while initially that sounds plausible, you have to now take into account the fact that the seagull isnt flying in a direct line anymore, therefore, it will take longer for him to reach the other guy coming the opposite way.
For him to do the same amount of curvy turns in the same amount of time, he will have to fly faster to cover the same amt of linear distance.
of course he might do fewer curvy turns now, and he still has his wings to keep him happy, and in the end he still goes 90Km in one hour, even if he's flying in a spiral.

God where's the wind?