The UK is indeed investing in supercomputers.
Look at the Snowden computer at Daresbury Lab.
Look at the Brunel supercomputer at Bristol - built with ARM processors and there is a lot of interest in that. The Goverment recently announced funding for machine learning, as reported on El Reg.
UK Met Office is currently at Number 15, which is pretty respectable.
So what are they doing?
UK - weather forecasting. Materials simulations. Jet engine simulations (Rolls Royce).
CFD (Formula 1, Bloodhound, Rolls Royce etc etc)
AWE - can imagine that would be atomic weapons design then.
GCHQ - hello!
US National Labs - nucelar stockpile stewardship. Simulating how materials age with radiation, and are the bombs safe to store, and are they going to go off when used.
NOAA - weather simulations
NASA - astrophysics and all the other stuff NASA does
Texas TACC - simulations of the human heart etc etc.
Swiss - probable lots of interesting research. But the Swiss centre also houses their meteo centre, so weather forecasting at least. And weather forecasting with the Swiss terrain needs a lot of detail.
China - no idea!