I wasn't sure which StackExchange I should ask this question, but since the story I am writing is basically a historically inspired fantasy, I decided to present it here.

The story in question is supposed to be a fairly short pirate adventure set in a Bronze Age world. My protagonist is an admiral from a fairly wealthy kingdom (inspired by the kingdom of Kush from our world) who is hunting down the ringleader of a large pirate organization. I imagine that, after learning where the pirates' fortified base of operations is located, she would go after them with a fleet of several galleys each manned with archers and infantry (think the war galleys of New Kingdom Egypt).

Now, it's important to the story that my admiral gets captured by the pirates in a sea battle, which would require that their fleet overwhelms hers somehow. What I imagine is that the pirates' ships are dhow-type vessels which are individually smaller than my admiral's galleys, but their fleet is numerically larger. In short, it's a small number of large galleys versus a much larger number of small dhows.

How would such an asymmetrical sea battle play out in a Bronze Age world? The scenario I imagined is that some of the pirate dhows would cut off my heroine's galley from the rest of her fleet by ganging up and encircling it (a bit like sharks swimming around their prey in cartoon depictions) before flinging out the grappling hooks and then boarding it to capture her. But then what would happen to the rest of the protagonist's fleet? Couldn't they barge in and save my heroine before the pirates carried her off?

Divide and conquer

The advantage of having a lot of small ships is that you have a lot more flexibility in your tactics and maneuvering. You likely have a shallower draft. Make use of this. Your pirates operate out of a shallow bay, scattered with reefs, with turbulent waters. Use their smaller ships to draw the large galleys in, and then send out fire ships to split them apart, and make them unable to follow each other. Isolate the flagship galley, then just ram it (bronze age should let you duplicate the ramming prows of triemes) with enough ships to allow your boarding parties to overwhelm what the troops on board can handle.

This approach also means that you can have the admiral have overwhelming force and still lose. Her forces cannot come to her aid: she only has her ship to bring to bear, as the others are floundering amidst the reefs and burning ships.

Is the purpose to capture the protagonist or defeat her fleet? Those are not necessarily the same thing.

If the pirates have the advantage of knowing the waters, you, as the author, can arrange for there to be a convenient reef they know about that, when the tide is right, just allows them to pass over it with their shallow-draft boats while the larger ships of the admiral can't. So they lure the admiral's ship in (the tech of the time means the admiral is going to be leading from the front) and gets it grounded on the reef, while the ebbing tide means her other ships can't get close to provide support (at least the ones not already aground). That allows them to attack it en masse, overwhelm it, and capture her, then making their getaway before the tide rises and the other ships can finally move in.

If you want the fleet defeated as well, then simply have them sail in and fling torches or whatnot aboard the stranded ships.

Its a numbers game during Bronze age

Sure they got Big boats, and as you have smaller ones, but your pirates dhows have better maneuverability than your protagonist galleys.

Their plan of attack:

The pirates will charge head on, since arrows will be the primary ranged weapon at this age, the galleys will have archers raining burning arrows at the dhows, one by one the pirate dhows sink and burn, but the attack does not cease. The pirates will attack the ships sides, throws hooks or burning arrows too into the galleys, some pirates board the ships and kill your crew with swords, others support them through ranged attack. The attack of the pirates will be relentless until they finally burned the last galley, capturing your protagonist in the process.

When I had to puzzle out a naval battle with a similar premise for a book of mine, I used a shallow bay with many submerged rocks. The larger ships had to maneuver slowly and carefully, so they couldn't come to each other's defense, while the smaller, shallow-draft boats could go where they pleased.

Another idea: if you've ever tacked upwind in a channel between two islands, then you know how the funnel effect makes each successive tack shorter and it seems you'll never get there. The point is, distance at sea is relative: supporting ships could be within shouting distance, and still half an hour away.

Your galleys are rowed, of course, but current does just as good a job. Supposing there's a tidal current past the mouth of the bay where the pirates are based. Being tidal, it changes quickly. The command ship, being larger and better crewed, can make way against the current just a bit more quickly than the other two vessels and enters the calm bay ahead of them. Meanwhile, the current is rising and effectively pinning the other two ships. Then the pirates attack.

Incidentally, did they have grappling hooks in the bronze age? I haven't done the research myself, but I'd be very skeptical. Grappling hooks require a lot of strong, long-length cordage that you are not using for anything else and that you can afford to lose when the enemy inevitably cuts it away. And rope was expensive. Check out one of Linybeige's instructive and funny rants about the value of rope in middle ages. I imagine his arguments are even more salient for bronze age.