The U.S. dollar lunged higher on Tuesday as China allowed its yuan to fall to three-year lows, a shift that heightened unease about the world’s second-largest economy even as it promised a much-needed boost to exports. China’s central bank described the move as a “one-off depreciation” of nearly 2 percent, and said it was based on a new way of managing the exchange rate that better reflected market forces. Investors reacted by selling the Australian dollar, often used as a liquid surrogate for the Chinese currency.