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Comment by rufus_foreman | Hacker News Reader

I was just thinking about this, I was at the beach so I was thinking about sneaker waves.

It sounds like the way it works is that a typical wave is a certain height, but if two waves from a wave train hit at the same time, they might be twice the normal height. But there's no reason it would only be two at time at a maximum, is there? Waves could hit from different angles and combine at the impact point (the beach), on rare occasions.

Waves are from Extremistan, using the Taleb terminology. If the maximum wave that hits a certain beach on a typical day is 10 feet, the maximum that might hit on an atypical day isn't going to be 20 feet, it's not going to be 100 feet or 1,000 feet. There's just no telling where the top of the "atypical" distribution is. The black swan wave might wipe out everything and everyone for miles around.

But that was just me thinking, not an expert on waves. The biggest ones I saw were 6 feet tops.

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I've gotten into surfing over the last few years (started during covid) and it's made me really appreciate how elaborate wave patterns are.

If you know the directions of the incoming swells and you're out in the water judging each wave to decide if you can ride it, you start to get a feel for how swells that have different frequencies and are coming from different directions can merge together.

There are times when a certain combination of swell forms a great peak—maybe the long period south swell and short period southwest swell are merging—and you realize it's happening on a regular basis, like once every three or four sets. This kind of thing can actually be very useful for getting waves when it's crowded. People will tend to concentrate where the peaks are showing up most consistently, but if you can identify a "weird" peak that reoccurs on a regular basis, you can get it to yourself each time it appears even if there are like 30 other surfers nearby.

Rogue waves/sneaker waves are the same kind of thing. In surfing there's the term "cleanup set" for a set of waves that are way larger than the typical pattern and break much further out. I tend to see at least one of these per session in northern CA, though it depends on the day—while you can get cleanup sets in relatively small conditions, they seem to show up more frequently as the swell gets larger and more powerful.

And then every once in awhile there are waves that are on a whole other level. I used to play poker a lot and statistically it reminds of something like getting a straight flush. It's quite rare obviously but if you spend a lot of time playing poker you'll eventually get some. I was surfing in Linda Mar on a fairly calm shoulder high day (3-4f) and then out of nowhere I got to experience what I'm pretty sure was a double overhead wave (10-12ft) during a cleanup set. Linda Mar is a beginner spot so you can imagine the carnage that it left behind :)

How does it work from an energy point of view. If a wave weighs ten tonnes per meter width per meter high, say, each collision needs to move increasingly large amounts of water up like a hanoi tower (although some of the energy may come from vacating space going down). Is that energy coming from currents or the waves? Can you really get 100x bar a tsunami or similar?

I don't think that such scenarios would fall under any sort of long-tail thinking, since the chance of having N waves converge at a point decays exponentially in terms of N, whereas the height/energy/damages/etc. increase polynomially at most. This means we can place finite (and not very large) 50th, 90th, 99th, etc. percentiles on the heights of combined waves, assuming we can accurately predict the height distribution of a single wave.

As a related thought experiment, suppose I jump down from a 5-foot ledge and land on the ground, sending a wave of pressure through it. In principle, I could be walking down the street, when a similar wave of pressure comes up through the ground and launches me 5 feet in the air. Yet the vibrations in the ground are normally so dispersed that such a ground wave will never occur in anyone's lifetime (outside of an earthquake, of course).

A 20 foot wave is likely to have approx 4 times the volume of a 10 foot wave. So combining 2 x 10 foot waves won't give you a 20 foot wave. More like a 14 foot wave.

I think the chances of three of anything colliding in a single place are extremely low

There are a lot of waves, and a lot of time, I wouldn't discount it ever happening.

Like he chance of someone somewhere winning a lottery.

If you have 2 periodic waves of amplitude a1 and a2 coming from different directions the peaks combine at every intersection, so there's always a grid of a1 + a2 double-peaks. If the wavelengths are around 100m, there's a double-peak every 10000 m^2 (1 hectare).

If you add a 3rd periodic wave from another direction, at any point in time some of these double-peaks will align with the peak of the 3rd wave to form a triple-peak. If you set the cutoff at a1 + a2 + 0.95a3, then about 10% of the double-peaks are triple-peaks (because cos(10% * pi) ~ 0.95).

Add a 4th orthogonal wave and about 1% are at least a1 + a2 + 0.95a3 + 0.95a4. So with 4 waves, we have a quad-peak every 100 hectares (a small farm).

Yes, this is the way. On a screen with mixed frequencies = a variable resultant. add a third dimension = voila. I knew this decades go - makes me wonder why it was missed?

you're right, I forgot that the periodic part would make a big difference!

Yeah but not zero - also see two/multi photon absorption.

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