REDUCED-ORDER MODELING OF NONCANONICAL LAMINAR WAKES

This paper aims at developing a reduced-order model (ROM) of noncanonical laminar wakes. To this end, we consider the wakes generated by an elliptic cylinder of axis ratio 0.4 whose major axis is kept perpendicular to the free-stream flow at low Reynolds numbers (Re) where the flow is found to be strictly two-dimensional and laminar. Low-dimensional bases for these infinite-dimensional wakes are obtained using the proper orthogonal decomposition (POD) method. While the most energetic low-dimensional basis of canonical wake shows only the primary structures which tend to decay in their strength along the downstream, the most energetic basis of noncanonical wakes contains secondary structures even at the near field of the wake and they become stronger in the far field. The eigenvalues of the correlation matrix of fluctuations no longer occur in pairs for the noncanonical wakes while they occur in pairs for canonical wakes. Consequently, the temporal coefficients do not exhibit 90° phase shift with one another in noncanonical wakes. Finally, we construct a reduced-order model by projecting the Navier–Stokes equation onto the low-dimensional POD bases using the Galerkin projection method. The nonzero elements of the quadratic tensor in the ROM is diagonally dominant for canonical wakes but loses its diagonal dominance for noncanonical wakes. We observe that, although the fluctuations are strong along the boundaries in noncanonical wakes, the pressure term does not contribute to the overall dynamics of the reduced-order model irrespective of the type of wake. The ROM yields results that are consistent with the numerical simulation.