If I am travelling to US from Aus for example on Saturday morning, zuhr of sat will occur while on plane. Now when I land in US it is still Saturday morning there and Zuhr of Sat will occur a second time for me. Now please guide me which Zuhr to pray and which one to leave or pray both? What will be the niyyat in both cases?

Pray the Zhuhr in the US and ignore the one during the flight.