Edouard Naville was the first to excavate the Tell el-Daba in the eastern delta. Since 1966, archaeological research is conducted by the Archaeological Institute of Austria and led by Manfred Bietak. This team, using the latest technologies, identified the contours of a Hyksos city on the edge of those of Pi-Ramesses. These two towns have been built on an island of the former Pelusiac branch of the Nile, largely open to the Mediterranean and to the East, thereby facilitating trade.
The site was occupied since the Middle Kingdom : a temple of the 11th dynasty and the 12th Dynasty was discovered at Ezbet Rushdi, at the north of the tell el-Daba. Under the 13th Dynasty, from 1780 to 1550, the indices of occupation of the site by a non-Egyptian population, probably having moved from the Levant and Cyprus, come from the type of architecture of the residential areas, close to those of Syria and Palestine, and the presence of graves in the basement of the houses.
The discovery of a carbon layer, suggesting of a destruction by fire, and many arrowheads, are other indications for an identifying at Avaris. The remains of Minoan-style frescoes, similar to those of Knossos, were found in a palace built on the ruins of Avaris by Thutmose III.
The most meaningful find of a Hyksos capital is a stele and seals of Khyan king of the 15th dynasty. Some researchers think that this name is that of Hayanu recorded in a list of Assyrian kings as ancestor of Samsi-Adad, well-known by the archives of Mari.
The Egyptian name admitted for this city, Hut-waret, which means "big house", would be pronounced "Haat-wurat" giving Avaris. However, the name arguments are slim. Some put forward more phonetic proximity to Hawwarat located at the entrance of the Fayum, which, reading hieroglyphic texts referring at Avaris, is also plausible. Especially at El-Lahun and Gurob, Petrie found many Asian objects.
The name of Pernefer is also a hypothesis for the port exhumed at the tell el-Daba. And I do not see why the same site would have different names during the different periods of the history of Egypt.
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My notes of veracity :
Avaris, Hut-waret in Egyptian, was at the tell el-Daba: 2.5 / 5
Avaris, Hut-waret in Egyptian, was at Hawwarat in the Fayum: 2.5 / 5