Abdelaziz Salhi

LINEAR STABILITY ANALYSIS OF PLANE QUADRATIC FLOWS IN A ROTATING FRAME WITH APPLICATIONS TO MODELING

The linear response of turbulence to a distortion and simple rotation is investigated in this paper from a fundamental theoretical standpoint. Quadratic flows are a special case of planar flows with constant mean velocity gradients, which can be characterized by a constant rate of strain D and a constant spanwise (normal to the plane) vorticity component −W=2Ω0, with arbitrary values (here, we can take D>0 and W>0 without any loss of generality). According to the sign of D2−Ω02, streamlines are hyperbolic, rectilinear (pure shear flow) or elliptic. Since these flows can also be considered as mean flows, when superimposing a three-dimensional disturbance (or fluctuating turbulent) field which satisfies statistical homogeneity, the linearized analysis of the disturbance field is of interest both from the point of view of hydrodynamic stability (e.g., the elliptical flow instability) and from the point of view of homogeneous rapid distortion theory (RDT) including applications to the basic statistics. The ca...