Underwater explosions have been studied by humanity for decades now. There is a short term for underwater explosion: undex.
Since water is (for practical purposes) incompressible, the energy of a blast suffers less dispersion over distance. In other words, the blast radius is much larger than what it would be, should the detonation happen in air.
About underwater nukes, you should read Wikipedia's main article on it, and then the one about Operation Hardtack's Wahoo Blast:
The nuclear device was positioned 500 feet deep in the Pacific Ocean (...) Within a second of detonation, a spray dome was created that reached a height of 840 feet [above the surface] after seven seconds (...) When the spray dome and base surge had dissipated, a foam patch could be seen spreading from the surface zero water to reach over 6,000 feet (...) The nuclear device had a blast that was calculated to be nine kilotons. All fallout stayed within the predicted fallout area with a maximum of 0.030 R/hr. The target ship at 5,900 yards was directly hit by the shockwave vibrating the entire ship and shaking it violently. The Moran, merchant marine ship moored at 2,346 feet away, was immobilized due to shock damage to its main and auxiliary equipment while also attaining minor hull damage.
That was a 9 kilotons blast, which is a relatively small yield. You can be sure that anything above the blast was obliterated. To the sides and further below, targets will take a hit from the blast wave.
But what if a larger payload was used? XKCD's What If number 15 was about detonating the Tsar Bomba (yield: 53 megatons, or 5,888.88 times the Wahoo test payload) underwater.
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:
$$ Radius = (\frac{3}{4\pi})^{\frac{1}{3}} \times (\frac{40\% \times 53 \space megatons \space of \space TNT}{Mariana \space Trench \space pressure + 1\space atm})^{\frac{1}{3}} \approx 580 \space meters $$
If we use the same equation for a smaller depth of 500 feet (approximately 152 meters):
$$ Radius = (\frac{3}{4\pi})^{\frac{1}{3}} \times (\frac{40\% \times 53 \space megatons \space of \space TNT}{16 \space atm})^{\frac{1}{3}} \approx 2367 \space meters $$
I don't have any data to make further extrapolations, so from now on it's just pure speculation. I think the water column, fauna, flora and people within the blast would be vaporized, making for a big mushroom cloud reaching almost as high as the original Tsar Bomba test one (which peaked at 56 kilometers above sea level, nearly seven times the altitude of Everest's peak). The sheer pressure of the shockwaves will keep the surrounding water from caving in at first, but once that passes, water will rush in in a very catastrophic manner. Expect a whirlpool of biblical proportions. Both the initial blast and the later rush-in would cause tsunamis that would travel for dozens to hundreds of kilometers. If the sea in that area is around 150 feet deep, then the seafloor will become very hard, very plain glass, and the blast will be detected by sismographs multiple times as the shockwaves travel through the crust and mantle of the planet.
Oh and once that settles you will see a black rain. The water itself should not be much radioactive, but the salt in it should give you more problems than hypertension.
