Are we watching the maturation of a key player in women's tennis' future?

A bit early to say that perhaps, but that was a supremely mature set of tennis from the supremely promising Naomi Osaka as she hunts the biggest scalp of her career so far.

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Suddenly there are gremlins crawling all over Naomi Osaka's previously free-flowing limbs.

She stumbles to 15-40. Two break-back points to Angelique Kerber.

Seen off in thrilling style as Osaka drills a superb winner down the line on the run to drag herself back to deuce.

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French Open champion Jelena Ostapenko is among those waiting for the rain to relent and the Latvian has already been given a test by Spanish world number 60 Lara Arruabarrena on court 17.

Ostapenko, the 12th seed, took the first set 6-2 but dropped the second 6-1. However, she has a break in the decider and leads 3-1.

Another duff second serve brings up Angelique Kerber's fifth double fault of the match so far and advantage Naomi Osaka.

And the Japanese's power overwhelms Kerber at the back of the court.

She serves for the set next!

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A double fault from Angelique Kerber gives Naomi Osaka a 0-15 leg-up into the game.

A walloped cross-court winner gives the Japanese 0-30 and a real chance to crowbar open this set.

Kerber is gravel gritty though. She battles back to take the game to deuce.

Gigi Salmon
BBC Radio 5 live sports extra commentator at Flushing Meadows

Image source, BBC Sport

The roof is closed on Arthur Ashe and the action continues as the rain falls.

Naomi Osaka is most comfortable playing a bazooka baseline game - standing and delivering with pinging power.

That is the template that takes her to 40-0.

She is a mite wide with another death-or-glory forehand stroke.

But a searing winner, on the stretch, down the line, wraps up the game and continues a very impressive start from the 19-year-old.

Piers Newbery
BBC Sport at Flushing Meadows

A grey start to day two has turned into a damp afternoon, which has bemused those of us accustomed to thumping humidity and punishing heat at Flushing Meadows. As a result, there is a great deal of milling around, rustling in bags and sizing up the food stands. A second roof is planned over the redesigned Louis Armstrong Stadium by next year, but for now it's all eyes on Ashe for the only tennis balls being hit right now.

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Angelique Kerber, with wrists as soft and malleable as putty, dinks away a winning drop-volley on the stretch for 30-15.

A crunching forehand winner from a crouching stance zips away for 40-15.

And that is game.

And a shot of confidence right into the main vein for the defending champion.

Angelique Kerber gets Naomi Osaka moving with some cutting forehand angles and eventually the Japanese breaks down to offer up 30-30.

A nothing-much swat into the top of the net from Osaka and we are looking at 30-40 and our first break point of the match.

Biff-bosh, bang-slam. Naomi Osaka plays it brave and gets her rewards, moving Kerber around the court and thumping away the drive volley to see off the danger.

A lovely biffed backhand for advantage before she runs down a clumsy Kerber drop-shot and gives it the contempt it deserves.

Angelique Kerber balances up the scoreboard, but she is not dancing around the main stage so far.

The forehand is twitchy, the brow is furrowed and none of it seems like much fun at the moment.

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Naomi Osaka's serve is a brute in the mould of her idol Serena Williams.

She has landed seven out of 10 first tee-offs so far, maxing out at 113 mph and averaging 104 mph.

Angelique Kerber - like a quivering opener facing Allan Donald - is still to get a read on it.

Angelique Kerber wobbles slightly with a double fault that gives Naomi Osaka a peek at 30-30.

But the German grits it out and grips a fist in celebration as Osaka's final forehand return floats long over the baseline under her careful gaze.

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No sign of the abdominal tweak that forced Naomi Osaka out of Toronto in the build-up to this tournament as the Japanese world number 45 plonks down some pacey serves on the way to an opening game hold.

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Right, both players - bedecked in seventies stylings of their German kit sponsor - have bounced to baseline.

Osaka to serve.

By the way, it is raining on the outside courts, which means Elina Svitolina - into a second-set tie-break after winning the first 6-0 against Katerina Siniakova - and Dominic Thiem - two sets up on Alex de Minaur - are cooling their heels at the moment away from the shelter of the Arthur Ashe roof.

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The US Open is the prize shopfront for tennis' big-rolling sponsors.

Which means excruciating promotional events ahoy.

Here she is alongside Sascha Zverev, Dominic Thiem, Garbine Muguruza and Jo-Wilfried Tsonga and upbeat beat maestro Pharrell Williams posing on some special umpires chairs.

It was all to big up her kit sponsors' new designs - from the pen of Williams himself apparently - that come wrapped up in campaign of beautiful model types doing a bit of trespassing and turning rebellion into money.

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World number one and last year's runner-up Karolina Pliskova made short work of Poland's Magda Linette in her US Open starter, winning 6-1 6-2 in 78 minutes in the day's first match on Arthur Ashe.

Japan's Misaki Doi, who took Angelique Kerber to match point in the first round of the German's ultimately successful Australian Open campaign last year, folded in straight sets to Russian 23rd seed Barbora Strycova.

Meanwhile Yanina Wickmayer upset 28th seed Lesia Tsurenko.

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Kerber is a victim of her own past successes.

She became for world number one for the first time at last year's US Open, beating Karolina Pliskova - the current holder of the ranking crown - in three sets.

That means she has to repeat that victory to stand still in ranking points terms.

She has not looked in the best nick on the hardcourt swing however, losing her opening match to world number 40 Ekaterina Makarova in Cincinnati and going out in straight sets to Sloane Stephens in the last 16 in Toronto.

Today, in her Flushing Meadows opener she is up against the big-hitting teenager Naomi Ozaka.

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Simona Halep, Garbine Muguruza, Elina Svitolina, Karolina Pliskova, Caroline Wozniacki, Johanna Konta, Svetlana Kuznetsova, Venus Williams.

All eight players came into this US Open with hopes of taking the world number one slot.

Notable for her absence from that list though is Angelique Kerber.

The German was top of the tennis tree as recently as mid-July, but it turns out, whatever Jay-Z and Alicia Keys might say, , externalthat there are some things that you can't do in the Big Apple.