It joins the Timor Sea in the west by the Clarence Strait near the city of Darwin . It joins the Arafura Sea in the north by Dundas Strait between Melville Island and Cobourg Peninsula . It is connected to the Timor Sea in the west by the Clarence Strait ( near the city of Darwin ) , and to the Arafura Sea in the north by Dundas Strait ( between Melville Island and Cobourg Peninsula ) .