The Line of Battle became the standard for naval warfare for quite some time. But we're there any other powerful tactics during the period of naval stagnation? Anything specifically to counter LoB?
As a side question, does anyone here happen to know about Dhows and their usefulness in naval warfare?"
I wrote an answer to this here related to Nelson's tactics at Trafalgar that may be of interest:
https://www.reddit.com/r/AskHistorians/comments/3ebdk5/how_did_nelsons_tactics_work_at_trafalgar/
To quote from that a bit:
The basic problem with the line of battle was that it tended not to produce decisive results, because ships of similar strength could fight each other, inflict similar amounts of damage, and concentrate strength against strength. (This was actually an advantage, in some ways, of the line of battle vs. earlier melee combat.) But naval tactics had stagnated since at least the Anglo-Dutch wars of the 17th century.
In the early 1780s, the French admiral Pierre André de Suffren had tried to mitigate these weaknesses by concentrating a larger part of his fleet against a smaller part of the enemy fleet, by essentially doubling the line (in other words, placing ships on either side of the enemy fleet and hoping to knock out that part of the enemy line before the other part of the line could respond). He was hampered by command and control issues, and this was unsuccessful. On the British side, George Rodney tried similar tactics at the battle of Martinique (1780) but also found it difficult to explain his tactics to his subordinates.
Rodney finally succeeded in breaking through the enemy line at the Battle of the Saintes in 1782, aided by a shift in the wind, and decisively beat the French fleet.
Nelson had studied these tactics, and saw the potential for their decisive use. In the battle of Cape St. Vincent (1797), when Nelson was still a captain, he broke his ship out of the line of battle without orders so he could engage the Spanish van (front part of their fleet), engaging three Spanish ships with his one and taking two of them as prizes. (The exact number of ships that came to his aid is in dispute, but his 74-gun HMS Captain engaged ships of 130, 112 and 80 guns for a period of time.) Nelson could have been censured for breaking the line without orders, and could quite possibly have lost his ship in the process. The British admiral, Sir John Jervis (later created Earl St. Vincent) did not reprimand Nelson, but also did not mention his action in dispatches. (Nelson himself used his tactics for propaganda purposes, but I'm getting away from the point.)
Nelson also used the tactic of concentrating the strength of his fleet upon a smaller portion of the enemy's line in his tactics at the Battle of the Nile (sometimes called the Battle of Aboukir Bay) in 1798. That battle came after a long and frustrating summer of chasing the French from one end of the Mediterranean to another, which provided Nelson (now an admiral) with the time necessary to meet with his captains and make his tactical intentions known. When Nelson finally caught up with the French fleet, it was at anchor, but he proceeded to attack immediately with the intention of pitting his ships 2-1 or 3-1 against the front of the French line. On his own initiative, Thomas Foley, captain of HMS Goliath, noticed that there was room between the French ships and the shoal water to the west, and passed down the west side of the French line. Other ships followed, so the French line was essentially doubled, allowing the British to anchor, beat ships into submission, weigh anchor and proceed down the line.
There's a lot more in that thread -- if you have other questions, please let me know!