An increase in gradient will generally increase stream velocity.

Tributary is the answer you are looking for, I believe.

Stream discharge physically depends on two factors: stream cross-sectional area and velocity. Area is composed of width and depth. Q (flow) = vel x width x depth.

Stream elevation change, or how steep a stream is, will affect the velocity. Higher sloping streams (like those with few meanders) will travel faster than sinuous, snaking streams that have a lower elevation drop per length of stream.

Stream velocity is dependent of four things. They are, the flow type, the gradient, the channel shape, and the discharge of the stream. Streams will flow faster in narrow channels on steeper grades.

The Gulf Stream has a warming effect on the climate of the UK. (See links below)