Connections between the Lower Stratosphere and Tropospheric Circulation

How does tropical tropospheric circulation impact the lower stratosphere and vice versa?

Relationship of Subtropical Jet and Hadley Cell in CMIP5 Model Output

Is the subtropical jet actually coupled to the Hadley Cell?

Subtropical Jet Behavior in Idealized Models

What are the necessary processes to decouple the subtropical jet from the Hadley Cell?