Flow stability over curvilinear moving surface relative to three-dimensional disturbances (Q2767649)

Flow stability in a boundary layer relative to three-dimensional longitudinal vortices (Goertler vortices), that are formed under centrifugal effect, is considered. It is shown that the vortices arise over a convex surface which moves along a curved trajectory unlike the case when the stationary curved surface is flowed around and the vortices are formed over a concave surface. The linear stability of the flow is studied and the stability diagram is constructed. It is found that the critical Goertler number is much more than similar critical number for the case when the stationary concave surface is flowed around. It is concluded that the flow over a curved surface moving along a curved trajectory is more stable in comparison with the flow over a stationary curved surface. The comprehensive calculations of the eigen functions for different Goertler numbers \(\text{Gr}\) and non-dimensional wave number \(\alpha \theta\), where \(\theta\) is the impulse thickness, are carried out. The graphs of these functions are plotted and the positions and values of the characteristic points of each function (maximum and minimum values, the points of intersection vertical axis) are found. These data permit to determine all components of the disturbed velocity and the pressure approximately if the information only about one component is known, for example, the maximum value of the longitudinal component of disturbed velocity measured in experiments is known. The location of the unstability region with respect to three-dimensional longitudinal vortices on the linearly moving dolphin's body, whose afterbody moves up and down, is discussed.