Tuesday, March 22, 2016

Wind and Waves, Part II


Where do those waves come from, then, that aren't caused by the current wind conditions?  Those waves are called swells, and are generally the remnants of far-off storms, with periods exceeding 10 seconds.  Apparently, waves with short periods tend to dissipate within a couple thousand miles, but waves with longer periods can propagate halfway around the Earth, or even farther, as long as they don't run into a continent.  This is where the really good surfing waves come from, and helps to explain why the West Coast and Hawaii have better surfing than the East Coast.  This is why I bothered listing wave period on my earlier tables (don't worry, I haven't forgotten to post the rest of them).  And that's about where the college intro level of research ends.

To find out how fast waves dissipate and how far they propagate required digging in pretty deep.  This is the "professional" level of research (so my way of thinking goes).  It's also pretty much the "in over my head" level of research.  To get any kind of idea how to work up some game-able numbers, I had to spend several hours finding the exact combination of Google search terms that eventually led to the 1966 edition of thePhilosophical Transactions of the Royal Society of London, specifically the paper Propagation of Ocean Swell across the Pacific, by F. E. Snodgrass, G. W. Groves, K. F. Hasselmann, G. R. Miller, W. H. Munk, and W. H. Powers.  I then spent several more hours poring over 65 pages or so of measurements and equations that were absolutely too complex to use in game preparation, except for the most obsessed, masochistic gamemasters.  Eventually, I happened upon a statement that short period waves decay by about a decibel for every degree of great circle they travel, and later found a series of measurements that gave me some long period decay rates.  Interpolating to find approximate decay rates for wave periods that weren't specifically listed, and reading up on how decibels apply to ocean waves as opposed to noise levels, I've been able to come up with a short table that now shows a game-able approximation of the end of the life cycle of waves.

 
Period Wave height as a proportion of original height
90.00% 80.00% 70.00% 60.00% 50.00% 40.00% 30.00% 20.00% 10.00% 1.00%
<10 55 116 186 266 361 478 627 839 1200 2400
10 73 155 248 355 481 637 837 1118 1600 3200
11 110 233 372 532 722 955 1255 1678 2400 4800
12 137 291 465 666 903 1194 1569 2097 3000 6000
13 183 388 620 887 1204 1592 2092 2796 4000 8000
14 275 581 929 1331 1806 2388 3137 4194 6000 12000
15 366 775 1239 1775 2408 3184 4183 5592 8000 16000
16 549 1163 1859 2662 3612 4775 6275 8388 12000 24000

So, a wave with a height of 28 feet and a period of 8 seconds will have a height of 14 feet after 360 miles.  A wave of equal height but a period of 12 seconds will still be at about 75% of its original height (21 feet) after 360 miles, and will take another 540 miles (total of 900) to decay to 14 feet.

Ah heck, here's the same table, but instead of miles, it's in 24 mile hexes.  I didn't do 6 mile hexes like the last table because most maps don't cover hundreds of miles of ocean 6 miles at a time:

Period Wave height as a proportion of original height
90.00% 80.00% 70.00% 60.00% 50.00% 40.00% 30.00% 20.00% 10.00% 1.00%
<10 2 5 8 11 15 20 26 35 50 100
10 3 6 10 15 20 27 35 47 67 133
11 5 10 16 22 30 40 52 70 100 200
12 6 12 19 28 38 50 65 87 125 250
13 8 16 26 37 50 66 87 117 167 333
14 11 24 39 55 75 100 131 175 250 500
15 15 32 52 74 100 133 174 233 333 667
16 23 48 77 111 151 199 261 350 500 1000

I, of course, embarked on a much more detailed, time-intensive course of number crunching before I realized that this short version would probably work more easily.  And thinking about it now, it's probably better to just randomly determine swell on a given day with a 2-3d6 table.  But I think that table will be easier to come up with now that I have a better handle on what it's supposed to represent.

No comments:

Post a Comment