Ram Pressure Stripping can remove gas from satellite galaxies in clusters via a direct interaction between the intracluster medium (ICM) and the interstellar medium. This interaction is generally thought of as a contact force per area, however we point out that these gases must interact in a hydrodynamic fashion, and argue that this will lead to mixing of the galactic gas with the ICM wind. We develop an analytic framework for how mixing is related to the acceleration of stripped gas from a satellite galaxy. We then test this model using three wind-tunnel simulations of Milky Way-like galaxies interacting with a moving ICM, and find excellent agreement with predictions using the analytic framework. Focusing on the dense clumps in the stripped tails, we find that they are nearly uniformly mixed with the ICM, indicating that all gas in the tail mixes with the surroundings, and dense clumps are not separate entities to be modeled differently than diffuse gas. We find that while mixing drives acceleration of stripped gas, the density and velocity of the surrounding wind will determine whether the mixing results in the heating of stripped gas into the ICM, or the cooling of the ICM into dense clouds.
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