Underwater Nuclear Explosions: How Deep Is The Ocean, How High The Sky?

A guest post by Joseph Friedlander 

Article Summary:  This is a longer article collecting and discussing data on underwater nuclear explosions and what they tell us of the physics of what happens when nuclear fire meets water from the inside. It is a follow up article to https://www.nextbigfuture.com/2010/12/sea-based-launch-option-for-nuclear.html which was the discussion of underwater launch for the Wang Bullet one-shot nuclear space launch system and researches the physics of underwater explosions.. But this article does not focus on space launch per se but rather on how big an underwater nuclear blast the oceans can contain (and how high you can raise a splash above atmosphere).  
Obviously if you blow some water to escape velocity it goes arbitrarily high and sublimes away. But we are trying  to get a feel  of the yields involved. The needless excuse for this is a hypothetical orbiting battlestation– could you shoot it down with a sub-towed very high yield device? I need not point out that this is not a serious proposal, just a science fiction daydream in the spirit of https://www.nextbigfuture.com/2012/06/irritating-science-fiction-technical.html But here we are not nuking the site from orbit but nuking the orbit from an ocean site. It’s the only way to be sure…
Key Points:  
  • The two most interesting kinds of relatively clean nuclear burst configurations underwater are WIGWAM style (deep, contained, multi-pulse bubble-overshoot–contract cycles till white cauliflower like surface burst) The picture below is probably from the Wahoo shot which was shallower and more spherical in surface burst.
  •  and UMBRELLA style (shallow detonation but deep enough to just depress the bottom but not scoop up and irradiate lots of seafloor muck followed by geyser like vertical jet)
  •  If you want a supersonic space vehicle launch with a single underwater detonation  you need to have the back end of said vehicle or accelerating sabot very near the explosion. This confirms the earlier Wang Bullet studies.
  • A random giant space impactor will find the oceans (at average 3.7 km depth) around 4 gigatons deep, and in even the deepest place in the ocean 100 gigatons would be a bottom strike.
  • Buoyant rising of megaton explosion clouds is around 300 m/sec and a very high altitude nuclear explosion will generate ballistic rising clouds at around 1500 m/sec– see the article below but this confirms my initial assumption– if you want true space launch to escape velocity in a single shot, either start very close to the bomb (if you can rig a way to survive it) and ideally with something massive behind you– ie underground or undersea, not just from a atmospheric zero point.
  • To answer our  title question, the oceans are about 4-100 gigatons deep, and the skies are about 400 megatons–9-30 gigaton range high depending if you’re just trying to blow air into the way of a targeted orbiting battlestation or the whole darn ocean depth at the deepest point up like a spear.

  How deep are the oceans, how high is the sky?–Irving Berlin
I am trying to remember where I saw a slide of a potential asteroid or comet impact with Earth’s oceans. If I recall correctly the shocking statistic was that the oceans are on average (average depth about 3.688 km) only 1-4 gigatons deep. Should a sufficiently large asteroid or comet impact with Earth’s ocean the depth would be no shield an impactor becomes a land strike and throws up dust not just  translucent spray and salt. 
That in turn can lead to global dimming of the sun and the equivalent of a nuclear winter if enough opaque stuff gets in the stratosphere where because of dryness it must settle out but can’t rain out.
Other writers have implied the true number is more like 30 gigatons (and interpolating the answers at  https://what-if.xkcd.com/15/
it looks like in the deepest part of the ocean, the 11 km deep Marianas trench 100 gigatons or so is the upper limit of how deep is the ocean.
 Perhaps they were taking different depths  into account for example 3.68 km  times 3 is 11 km so a 3 x 3 x 3 times bigger explosion ie 27 times the yield would hit bottom there too.
Checking that– 100 gigatons divided by 27 is around 3.7 gigatons, right around the 4 gigaton range for the AVERAGE depth of the oceans. This checks out well enough that I can regard it as provisionally confirmed–or to restate the rule, a random impactor (or gigaton mine) will find the oceans (at average 3.7 km depth) around 4 gigatons deep, and in even the deepest place in the ocean 100 gigatons would be a bottom strike.
That is how deep are the oceans, as a 40’s singer might have crooned.
 But how high is the sky? (ie what nuclear yield underwater will produce a jet capable of reaching the stratosphere or greater heights?
In the interest of being environmentally sensitive (TM)  this article will not consider the yield necessary to achieve the launch parameter in the trifecta of Irving Berlin’s lyrics– How far is the journey 
From here to a star? 
(Bit then again—: In case of planetary emergency could a Dragon like capsule armed with nuclear devices  move an asteroidal impactor into a position to hit Earth in exactly the right configuration of impact to launch into space a giant space ark by the resulting non radioactive explosion? My mind reeled with the precision of trajectory and the toughness of space ark capsule needed to survive such events. https://www.nextbigfuture.com/2016/01/what-if-humans-could-survive-4000-g.html  But that is another separate article, so back to this one.)
On this general topic of large underwater explosions naturally I began thinking of the Wang Bullet nuclear launch system 
like any normal person would,  and wondered– what are the controlling parameters of nuclear ocean launch?
  How much of a kick do you get with a bomb in the water under a massive space vehicle with no cannon walls to hold in the blast (Whatever the effect it would be greatly amplified by a cannon tube if deep enough burst to force the gas to go up the cannon tube behind the launching vehicle)
Then I wondered if we could compare various historical underwater tests  to get a feeling for how this works (the Bikini test Baker, was in fact shallow enough that it threw up mud and activated products exactly analogous to a deep huge ocean strike of an incoming impactor) 
Then I began to wonder how big an explosion would touch the bottom of the sea or blow ocean water up into space in the path of an orbiting battlestation. 
Hopefully a hollow Death Star sized but really low mass one at absurd closeness to the planet, (which would by the way induce needless tidal stresses but it sure looks cool) .http://tvtropes.org/pmwiki/pmwiki.php/Main/NoEndorHolocaust
So  I began examining  several documented underwater nuclear explosions to get a feel for the phenomenae involved. 
Shallow, and you get a rebound from the nearby seafloor.
 Deeper, and bubble oscillation phenomenae predominate. 
The 1946 Baker Test
The 1955 Wigwam Test
The 1958 Wahoo Test
The 1958 Umbrella Test
The 1962 Swordfish Test
are the famous US tests in this submarine realm.
I found this reference after assembling much of this article but it’s quite a useful summary with the following beautiful annotated graphs–

Blast bubbles from deep nuclear explosions become mere hot water in about six seconds and leave no “regular” bubbles to float up to the surface. This is sooner than blast bubbles from conventional explosives:

This drastic loss of energy between cycles is caused in part by the extreme force of a nuclear explosion pushing the bubble wall outward supersonically (faster than the speed of sound in saltwater). This causes Rayleigh–Taylor instability. That is, the smooth inner wall surface becomes turbulent and fractal, with fingers and branches of cold ocean water extending into the bubble. That cold water cools the hot gas inside and causes it to condense. The bubble becomes less of a sphere and looks more like the Crab Nebula, the deviation of which from a smooth surface is also due to Rayleigh–Taylor instability.
 Friedlander here again. What these last two  graphs  tell you is that if you want a supersonic space vehicle launch with a single underwater detonation  you need to have the back end of said vehicle or accelerating sabot very near the explosion or you have to make do with subsonic velocities. 
Keep in mind though that the speed of sound is 4 times faster in water than air!  (1,484 m/s) https://en.wikipedia.org/wiki/Speed_of_sound
Yet the force of a nearby detonation is sufficient to disintegrate most structures. 
This of course is the same conclusion we came to in the other Wang Bullet studies,  https://www.nextbigfuture.com/2010/12/sea-based-launch-option-for-nuclear.html   which is why I came up with the Friedlander Sabot to take the disintegrating force that comes so close to the detonation. And transmits it to the (at least partially) unharmed actual projectile at the cost of loss of energy– but even a small percentage of a nuclear blast is a lot of energy to play with.
I’m pretty sure the above difference is caused by the sharper power over time curve by nukes; faster in, faster out.
The 1946 Baker Test
 in HD ultraslow motion
Nice magician like soundtrack– they are making the ships disappear after all–

from The Effects of Nuclear Weapons, 1977: Underwater data http://www.abomb1.org/nukeffct/enw77b2.html



2.63 Certain characteristic phenomena are associated with an underwater nuclear explosion, but the details vary with the energy yield of the weapon, the distance below the surface at which the detonation occurs, and the depth and area of the body of water.

 The description given here is based mainly on the observations made at the BAKER test at Bikini in July 1946. In this test, a nuclear weapon of approximately 20-kilotons yield was detonated well below the surface of the lagoon which was about 200 feet deep.
(IIRC at -90 feet–JF)
2.65 In the course of its rapid expansion, the hot gas bubble, while still underwater, initiates a shock wave. Intersection of the shock wave with the surface produces an effect which, viewed from above, appears to be a rapidly expanding ring of darkened water. This is often called the “slick” because of its resemblance to an oil slick. Following closely behind the dark region is a white circular patch called the “crack,” probably caused by reflection of the water shock wave at the surface.

2.66 Immediately after the appearance of the crack, and prior to the formation of the Wilson cloud (¤ 2.48), a mound or column of broken water and spray, called the “spray dome,” is thrown up over the point of burst (Fig. 2.66). This dome is caused by the velocity imparted to the water near the surface by the reflection of the shock wave and to the subsequent breakup of the surface layer into drops of spray. The initial upward velocity of the water is proportional to the pressure of the direct shock wave, and so it is greatest directly above the detonation point. …

Spray Dome
Figure 2.66. The “spray dome” formed over the point of burst in a shallow underwater explosion.

2.67 If the depth of burst is not too great, the bubble remains essentially intact until it rises to the surface of the water. At this point the steam, fission gases, and debris are expelled into the atmosphere. 

Part of the shock wave passes through the surface into the air, and because of the high humidity the conditions are suitable for the formation of a condensation cloud (Fig. 2.67a).

 As the pressure of the bubble is released, water rushes into the cavity, and the resultant complex phenomena cause the water to be thrown up as a hollow cylinder or chimney of spray called the “column” or “plume.” The radioactive contents of the bubble are vented through this hollow column and may form a cauliflower-shaped cloud at the top (Fig. 2.67b.)…

2.68 In the shallow underwater (BAKER) burst at Bikini, the spray dome began to form at about 4 milliseconds after the explosion. Its initial rate of rise was roughly 2,500 feet per second,
762 meters per second

but this was rapidly diminished by air resistance and gravity. A few milliseconds later, the hot gas bubble reached the surface of the lagoon and the column began to form, quickly overtaking the spray dome

. The maximum height attained by the hollow column, through which the gases vented, could not be estimated exactly because the upper part was surrounded by the radioactive cloud (Fig. 2.68). The column was probably some 6,000 feet high and the maximum diameter was about 2,000 feet. The walls were probably 300 feet thick, and approximately a million tons of water were raised in the column.
The 1955 Joe 17 Test 
warning more deadly than the bomb is the soundtrack, recommend muting it
I believe but cannot prove that the many secondary explosions you see about 45 seconds in are a test minefield of pressure mines– this was a nuclear torpedo test, much feared in NATO around 1955.
Later on the Soviet weapons complex considered the use of 100 megaton torpedos http://militaryanalysis.blogspot.co.il/2014/08/t-15.html
 A great article about why we don’t need to worry about gigaton weapon generated tsunamis– the bubble expansion/contraction cycle prevents the energy going into circular ripples…

What if you exploded a nuclear bomb (say, the Tsar Bomba) at the bottom of the Marianas Trench?

The explosion at the bottom of the Mariana Trench will create a quickly-expanding spherical cavity of hot steam. To figure out how big it gets, we can try a formula from the 1971 paper Evaluation of Various Theoretical Models For Underwater Explosion:
Radius=(34π)13(40%×53 megatons of TNTMariana Trench pressure+1 ATM)13≈580 meters

The bubble grows to about a kilometer across in a couple of seconds. The water above bulges up, though only slightly, over a large area. Then the pressure from that six miles of water overhead causes it to collapse. Within a dozen or so seconds, the bubble shrinks to a minimum size, then ‘bounces’ back, expanding outward again.
It goes through three or four cycles of this collapse and expansion before disintegrating into, in the words of the 1996 report, “a mass of turbulent warm water and explosion debris.” According to the report, as a result of such a deep-water closed bubble creation and dissipation, “no wave of any consequence will be generated.”

The seminal work in the field of nuclear ocean waves is Water Waves Generated By Underwater Explosions, a sprawling 400-page report produced for the Department of Defense by Bernard Le Mehaute and Shen Wang. The report, published in 1996, exhaustively examines and summarizes all available research about the ocean waves created by nuclear explosions.
 That file linked:
PDF Water Waves Generated by Underwater Explosions
by B Le Mehaute – ‎1996 – ‎Cited by 7 – ‎Related articles
N/A since Unclassified. … and propagation of water waves from underwater explosions. … The effects of the waves on various structures, fixed or floating, in deep water, on the ….. Schematic representation of the shallow water explosion phenomena. …… Because the wave motion is assumed linear and defined by a potential …
Details on Soviet nuclear testing at  Novaya Zemlya https://www.ldeo.columbia.edu/~richards/my_papers/khalturin_NZ_1-42%20.pdf 
 below from
 Nigel B. Cook’s Glasstone.Blogspot Blog
www.glasstone.co.uk blog post  
A fantastic (and unless mistaken formerly classified guide to calculating crater sizes retarcs and yes underwater explosion effects is here courtesy of Nigel B. Cook (as is much of the data in the article here)  https://nige.files.wordpress.com/2009/10/em1-ch-2-second-sections-ada955386.pdf)

Above: The first nuclear explosion at Novaya Zemlya was a 3.5 kt nuclear warhead RDS-9 for Torpedo T-5 at a depth of 9.8 metres (32 feet) underwater on 21 September 1955. Some 30 ships including 4 destroyers and 3 submarines containing 500 goats and sheep and 100 dogs were located at distances of 300-1,600 m; only the destroyer at 300 m sank immediately from water shock wave damage. (V. A. Logachev, et al., Novaya Zemlya Test Site. Ensuring the General and Radiological Safety of the Nuclear tests: Facts, Testimonies, Memories, IzdAT, Moscow, 2000, 485 pp.) 

This was a scaled-down version of the American 1946 Baker test. 

Early American information released about Baker falsely indicated that it was detonated at 50 feet depth in 200 feet of water, whereas it was actually detonated at 90 feet depth in 180 feet depth of water; it is interesting that this deception slightly confused the precise choice of the scaled depth to be used in this Russian underwater test: they simply scaled down from the supposed 50 feet depth of burst for supposedly 20 kiloton Baker to get 32 feet for 3.5 kilotons using the 1/4-power scaling law, i.e., 50*(3.5/20)1/4 = 32 feet. 

This Russian test was also interesting because of the low humidity of the cold arctic air at Novaya Zemlya, within the arctic circle, compared to the high humidity (73%) in the Baker test at Bikini Atoll. It is significant that the base surge, column and cauliflower cloud are exactly as occurred in the Baker test, although unlike Baker there is no Wilson condensation cloud around the column, due to the low humidity at Novaya Zemyla.
…all three Russian underwater nuclear tests were detonated in the same location: 70.703 degrees North, 54.60 degrees East, Guba Chernaya Bay, Novaya Zemyla. (That bay has relatively shallow water, like Bikini or Eniwetok Lagoon.)
Above: on 10 October 1957, a 9 kt T-5 nuclear torpedo detonated at a depth of 29.3 m (96 feet) in the same location as the previous Russian underwater test at Novaya Zemlya. A submarine launched the torpedo. Three destroyers, three submarines, two minesweepers, and smaller target ships, were sunk by the shock. (V. A. Logachev, et al., ‘Novaya Zemlya Test Site. Ensuring the General and Radiological Safety of the Nuclear tests. Facts, Testimonies, Memories’, IzdAT, Moscow, 2000, 485 pp.) 

This second Russian underwater test was very similar to the American Umbrella test, producing a tall column with no mushroom top or cauliflower cloud atop the stem or column.

 The reason for the difference in cloud shape is the bubble pressure when it vents at the air-water surface. The bubble from a 1 kt burst detonated at a depth in excess of 23 metres will only reach the surface after the pressure in the bubble has fallen below ambient air pressure, hence there is ‘blow in’ of air to the cavity. 

This occurs because the greater depth gives steam the chance to condense into water, reducing the steam pressure in the bubble. 

Hence, there is no ‘blow out’ of steam in such a detonation, and no cauliflower shaped top to the cloud, merely a column of water.

 Underwater bursts of 1 kt at depths shallower than 23 metres cause the bubble to reach the surface sooner and erupt while there is still some steam pressure remaining, so you get a ‘blow out’ of the bubble steam, which quickly condenses in the unconfined air to form the cauliflower-shaped top of the mushroom cloud above the water spray column. 

This Russian test was detonated at a scaled depth near the borderline between bubble ‘blowout’ (bubble steam above ambient air pressure when venting) and bubble ‘blowin’ (bubble steam below ambient air pressure when venting), so it was probably near ambient air pressure when venting.

 It is therefore really in the transition zone between the blowout of Baker shallow bursts and the blowin of Umbrella (slightly deeper) bursts. 

(The third and final Russian underwater test, at exactly the same location as the two previous Russian underwater tests, was 4.8 kt at 19.5 metres (64 feet) depth on 23 October 1961, and was the system proof test of a nuclear torpedo launched from a B-130 submarine. 
Altogether, there have been a total of nine underwater nuclear weapon tests: the three Russian shots, the five American shots Baker, Wigwam, Wahoo, Umbrella, and Swordfish, and the British very shallow underwater test in very shallow water, .)
The 1955 Wigwam Test.
Underwater Atomic Test, Mark 90 Betty A-Bomb: “Operation Wigwam” pt  2-3 1955
the short version
The long version very nice details:
200  mph  89.4 meters a second break through  of the water surface In the Wigwam test after rising nearly 2000 feet through deep water.
Surplus real subs weren’t cheap enough or pristine enough to use as instrumented targets, so the Long Beach Naval Shipyard built three identical 4/5-scale sub hulls to hold instruments while submerged.
…. We’ll refer to them as “tubs.”
The tubs were a little more than 140 feet long and 20 feet in beam, painted white and stiffened with internal bulkheads. Weights designed to simulated engines and other fittings sat inside compartments equipped with cameras and instruments.
The tubs contained ballast systems that the testers on a support barge operated through thick high-pressure hoses. The tubs could sink or rise just like real subs.
The support barge also carried semi trailers full of gear from labs around the country. Instruments aboard the barge recorded readings from the tubs’ on-board gauges and sensors as well as data on radiation, sea states and water quality.
The test instrumentation array formed the Navy’s longest-ever towed assembly. The column of cables, barges, floats and tubs stretched almost six miles behind the fleet tug USS Tawasa. Sea trials off San Clemente Island went off without a hitch….
Wigwam’s nuclear device was a Mk-90 “Betty” atomic depth charge. The Betty yielded 30 kilotons, twice the force of the Hiroshima bomb. Shorn of its fins and other equipment, the nuke depth charge sat in a specially-built steel pressure housing suspended 2,000 feet below the shot barge.
The tubs were supposed to float 260 to 290 feet below the surface between one and two-and-a-half miles from the bomb. Giant salvage floats supported the tubs at depth using huge chains. Testers evacuated the support barge before the test.
By the day of the test—May 14, 1955—the Pacific was anything but peaceful. Twenty-knot winds and 15-foot seas twisted the carefully-planned line of barges and tubs into a writhing snake.
Submerging the tubs proved far more difficult than during previous trials. 
The 1958 Wahoo Test 1:30 GMT 16-May-58 
 A 9 kt Mk-7 was detonated at a depth of 500 ft (150 m) in deep water. The spray dome rose to a height of 900 ft (270 m). Gas from the bubble broke through the spray dome to form jets which shot out in all directions and reached heights of up to 1,700 ft (520 m). The base surge at its maximum size was 2.5 mi (4.0 km) in diameter and 1,000 ft (300 m) high https://en.wikipedia.org/wiki/Underwater_explosion
500 feet depth of burst  water depth 3200 ft.
Papers of Nigel B. Cook are also available here http://vixra.org/author/nigel_b_cook and on the internet archive. An extensive range of physics related content, some dealing with nuclear, others on the nature of science and so forth.

Wigwam very deep underwater burst in 1955 (32 kt at 610 m depth in water nearly 5 km deep) gamma dose rate in water at 1.4 hours after detonation. Because of the depth of the explosion, the bubble mixed with the water and largely disintegrated into foam before venting, so that relatively little radioactivity reached the surface.

Above: comparison of base surge gamma radiation dose rates and total accumulated doses from 1958 Hardtack underwater shots Wahoo (9 kt, 152 m depth of burst in deep water) and Umbrella (8 kt, 46 m depth of burst on the lagoon bottom).
(Note from Friedlander– the Umbrella radiation map is missing on the source page
Here are 2 links for the fallout data compilation
Note the contrast with a conventional air or surface burst–the dosage rate at 1 mile–
 underwater bursts are much cleaner for a given yield as long as they don’t suck up irradiate and expel bottom muck. But when they do they are much dirtier.
Notice the difference between wet Pacific soils and likely designated ground zero target area  temperate or arctic cold dry soils–cratering is less extensive than Pacific tests would indicate

Philip J. Dolan’s 1972 DNA-EM-1 Capabilities of Nuclear Weapons by contrast gives a far more complete treatment of all the underwater burst problems. The final sections of Chapter 2 on blast and shock phenomena (over 300 pages) includes water shock, base surge, water waves from surface and underwater bursts, and so on, while chapter 5 on nuclear radiation phenomena gives computer predictions of base surge and water ‘pool’ dose rates and accumulated doses for yields of 1, 10 and 100 kt for various depths underwater and proximities of the bomb to the ocean bottom (the 1958 Umbrella test was detonated on the seabed, so there is evidence to validate such a preduction). The base surge part of that computer model was developed by I. O. Huebsch of the U.S. Naval Radiological Defense laboratory; see his 106 pages long May 1963 report USNRDL-TR-653, A Model for Computing Base-Surge Dose-Rate Histories for Underwater Nuclear Bursts (Confidential-Formerly Restricted Data):
‘A model for calculating transit-radiation dose rates and doses from the base surge of an underwater nuclear burst is described. Calculated values are compared with measurements made at Hardtack Wahoo and Umbrella, Crossroads Baker, and Wigwam, and with predicted values for two proposed underwater shots. The model is a geometrical-radiological representation of of the base surge, whose characteristics depend on weapon yield, burst depth and surface wind speed. The model is estimated to be valid for 1-kt to 100-kt underwater bursts for minimum depths of 20 to 90 ft, respectively, and for times at least 30 seconds after burst. Dose rates and doses can be computed for either fixed or moving points in the radiation field. The comparisons show that the calculated values, in almost all cases, agree within +/- 50% of the measured values. (Abstract UNCLASSIFIED.)’

This base surge radiation model for underwater bursts was later supplemented with a code that predicts dosage from the expanding ‘pool’ of contaminated water (which is water that has been heated and contaminated with fission products by the pulsating bubble of the detonation as it rises, before erupting through the water). In nuclear tests, underwater radiation probes were able to distinguish this effect from the base surge radiation which was measured by probes above the water. The full computer code was finished in 1968 and is called ‘Daedalus’ (the ‘cunning worker’ of Greek mythology), the underwater equivalent of the land surface burst fallout computer code DELFIC:
Edward A. Schuert, et al., DAEDALUS: A Gamma Exposure Rate Prediction Code for Underwater Nuclear Explosions, U.S. Naval Radiological Defense Laboratory, report USNRDL-TR-68-137, July 1968, Secret-Formerly Restricted Data.
Above: example of an underwater burst base surge dose rate and expansion prediction given in Philip J. Dolan’s originally secret manual Capabilities of Nuclear Weapons, DNA-EM-1, U.S. Department of Defense, Chapter 5, Nuclear Radiation Phenomena, August 1981 revision.
Above: example of an underwater burst expanding water pool dose rate prediction given in Philip J. Dolan’s originally secret manual Capabilities of Nuclear Weapons, DNA-EM-1, U.S. Department of Defense, Chapter 5, Nuclear Radiation Phenomena, August 1981 revision.

A study of the hard-to-decontaminate soluble ionic fallout effects on adjacent land from a large underwater or water surface burst in San Francisco Harbor, based on nuclear test decontamination data, was presented to the U.S. Congressional Hearings on The Nature of Radioactive Fallout and Its Effects on Man in June 1957 (vol. 1, p. 318). The study assumed that 25 square miles would be decontaminated, consisting of all paved areas, all industrial and commercial areas and buildings, 50% of park areas, and 10% of the outlying residential areas (homes). Firehosing and earth moving were the methods considered, using nuclear test results.

It was calculated that the decontamination would take 10,900 people altogether 28.5 days to complete, requiring 676,000,000 gallons of water, 341,000 gallons of gasoline and 195,000 gallons of diesel: ‘The water requirements are within the capability of the normal supply. Fuel consumption is less than normal daily requirements. The greatest problem would undoubtedly be that of organizing, training, supervising, and controlling …’
More on the Baker test contamination

(Waves approaching with 1.8-m height increased to 4.6 m in water 6 m deep then broke.) The mushroom subsided, to produce a misty ‘base surge’, emitting 4,000 R/hour of gamma at 2 minutes, followed by radioactive salt slurry rainout. Hosing and scrubbing ship decks at 7-16 days removed 50-80% of the radioactivity; the rest was chemically attached metal ions.
Note from Friedlander– that means you have to sandblast to decontaminate and if you don’t have robots doing it you basically have to mothball the ships and wait a generation unless you have disposable slave labor (the communists did)

…from The Effects of Nuclear Weapons, 1977: Underwater data http://www.abomb1.org/nukeffct/enw77b2.html


2.83 Because the effects of a deep underwater nuclear explosion are largely of military interest, the phenomena will be described in general terms and in less detail than for a shallow underwater burst. The following discussion is based largely on observations made at the WAHOO shot in 1958, when a nuclear weapon was detonated at a depth of 500 feet in deep water. The generation of large-scale water waves in deep underwater bursts will be considered in Chapter VI.

2.84 The spray dome formed by the WAHOO explosion rose to a height of 900 feet above the surface of the water (Fig. 2.84a). Shortly after the maximum height was attained, the hot gas and steam bubble burst through the dome, throwing out a plume with jets in all directions; the highest jets reached an elevation of 1,700 feet (Fig. 2.84b). There was no airborne radioactive cloud, such as was observed in the shallow underwater BAKER shot. The collapse of the plume created a visible base surge extending out to a distance of over 2 miles downwind and reaching a maximum height of about 1,000 feet (Fig. 2.84c). This base surge traveled outward at an initial speed of nearly 75 miles per hour, but decreased within 10 seconds to less than 20 miles per hour.

Spray Dome
Figure 2.84a. Spray dome observed 5.3 second after the explosion in deep water.

Spray Dome Forming
Figure 2.84b. Plume observed 11.7 seconds after explosion in deep water.

Base Surge
Figure 2.84c. Formation of base surge at 45 seconds after explosion in deep water.

2.85 There was little evidence of the fireball in the WAHOO shot, because of the depth of the burst, and only a small amount of thermal radiation escaped. The initial nuclear radiation was similar to that from a shallow underwater burst, but there was no lingering airborne radioactive cloud from which fallout could occur. The radioactivity was associated with the base surge while it was visible and also after the water droplets had evaporated. The invisible, radioactive base surge continued to expand while moving in the downwind direction. However, very little radioactivity was found on the surface of the water.

2.86 The hot gas bubble formed by a deep underwater nuclear explosion rises through the water and continues to expand at a decreasing rate until a maximum size is reached. If it is not too near the surface or the bottom at this time, the bubble remains nearly spherical. As a result of the outward momentum of the water surrounding the bubble, the latter actually overexpands; that is to say, when it attains its maximum size its contents are at a pressure well below the ambient water pressure. The higher pressure outside the bubble then causes it to contract, resulting in an increase of the pressure within the bubble and condensation of some of the steam. Since the hydrostatic (water) pressure is larger at the bottom of the bubble than at the top, the bubble does not remain spherical during the contraction phase. The bottom moves upward faster than the top (which may even remain stationary) and reaches the top to form a toroidal bubble as viewed from above. This causes turbulence and mixing of the bubble contents with the surrounding water.

2.87 The momentum of the water set in motion by contraction of the bubble causes it to overcontract, and its internal pressure once more becomes higher than the ambient water pressure. A second compression (shock) wave in the water commences after the bubble reaches its minimum volume. This compression wave has a lower peak overpressure but a longer duration than the initial shock wave in the water. A second cycle of bubble expansion and contraction then begins.

2.88 If the detonation occurs far enough below the surface, as in the WIGWAM test in 1955 at a depth of about 2,000 feet, the bubble continues to pulsate and rise, although after three complete cycles enough steam will have condensed to make additional pulsations unlikely. During the pulsation and upward motion of the bubble, the water surrounding the bubble acquires considerable upward momentum and eventually breaks through the surface with a high velocity, e.g., 200 miles per hour in the WIGWAM event, thereby creating a large plume. If water surface breakthrough occurs while the bubble pressure is below ambient, a phenomenon called “blowin” occurs. The plume is then likely to resemble a vertical column which may break up into jets that disintegrate into spray as they travel through the air.

2.89 The activity levels of the radioactive base surge will be affected by the phase of the bubble when it breaks through the water surface. Hence, these levels may be expected to vary widely, and although the initial radiation intensities may be very high, their duration is expected to be short.
The 1958 Umbrella Test 23:15  GMT 8-Jun-58
Test Height and Type: Underwater, -150 feet
Yield: 8 kt

Umbrella was a DOD sponsored weapons effects test for a medium depth underwater explosion. A Mk-7 bomb was used for the test (30 inches in diameter, 54 inches long, device weight 825 lb.) in a heavy pressure vessel (total weight 7000 lb.). Very similar to the Wahoo device. The device was detonated on the lagoon bottom NNE of Mut (Henry) Island. An underwater crater 3000 feet across and 20 feet deep was produced.

The 1962 Swordfish Test
The ASROC (Anti-Submarine Rocket) system https://en.wikipedia.org/wiki/RUR-5_ASROC  that launched this the only live warhead nuclear missile test of the underwater detonation series (unless you count the 1955 Soviet A-Torpedo as a missile)
We should mention in passing that buoyant rising of megaton explosion clouds is around 300 m/sec and a very high altitude nuclear explosion will generate ballistic rising clouds at around 1500 m/sec– see the article below but this confirms my initial assumption– if you want true space launch to escape velocity in a single shot, either start very close to the bomb (if you can rig a way to survive it) and ideally with something massive behind you– ie underground or undersea, not just from a atmospheric zero point.

BLUEGILL (410 kt, 48 km detonation altitude, 26 October 1962) fireball was still fully ionized at a temperature of about 10,000 K and ‘several kilometres in diameter’ when the shock wave departed from the fireball at 0.1 second. The fireball expanded to 10 km in diameter at 5 seconds, at which time it was buoyantly rising at 300 m/sec. It was filmed from below and within a minute transforms while rising into a torus or doughnut shape. It attained a diameter of 40 km at 1 minute, and stabilised at an altitude of 100 km a few minutes later.

KINGFISH (410 kt, 95 km detonation altitude, 1 November 1962) initially had a fireball size is 10 times bigger than BLUEGILL, because of the lower air density at the higher detonation altitude. The KINGFISH fireball rises ballistically (not buoyantly) at 1,500 m/sec (which is 5 times faster than the buoyant rise speed of the lower altitude detonation BLUEGILL). The fireball diameter longways is 300 km at 1 minute, and it is elongated along the natural geomagnetic field lines while expanding. It reaches a maximum altitude of 1,000 km in 7.5 minutes before falling back to 150-200 km (it falls back along the magnetic field lines, not a simple vertical fall). The settled debris has a diameter of 300 km and a thickness of 30 km, emitting beta and gamma radiation which ionize the air in the D-layer, forming a ‘beta patch’….
To me the 30 KT Wigwam test was the most interesting of all these tests because of the depth of the charge.
There was a document at http://www.dtra.mil/documents/ntpr/factsheets/Wigwam.pdf
now unfortunately a dead link that had data as follows:
During the first three seconds after the detonation, the radioactive debris was primarily contained within an initial bubble formed by the interaction of thermal energy with the water. Then, beginning at approximately H + 10 seconds (ten seconds after the detonation) these gaseous products began to reach the water surface, forming spikes and plumes reaching maximum heights of 900 to 1,450 feet and emerging from an area roughly 3,100 feet in diameter. As the plumes fell back into the water, a large cloud of mist was formed. This was the base surge, which at H + 90 seconds had a radius of 4,600 feet and a maximum height of 1,900 feet. The visible surge persisted to H + 4 minutes. At H + 13 minutes, a foam ring appeared with a 10,400 foot diameter. The area within this ring probably approximated the extent of the contaminated water.
While the surface water initially showed significant contamination levels, the water dispersed and radiation decayed rapidly, so that by May 18 the maximum radiation reading found over an 80 square mile area was on the order of one milliroentgen per hour (mR/hr) at 3 feet above the surface.
Wahoo was less contained and Umbrella less still.
The 1958 Wahoo Test 1:30 GMT 16-May-58 
 A 9 kt Mk-7 was detonated at a depth of 500 ft (150 m) in deep water. The spray dome rose to a height of 900 ft (270 m). Gas from the bubble broke through the spray dome to form jets which shot out in all directions and reached heights of up to 1,700 ft (520 m). The base surge at its maximum size was 2.5 mi (4.0 km) in diameter and 1,000 ft (300 m) high https://en.wikipedia.org/wiki/Underwater_explosion
500 feet depth of burst  water depth 3200 ft.

So let’s play with the data: 

Selected Deep Ocean sites for deepest possible launch basin
Med 5121 4486 2900 near Cyprus
Read sea 2635 (1207 near Sinai)
Indian Ocean 5203 off Oman
5824  off Somalia  7455 off Indonesia
Pacific ocean multiple 8-9-10 km holes deepest 11034 according to one reference, sub 11 km by Wikipedia.
 Atlantic deep site 7758 
south of New Zealand 8582
 near south  sandwich in Atlantic 8264
(9219 off Puerto Rico Trench)
 WIGWAM style deep detonation 610 m (2,000 ft), 30 kt maximum height spray 1,450 feet  442 meters
so 30 megatons-4.4 km Need 6 km depth maximum spray height 4.4 km

so 30 gigatons 44 km   like a supervolcano, into the stratosphere but need 60 km depth not going to get it so much more like shallow water shot–GO to Wahoo or Umbrella tables below- Also above a few hundred megatons the atmosphere directly above the bomb itself may achieve escape velocity as well as part of the water

Wahoo style semi-deep detonation depth of (150 m – 500 ft ) 9 kt maximum height spray 1,700 ft (520 m).

For a 6 km deep Wahoo like burst the yield would be around 600 megatons and the spray dome going 20 km high

so 9 gigatons 50 km high– like a supervolcano, into the stratosphere. ( need 15 km depth and not going to get it–  so go to Umbrella for shallower launch data)

UMBRELLA style shallow jet generating detonation depth of 50 m (160 ft), 9 kt maximum height not listed  but the 20 kt BAKER test generated a mile high column so .45 x the yield or  .77 the height or 1.2 kilometers height is plausible

So, 9 megatons causes a 12 km high splash

9 gigatons 120 km high splash knock down orbiting satellites with seawater . (bottom effect interactions may alter this) Also above a few hundred megatons the atmosphere directly above the bomb itself may achieve escape velocity as well as part of the water.

To be blunt the big yields are really unnecessary. A space station, battle station or possible alien Death Star can be destroyed just as well up upwelling atmosphere blown upward as sea water. Just not as dramatically.

I can see a character saying ‘crude but effective’ after a gigaton splash shootdown of such a battlestation.

But to answer our opening musical question, the oceans are about 4-100 gigatons deep, and the skies are about 400 megatons–9-30 gigaton range high depending if you’re just trying to blow air into the way of a targeted orbiting battlestation or the whole darn ocean depth at the deepest point up like a spear.