Why does a shower curtain billow inward and cling to you?

Partly settled. Some of it is understood, some is still argued about.

The popular explanation invoking Bernoulli's principle (fast air/water flow from the shower head causes locally low pressure) is intuitive but, when David Schmidt ran a full computational fluid dynamics simulation of a bathroom shower in 2001 (earning him the Ig Nobel Prize in Physics), the numbers did not support Bernoulli as dominant, since the droplet spray does not behave like a simple fast airflow. Instead, his simulation showed the shower spray drives a horizontal vortex in the enclosed shower stall, with a low-pressure core near its axis that pulls the curtain inward -- explicitly described by Schmidt himself as only a 'partial solution,' since real bathrooms vary widely in geometry, temperature, and airflow, and buoyancy and turbulent entrainment likely also contribute in varying amounts.

One of the most universal bathroom annoyances turned into an Ig Nobel-winning computational fluid dynamics problem, and the 'obvious' textbook answer (Bernoulli) turned out to be wrong.

Explanations that circulated

• Bernoulli's principle (fast-moving shower spray creates low pressure that sucks the curtain in) -- computationally shown by Schmidt not to be the dominant effect
• The curtain moves because warm humid air rises and pulls it inward via buoyancy alone

References

• The Physics of a Shower Curtain (simulation study, 2001 Ig Nobel Prize in Physics), D. P. Schmidt, University of Massachusetts Amherst (CFD study; summarized in press), 2001