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Winds from massive stars have velocities of 1000 km/s or more, and producehot, high pressure gas when they shock. We develop a theory for the evolutionof bubbles driven by the collective winds from star clusters early in theirlifetimes, which involves interaction with the turbulent, dense interstellarmedium of the surrounding natal molecular cloud. A key feature is the fractalnature of the hot bubble's surface. The large area of this interface withsurrounding denser gas strongly enhances energy losses from the hot interior,enabled by turbulent mixing and subsequent cooling at temperatures T =10^4-10^5 K where radiation is maximally efficient. Due to the extreme cooling,the bubble radius scales differently (R ~ t^1/2) from the classical Weaver77solution, and has expansion velocity and momentum lower by factors of 10-10^2at given R, with pressure lower by factors of 10^2 - 10^3. Our theory explainsthe weak X-ray emission and low shell expansion velocities of observed sources.We discuss further implications of our theory for observations of the hotbubbles and cooled expanding shells created by stellar winds, and forpredictions of feedback-regulated star formation in a range of environments. Ina companion paper, we validate our theory with a suite of hydrodynamicsimulations.

Efficiently Cooled Stellar Wind Bubbles in Turbulent Clouds I. Fractal Theory and Application to Star-Forming Clouds