Hurricanes seem to run out of steam when they make landfall.
If our planet were entirely covered by ocean, would hurricanes continue indefinitely? Would they keep gathering energy and increasing in intensity until...?
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No. As it is, many hurricanes never make landfall. In an oceanic world I could see three fates happening:
Hurricanes that dissipate due to dynamical features or climatological features.
By dynamical features, I mean things like two hurricanes that shear each other out or produce an environment that can't be sustained. An example of the latter is upwelling, which generates cooler water that saps the energy from the hurricane. A climatological feature that might prevent a hurricane from developing indefinitely might be the Azores high. As it is, there are places that hurricanes don't seem to go.
Hurricanes that undergo extratropical transition.
Notice in the figure above, the hurricanes just disappear near the poles? As they come closer to the poles, the temperature difference becomes larger. Eventually they no longer look like tropical cyclones/hurricanes (little to no temperature difference), but rather look like an extratropical cyclone (see this link for some differences). This process is called Extratropical transition.
While looking up papers for this question, I stumbled upon this paper. It implies that we would get longer lived hurricanes spreading the entire planet. I'd be a little skeptical of this result though, since it ignores the fact that the earth is heated unevenly, which drives most of the climate.
On a side note, such simulations do exist. These are called Aquaplanet simulations. Some studies I found include:
What is possible in a low-friction world is illustrated by the Great Red Spot on Jupiter, an anticyclonic storm that has has been continuously observed that fluid planet's surface at least since 1878 (142 years). Though it has shrunk a bit from its biggest size, it's still big enough to cover the Earth. The Great Red Spot may have had a longer history, possibly going back another two centuries:
The Great Red Spot may have existed since before 1665, but the present spot was first seen only after 1830, and well-studied only after a prominent apparition in 1879. The storm that was seen in the 17th century may have been different than the storm that exists today.
Our own planet is too small for that, but a storm covering a similar fraction of Earth's surface would be as large as the contiguous 48 United States.
1. Karl Hille (2015-08-04). "Jupiter's Great Red Spot: A Swirling Mystery". NASA. Retrieved 2017-11-18. Link