Thunderstorms at sea and TC (Tropical Cyclones) both require unstable atmospheric conditions however the characteristics of each are very different.
The most obvious difference is the eye of the TC:
Here’s another interesting paper: Fluid Mechanics of Tropical Cyclones(pdf). by Sir James Lighthill
In every cyclone, of course, the surface winds spiral inward cyclonically; yet in TCs, on the other hand,
this spiral motion’s inward component performs an extraordinary “disappearing trick” at the eyewall: that
circular wall of extremely dense cloud (of the type known to meteorologists as “convective”) which surrounds
an eye often nearly free of cloud. What causes the inward component of the spiral motion to disappear
there?
The answer is somewhat astonishing: in the eyewall, fast upward motions are able to lift the air right up to
the base of the stratosphere (situated at about 15 km altitude), where—as Figure 1(d) shows—it then spirals
outward in a broadly anticyclonic (although not usually very symmetrical) motion. Thus, the surface spiral
“disappears” because fast upward motions lift surface air to stratospheric altitudes.
This part of the discussion is familiar to mariners with a basic understanding of lapse rates:
Yet, under ordinary circumstances, air simply cannot rise like this! This is because rising air, as its
pressure drops, expands and therefore cools; actually (see below) by 1 °C per 100 m through energy lost in
the work of expansion. Now, in any stable atmosphere, the surrounding air is not so cold; in other words,
the atmosphere’s temperature drop with height is less than 1 °C per 100 m. The rising air, then, being colder
than its surroundings, necessarily falls back.
(left out some math equations)
This is the release of latent heat:
By contrast, any corresponding conclusions from wet-air thermodynamics are altogether different. Wet air
here means air that is 100% humid; in other words, saturated with water vapour. Now, whereas rising air
that is wet (in this sense) does still cool, nevertheless this cooling causes some condensation of water vapour
into rain drops; in which process latent heat is released, so that the degree of cooling is less.
In wet-air thermodynamics the equation governing rising air is changed…
For rising wet air, then, the resulting rate of temperature drop with height…
assumes very roughly half the former value (2), becoming about 1/2°C per 100 m.
Later the paper discusses the Carnot heat engine:
Emanuel (1986, 1991) has pointed out how wet-air thermodynamics allows us to view the TC as a heat
engine where the working fluid is just that mix of dry air with water in all its forms (vapour, droplets, ice
crystals) which appears in the atmosphere. From this standpoint all the heat intake occurs over the ocean, and
essentially consists of latent heat of evaporation transferred during the long spiral path pursued by winds
before they reach saturation. Somewhat remarkably, all this heat intake occurs at a practically constant
temperature (that of the ocean surface). This is because most of the cooling of air which could be expected
to result from provision of latent heat is cancelled by the vigorous processes of radiative and turbulent heat
transfer which take place at the interface between ocean and atmosphere. After that the heat engine’s nearly
adiabatic work-output phase is concentrated in the eyewall; while, finally, the heat-loss phases takes place
at a nearly stratospheric temperature.
Unlike thunderstorms TCs cover large areas of ocean and the long path followed by high winds results in the uptake vast quatities of heat.
This is the key: “latent heat of evaporation transferred during the long spiral path pursued by winds”
From NOAA Hurricane Research Division
In 1948 Erik Palmen observed that tropical cyclones required ocean temperatures of at least 80°F (26.5°C) for their formation and growth. Later work (e.g., Gray 1979) also pointed out the need for this warm water to be present through a relatively deep layer (~150 ft, 50 m) of the ocean
Hurricane force winds typically out 100 mile diameter, gale force winds out to a diameter of 300 or 400 miles in 80°F water in a layer 50 meters deep…that’s a lot of heat energy.