TShark and Rotating JSON Files

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This is more a tshark questions. Never tried myself, but have you tried with the -b flag?

$ tshark -h
...
Capture output:
  -b <ringbuffer opt.> ... duration:NUM - switch to next file after NUM secs
                           filesize:NUM - switch to next file after NUM KB
                              files:NUM - ringbuffer: replace after NUM files
...