Non-isothermal flow through a curved rectangular duct for large Grashof

Non-isothermal flow through a curved rectangular duct of differentially heated vertical sidewalls is investigated numerically by using the spectral method, and covering a wide range of the Dean number, Dn, 10000 ≤< Dn, and the Grashof number, Gr, 20001000 ≤ ≤ Gr. After a comprehensive survey over the parametric ranges, five branches of asymmetric steady solutions are obtained with two- and multi-vortex solutions by using the Newton-Raphson iteration method. Linear stability of the steady solutions is then investigated. When there is no stable steady solution, time evolution calculations are performed, and it is found that for any Gr in the range, the steady flow turns into chaos through various flow instabilities, if Dn is increased