For example, if a hurricane has 200km/h wind speed, and it increases the translation speed from 10km/h to 30km/h, would the intensity become 220km/h?


It is not the quite the numerical relationship you have described in your question but YES the effect of translation(or forward speed) upon the intensity of tropical cyclones in the tropical oceans has been studied in this peer reviewed reference - Tropical cyclone translation speed and intensity correlation

The conclusions that the authors have reached is that there is a positive correlation with translation speed and tropical cyclone intensity. The explanation for this correlation is that a tropical cyclone with a faster translation speed reduces the exposure time of the cooling to the TC. The sea surface cooling is induced by the effect of the surface winds on the ocean and and strong winds can bring cooler subsurface water to the ocean surface . A slower moving TC is exposed to the sea surface cooling for a longer period of time and hence contributes to a negative SST feedback and has lesser chance for reaching higher intensity.

You can read a popular science version of the peer reviewed reference in this website - Hurricane speed intensity


Would a hurricane increase intensity due to increasing translation speed?

As depicted below, meteorologists account for this effect in announcing the highest sustained wind speeds. The highest sustained winds account for both the motion of the storm itself and the motion of the winds relative to the moving storm.

Cartoon of a hurricane moving to the northwest. Winds are strongest to the northeast, weakest to the southwest.
Source: http://www.aoml.noaa.gov/hrd/tcfaq/D6.html

The hurricane in the above diagram is moving to the northwest at 10 mph and is capable of sustaining 90 mph winds relative to the storm itself. That means that relative to land, those 90 mph winds become 100 mph winds in the northeastern portion of the storm, but only 80 mph in the southeastern portion of the storm. The highest sustained winds would be reported as 100 mph for the hurricane depicted above.

That northeast section of the storm where the winds are strongest is the so-called dirty side of the storm. Note that which side is the dirty side depends on the storm's motion. The dirty side is to the east during a sharp landfall along the Gulf Coast, to the north during a sharp landfall along the US Eastern Seaboard, and to the south for eastern Pacific hurricanes making landfall on Baja California. Because tropical storms rotate clockwise in the southern hemisphere (as opposed rather to counterclockwise as depicted above), which side is the dirty side also depends on the hemisphere.


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