(to) bear down on (something or someone)

Here's important news for many people:

Isaac Gains Hurricane Strength, Bears Down on Gulf Coast

Anybody who is in the hurricane's path had better beware, and prepare.  Most of the time when this term is used, it's in reference to a hurricane or severe storm.

Isaac grows stronger as it bears down on Florida Keys, hurricane watch extended to New Orleans
***

Here's another example:

Typhoon Tembin Bears Down On Taiwan 

But not always.

Currency crisis, economic weakness bear down on Europe's car industry

But the effect is the same:  Watch out, European car industry, because it's going to be feeling the full weight of the currency crisis and the weak economy for a while.***