By Matt Siegel
SYDNEY, Nov 11 (Reuters) - Australian Prime Minister Malcolm Turnbull will be looking to reset a vital diplomatic and economic relationship badly strained under his predecessor when he visits Jakarta on Thursday to meet Indonesian President Joko Widodo.
Australia and its giant neighbour have a history of diplomatic turbulence stretching back decades, but relations reached historic lows under Prime Minister Tony Abbott, who was ousted in a party coup in September.
Turnbull inherited ties strained by rows over spying, the execution of Australian citizens in Indonesia and Abbott's tough asylum seeker policies, all amid an atmosphere of growing Chinese assertiveness in the region.
But with anxiety in Jakarta growing over Beijing's intentions and Turnbull looking to build bridges to Asia, the visit was key for both sides, said Adrian Vickers, director of the Asian Studies Centre at the University of Sydney.
"The big thing for Turnbull will actually just be getting enough attention from Indonesia, where there is a potential at this moment to really refocus the relationship given the problems between Indonesia and China," he told Reuters.
"It might also be a good way to remind Indonesia of Australia and the potential benefits of the economic relationship."
Indonesia is Australia's tenth largest overall trading partner and is the largest export market for Australian wheat worth A$1.3 billion ($917 million) in 2014, as well as a major destination for live cattle and sugar.
They also cooperate closely on counter-terrorism, an area of growing concern as Islamic State militants seek footholds outside the Middle East, where Australia is bombing the group as part of a U.S.-led military campaign.
But in recent years, perpetual crisis became the norm, said Vickers, with Abbott very much its public face in Indonesia.
Just one month after he took office in September 2013, revelations that Canberra had spied on President Susilo Bambang Yudhoyono and his wife sent relations plummeting.
His policy of towing back to Indonesia vessels carrying asylum seekers, while popular at home, infuriated Jakarta, which sees it as an infringement on its sovereignty.
Tensions reached their peak in May when Indonesia executed two Australian members of the so-called "Bali Nine" drug trafficking ring, despite intense lobbying from Canberra.
Indonesia saw Turnbull's visit as a sign that both sides were looking to do the same in the economic and diplomatic spheres, said Armanatha Nasir, Indonesian foreign ministry spokesman.
"The fact that Australian ministers have been visiting us frequently and that there is a big delegation of business people coming here with the prime minister shows efforts on both sides to move on," he said.