There is a link but it doesn't necessarily always manifest.

Two reads:

Tropospheric Precursors of Anomalous Northern Hemisphere Stratospheric
Polar Vortices
Chaim I. Garfinkel and Dennis L. Hartmann
http://www.eps.jhu.edu/~cig4/GHetal10.pdf

The Life Cycle of the Northern Hemisphere Sudden Stratospheric
Warmings
Varqvut Limpasuvan, David W. J. Thompson, Dennis L. Hartmann
http://www-k12.atmos.washington.edu/...l_JClim_04.pdf

The polar vortex is certainly being displaced and disrupted by
stratospheric warming and cold cyclonicity in the troposphere will
ensue end of next week. Northern blocking is another matter, though,
and maybe people (not here) jump too quickly on the idea that any
stratospheric warming automatically means high latitude blocking and
subsequent frigid E-NE'lies for the UK. The EPV at 60N/10hPa might
need to be more poleward than it's been or is forecast for that. In my
opinion.

Stephen.