Topping off sour secondary

[t_met]

I'm in the process of aging my first sour. After moving to the secondary 5 gallon glass carboy. I have about 4.25 gallons, so the top of the fill line hasn't reached where it becomes narrow. Should I top this off with some fresh wort? Or just leave it be?

I should add this is a 1.050 pale sour.

My concerns are with oxidation and acetic acid.

 

[BigPerm]

I'm going to bump this, and add something.

I have my sour aging in a small (5gal) bourbon barrel. How do most of you top up? I've done it a couple of ways, but the obvious correct answer (racking) is a PITA for such a small volume. Just curious what others do; the last couple batches i did in this barrel seemed to have less of an evaporation/absorption rate.

 

[Osedax]

I am fairly new at souring but, this is how I did it. I brewed about a gallon more than I needed, fermented in a carboy with primary strain, racked all but the gallon to the barrel, and racked the gallon to a gallon jug. I inoculated the gallon with just brett to help with oxidation and reduce the FG. Every 3-4 months I just add some to the barrel. Probably not the beat way but, it is how I did it and it seems to be working. I don't even have a pellicle in the barrel yet and I'm not trying extremely hard to not aerate. Just some sprays of CO2.