Naval fighting on the Rhine in the Napoleonic era

Were there British or Prussian naval battles against the French on the Rhine during the Napoleonic Wars?

There were river actions, but they usually resembled contested crossings supported by artillery barges rather than conventional fleet battles.

The Rhine fighting is framed as land warfare extended onto an inland waterway. Barges carried artillery to support or oppose river crossings, so the naval element served armies rather than operating as an independent fleet. Prussia remained much stronger in infantry, cavalry, and artillery than in naval institutions. Capable naval officers sometimes appeared, but poor promotion prospects encouraged some to seek pay, titles, and respect in Russian service.