How is the continuity of transparent discharges, which have no specific time and whose emission is not felt, determined in order to ascertain whether or not they invalidate ablution?

If the discharge does not cease for a time sufficient for purification and prayer, or if the time of its cessation is unknown (it appears sometimes and not others, and it comes earlier sometimes and later others), then your ruling is that of one afflicted with سلس (incontinence). You perform ablution for prayer after its time has begun, and you pray with this ablution the obligatory prayer and whatever supererogatory prayers you wish. And these discharges are pure, according to the more preponderant opinion.