They are unlikely partners: a cool and unflappable U.S. president and a proud, sometimes hot-tempered Turkish prime minister. But they have developed a working relationship that is one of the most important but least discussed developments shaping this year of change in the Arab world.

If you’re looking for factors that can keep the Arab Awakening from turning into a nightmare, the U.S.-Turkey partnership is mildly reassuring. President Obama and Prime Minister Recep Tayyip Erdogan have worked closely to manage events in Egypt, Libya, Syria and, increasingly, Iran.

They have talked by phone 13 times this year, according to the White House. The two didn’t start off as friends but became so after a blunt conversation last year in Toronto. The relationship that emerged exemplifies Obama’s basic formulation of “mutual respect and mutual interest.”

For an administration that wants to influence Arab turmoil but also stay in the background, Erdogan has been the perfect cut-out: He has high credibility on the Arab street, especially with the Muslim Brotherhood and other Islamist parties empowered by the Arab revolutions. And he has a foreign minister with Kissingerian ambitions, Ahmet Davutoglu.

Erdogan embodies the “Turkish model” — a strong Islamist governing party that is committed to the free market and backed by a solid, pro-American military — which many administration officials see as the best hope for Egypt and its neighbors. But critics caution that Erdogan has narrowed the scope of democracy in Turkey by reducing the independence of the media, the judiciary and the army. In that sense, the Turkish model has dangers as well as benefits.

I’ve seen Erdogan’s temper firsthand, when he walked out of a Davos panel I was moderating in 2009 because he thought he hadn’t been given a fair chance to express his criticism of the Gaza war. That spark of populist anger is part of why Erdogan is so popular in a region where the public increasingly wants politicians to stand up to the West.

As White House officials reconstruct the evolution of this special relationship, they go back to Obama’s decision to add a stop in Ankara on his first overseas trip as president in April 2009. The initial itinerary was standard fare — Group of 20 and NATO summit meetings in Europe — but Obama wanted to reach out to newly emerging powers, starting with Turkey.

The Ankara speech went well enough, but relations soured in early 2010 when Turkey tried to broker a deal with Tehran over fuel for the Iranian nuclear program. Obama saw the Turks undermining U.S. policy — especially when they voted in the U.N. Security Council against a new sanctions resolution on Iran in June.

Obama and Erdogan had a showdown later that month at the G-20 summit in Toronto. Obama protested, “You knew how important this was to me, and you didn’t come with me,” recalls a senior administration official. Erdogan responded equally bluntly. Over several hours, they moved into “a long discussion about evolving trends in the world and what it means to be allies.” Turks agree that a real partnership was born at that meeting.

As examples of “really close cooperation,” the official cites Turkish help in forming an Iraqi government under Prime Minister Nouri al-Maliki; joint efforts against terrorist groups, including the Kurdish PKK; partnership on Afghanistan; and shared strategy during the Arab Spring.

The alliance has continued even as Turkey’s relations with Israel were scuttled by the Gaza flotilla incident in May 2010. The United States tried to negotiate a truce, but it failed when Israeli Prime Minister Benjamin Netanyahu refused Erdogan’s demand for an apology. The fact that Obama has such good relations with Erdogan probably adds to Israeli uneasiness with this White House.

The most delicate piece of Turkish-American business is trying to organize a peaceful transfer of power in Syria. Erdogan, once the closest foreign ally of Syrian President Bashar al-Assad, is now a bitter foe. As often with Erdogan, it’s personal: He feels Assad backed out on a reform promise he made several months ago. When Assad reneged, after Erdogan had told Obama he would have a deal within 72 hours, the Turkish prime minister was embarrassed and angry. That anger continues, and it’s driving the Turks to take a tough stance.

Washington and Ankara are planning an escalating pressure campaign against Assad, which will include economic sanctions, secret activities to support the opposition and perhaps a haven along the Turkish border and a humanitarian corridor inside Syria.

And what about Turkish relations with Iran, the ticking time bomb on its border? Administration officials note that Erdogan recently agreed to deploy a forward-based radar system as part of a NATO missile defense plan aimed chiefly at Iran.