A Flight Instructor in the traffic pattern and the Tower CIC reported a NMAC when an aircraft executed a missed approach and turned toward the Flight Instructor's aircraft.
Synopsis
A Flight Instructor in the traffic pattern and the Tower CIC reported a NMAC when an aircraft executed a missed approach and turned toward the Flight Instructor's aircraft.
Narrative
A near miss occurred with Aircraft Y while my student and I (Aircraft X) were in the downwind for runway XXL. Aircraft Y was inbound on a practice approach to runway XY; with a southbound missed approach. Tower had instructed them to report when they were going missed. The field was busy that day; and tower seemed overwhelmed; but they did advise both Aircraft Y and us of the traffic.We acknowledged the traffic advisory and responded that we were looking for traffic; while Aircraft Y reported they had the traffic in sight. My student and I were unable to visually spot the traffic; but we did see it on our Lynx ADS-B In screen. The last we remember seeing; the traffic was 300 feet below us. Aircraft Y then reported they were starting their missed approach as my student spotted them off the left side of the aircraft; below us. I saw the aircraft for the first time as it passed behind us; appearing to be within 100-150 feet vertically.We continued in our downwind and did not mention the incident to tower; as they seemed to have noticed the near miss and were already stressed. Tower then instructed us to transition to runway XXR and contact the other tower frequency. We landed full stop on XXR and called off the flight there. I decided not to let my student solo; as I considered the environment unsafe at that time.I believe Aircraft Y had the wrong traffic in sight or lost sight of us. This is not a normal occurrence at ZZZ as tower will generally tell traffic to start their southbound missed at the building on the approach path; prior to runway XY; or tell them when to begin their missed.
Second reporter narrative
Aircraft Y was on an IFR approach into Runway XY. Aircraft Y cancelled IFR while on a 2 mile final and informed the tower controller that they planned to fly VFR southbound. As the CIC (Controller in Charge); my job is to overlook the entire operation. As I was working my scan back to the LC1 (Local Control 1) position; I; as well as the CD (Clearance Delivery) controller pointed out to LC1 that his aircraft on final for XY seemed too high; reference his traffic in the pattern. LC1 told us that the aircraft on final had his traffic in sight. Looking out the window; they appeared to be close; but since LC1 assured us that traffic was issued; and they had each other in sight; we moved on to other areas to work/scan.Giving a solid point of reference to turn for anyone on final for runway XY when they plan to go VFR missed; with a full traffic pattern for XXL is a good idea. The building is an excellent visual marker that keeps them well clear of the XXL pattern.
Source: NASA Aviation Safety Reporting System (public domain). Reports are voluntary submissions and are not verified by NASA.