Medvedev at home in Melbourne

Daniil Medvedev is reprising a familiar sense of belonging.

The mercurial Russian made Flushing Meadows home last September despite a pitched battle with New York fans.

Melbourne Park, while far less volatile, is now feeling reassuringly comfortable to the sublimely talented Russian.

Elated after a clinical 7-5 6-1 6-3 over Spanish qualifier Pedro Martinez, a former junior rival, the world No.4 is trucking menacingly towards the second week.

With 40 winners, 19 aces, just two double faults and only one service break, the fourth seed had good reason to be pleased despite a brief interruption to have eye drops inserted.

"It was not an easy match, especially the first set," the US Open finalist said.

"I managed to stay there the whole match. He can be really on fire. I knew I had to stay in the match and stay in front."

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Medvedev, 23, faced Martinez, 24, in the French Open juniors but their paths hadn't crossed for several years.

"I played him in Roland Garros juniors but I didn't see him for four years," Medvedev said.

He's getting to the top now, which is good.

"You don't know if he is stronger in the forehand, stronger on the backhand. The guys in the top 50, you know what to expect."

Medvedev was more assured against Martinez than dangerous American Frances Tiafoe in the first round.

"Today was much better than the other day," he said.

"I can be here and have a long tournament and hopefully make many more aces (and a donation) for the bushfires."