After cyclone Peter lost intensity over eastern Cape York Peninsula in the first few days of January, the trough system in which it was embedded remained over the southern Gulf of Carpentaria-Cape York area. During the next few days the weak, complex low, which remained after Peter , migrated slowly westwards across the southeast and southern Gulf. By late on 7 January 1979 satellite photographs indicated a weak circulation. The system exhibited an erratic course to the northeast of Groote Eylandt and did not intensify until it began to move in an east-northeasterly direction after 2000 UTC 8 January 1979. The path of the low continued in an east-northeasterly direction, with gradual deepending to cyclone intensity and acceleration as it crossed the Gulf. Ship reports at 2100 UTC 9 January 1979 indicated 68 km/h winds 270 km north-northwest of the centre and near 68 km/h winds 100 km to the east-northeast.
Greta , moving eastwards at 25 km/h, crossed the coast between 0200 UTC,and 0300 UTC 10 January 1979 about 20 km south of Weipa. Weipa recorded a maximum gust of 78 km/h and a 30-minute calm as the cyclone passed, as well as a minimum pressure of 986 hPa. Little damage was experienced. Greta maintained a well-marked cyclonic circulation during its continued eastward overland movement, but then crossed the Cape York Peninsula east coast, changed course to the south-southeast and then moved parallel to the coast at 15 km/h.
The coast was re-crossed at 0500 UTC 11 January in Princess Charlotte Bay with an estimated central pressure of 990 hPa. Banding features remained evident on satellite pictures as it moved inland in a west-southwest direction. It eventually passed close to Alice Springs at 0200 UTC 16 January 1979 with a central pressure near 996 hPa.
Greta produced flood rains over northern Cape York Peninsula with heavy rain extending south of Cairns. Flooding was not as serious as with the earlier Peter . No significant wind damage was reported.