Multiple stable solutions in the 2D symmetrical two-sided square lid-driven cavity

• Multiple stable solutions of the symmetric two-sided driven cavity are determined.
• The transition from non-symmetric to symmetric solution is commented.
• The symmetric and non-symmetric solutions have distinct energetic budgets.
• The symmetrical solution is steady up to Re = 4000.
• Two characteristic critical-Re values are measured for the non symmetric solution.

Stable solutions of a 2D symmetrical two-sided square lid-driven cavity are numerically determined with spectral accuracy. In addition to the expected symmetrical solutions, a set of two non-symmetrical solutions, mirror images of one another, are obtained for Reynolds number (Re  ) greater than a critical value, Re1Re1 by suitably eliminating one of the symmetrical solutions. The symmetrical solutions which are reported in this paper are obtained for Re⩽4000Re⩽4000 and are all steady. The non-symmetrical solutions are computed for large values of Re   until these solutions become unsteady, at a second critical Re,Re2, viz., for Re⩾Re2>Re1Re⩾Re2>Re1. The transition from a non-symmetrical solution to its symmetrical counterpart upon reducing the Re   below Re1Re1 is addressed. It is observed that the symmetric solutions are those which maximize the flow kinetic energy per unit input energy.