Why doesn't my cheese cake rise when cooked in a water bath?
The water bath is doing exactly what it should. Most recipes are designed to make your cheesecake rise as little as possible. 

Baking a cheesecake is kind of like baking a souffle, except instead of encouraging rise, you combat it. 

Cheesecake doesn't have the structure to sustain rising. Cream cheese can't hold the air, so when it rises, it eventually collapses &amp; cracks. 

Overmixing can incorporate too much air, which expands when it gets hot and collapses when it cools. Most recipes therefore advise against over mixing. A too-high temperature can have a similar result, converting too much liquid to steam, which expands, then collapses. A water bath insulates against the heat, allowing the cheesecake to cook more gently to combat that "too hot rise"