolis was a 19th century CE French engineer who studied waterwheels and computed the apparent forces in rotating systems. – AlexP Jun 19 '18 at 21:37
• @AlexP true. I plead an over-literate autocorrect. – Bob Jacobsen Jun 19 '18 at 21:45
• This is called fetch (sometimes known as stretch). – user3106 Jun 20 '18 at 10:34

Just two things off the top of my head:

• The lower the water density, on Earth lower densities are caused by lower salinity, the higher average wave height becomes because the water is easier to move. I understand that this is why the Black Sea and the Great Lakes are, in some ways, more dangerous to shipping than the open oceans.

• The further a "wave train" travels without being disrupted the bigger the waves can get. As waves caused by wind effect on the water surface travel under a continuous prevailing wind they build in height, obviously there is a limit but it takes a lot of ocean miles to get there. This is part of why the Southern Ocean is so dangerous, wind and waves can travel for thousands of miles without being interrupted and thus waves grow very large.

So a relatively freshwater ocean, oriented with a strong prevailing wind, and having few islands or other landmasses would have very high average wave heights.

• Is pure fresh water the least dense possible? Is there a way to make it less dense than that somehow? – Arash Howaida Jun 19 '18 at 17:33
• @ArashHowaida I'm not sure, I would expect pure water to be the bottom line but there might be ways to get the density lower with selective chemical additives, the problem then becomes believable solubility adjustments etc... – Ash Jun 19 '18 at 17:35
• It won’t remain pure for long if there’s any life in it. Even without life, water will erode the rocks around it to add sediment. You can bring the density down, but not to the point of pure water (barring some non-natural filtration system). – SRM Jun 19 '18 at 21:28
• @SRM Yup like I said, mineral solubility is a serious limiting factor. – Ash Jun 20 '18 at 9:57
• Your second point is roughly how I would have begun my answer. An unbroken band of ocean enables the potential for very large waves indeed. – PCARR Jun 20 '18 at 15:42

Actually it's not that complicated: place your planet around a gas giant and make it orbit relatively close, like Io, et voilà, the gravity pull would generate monstrous waves.

The only disadvantage is that such a gravity pull would create huge internal frictions leaving the planet incredibly active with volcanic activity, probably a couple of huge eruptions a year would be usual in such environment.

• So, the easy solution is to put an ocean on the moon. Low gravity, high tidal force. You'll just need some trick to hold an atmosphere to provide wind. – Madlozoz Jun 20 '18 at 11:46
• yea, pretty much, and the atmosphere its not that much of an issue if its a gas giant, I mean, the Earth could easily orbit Jupiter – Eric Jun 20 '18 at 18:04
• "The only disadvantage is that such a gravity pull would create huge internal frictions leaving the planet incredibly active with volcanic activity," - excuse me, but how are tsunamis disadvantage when we want to maximize average wave height? I'd consider them OK – Mołot Jun 21 '18 at 22:04

If the planet is somewhat larger in size than Earth, and has equatorial oceans, so that the winds and waves can build up all the way around the world several times, the waves are likely to have an average height several times those on Earth.

Ash's answer says that lower water density allows for higher waves, so the water should have as low salinity as possible. If the planet has has a low density it could be larger in dimensions than Earth but have a lower surface gravity, which might compress the water in the oceans less.

I note that rubbing alcohol, corn oil, motor oil, and mineral oil are among liquids less dense than water. I also note that there are some atmospheric gases mixed in with water - sea life extracts oxygen from the water to "breathe".

Apparently there is a lot of methane gas trapped beneath the sea, and if it was released in large enough bubbles ships passing over those bubbles could lose support from the water and sink.

So possibly you could come up with a mixture of liquids and dissolved gases to dilute sea water on your planet and thus make waves bigger.

Bob Jacobsen's answer says that storms raise larger waves. And hot water makes storms stronger. So if your planet is close enough to its star,and/or the star is hotter enough than the Sun, the planet will receive a lot more heat and light hand have much bigger storm waves in its tropics. Hotter water would expand a little and be a little less dense than Earth water.

But as far as I can tell the most important way to make bigger wind driven waves on your planet is to have very large oceans going all around the planet so the winds can drive the waves around the world several times so the waves build up larger and larger. I don't know what the limit for wave size would be in that case.

I note that waves several times larger than the surrounding waves - rogue waves - are now known to be many times more common than were thought. So if someone travels to the region of that planet with the highest waves to watch them from a safe point they might perhaps see a really giant wave rising in the distance and headed toward them.

All of the answers so far post to the wind patterns, etc.

But those wind patterns only start the wave. The wave heights close to shore are determined by a few things already mentioned in the other answers, but also under surface geography.

Wave is moving, it has a certain amount of momentum. That momentum carries it forward, and closer to shore as the water starts getting shallower the wave rises up. Undisturbed forward momentum, combined with "climbing" the slope of the ground underwater, minus the effect of gravity pulling the peak of the wave down gives you your waves in general. Want them taller? More momentum, less disturbance of the momentum as it approaches shore, and a long slow rise from deeper water to shallow.

For details see this article on some cool mapping of the Mavericks in Half Moon Bay, California. Known for big waves (15m), famous surfing.

https://www.newscientist.com/article/dn11667-map-reveals-secret-of-awesome-mavericks-waves/

As waves get close to shore, their base begins to run into the seafloor, slowing the deeper parts of the wave. The shallower part of the wave keeps moving at the same pace, causing the wave to stand up and then pitch forward. This creates the wave face that is so sought-after by surfers.

Kvitek says that a long gradual slope, like the one at Mavericks, creates an exceptionally tall wave that holds up for some time before it breaks.

And the deeper waters on both sides of Mavericks’ “ramp” allow waves to draw additional energy from the calmer waters on either side. “It’s a combination of a gradual and steady decrease in depth combined with a wave convergence due to the deep troughs on either side of the ramp,” Kvitek says.

You can see similar slope off the North Shore area of O'ahu Hawaii in this (very large) picture .

• so you mean there is a certain topography of the ocean floor that could help the waves be bigger? – Arash Howaida Jun 21 '18 at 15:44
• @ArashHowaida yes. Editing answer to add more details. – ivanivan Jun 21 '18 at 16:05

Put the moon closer, or get a heavier one, so you will have a tidal wave four times a day, and probably much larger "usual" waves before and after tidal ones.