The influence of control on proper orthogonal decomposition of wall-bounded turbulent flows

This paper explores the effects of several wall-based, turbulence control s trategies on the structure of the basis functions determined using the prop er orthogonal decomposition (POD). This research is motivated by the observ ation that the POD basis functions are only optimal for the flow for which they were created. Under the action of control, the POD basis may be signif icantly altered so that the common assumption that effective reduced-order models for predictive control can be constructed from the POD basis of an u ncontrolled flow may be suspect. This issue is explored for plane, incompre ssible, turbulent channel flow at Reynolds number, Re-tau=180. Based on wel l- resolved large eddy simulations, POD bases are constructed for three flo ws: no control; opposition control, which achieves a 25% drag reduction; an d optimal control, which gives a 40% drag reduction. Both controlled flows use wall transpiration as the control mechanism and only differ in the tech nique used to predict the control. For both controlled flows, the POD basis is altered from that of the no-control flow by the introduction of a local ized shear layer near the walls and a nearly impenetrable virtual wall that hinders momentum transfer in the wall-normal direction thereby leading to drag reduction. A major difference between the two controlled flows is that the shear layer and associated virtual wall are located farther away from the physical wall when using optimal compared to opposition control. From t his investigation, it is concluded that a no-control POD basis used as a lo w-dimensional model will not capture the key features of these controlled f lows. In particular, it is shown that such an approximation leads to grossl y underpredicted Reynolds stresses. These results indicate that a no-contro l POD basis should be supplemented with features of a controlled flow befor e using it as a low-dimensional approximation for predictive control. (C) 2 001 American Institute of Physics.