Research Projects

Because of their numerous applications in atomization technology, such as fuel spray formation, high-tech surface cleaning, rocket propulsion, and advanced material processing, studies of oscillatory fluid flows are one of the most fascinating topics in fluid mechanics. Apart from their technological applications, such flows are very pertinent in the biomedical field for the treatment of vascular diseases in the cardiovascular system. In fact, investigations of oscillatory flows have special importance in vibrating media for exploring the resonance phenomenon when frequency of the oscillation coincides with the natural frequency of the vibrating media. As a result, it is not surprising that researchers are becoming increasingly interested in the study of oscillatory flows. Furthermore, the unsteady basic state makes investigating oscillatory flows more difficult than investigating steady state flows, even from a computational standpoint. For this reason, there are not many articles in the literature for the study of primary instability in oscillatory fluid flows. These facts stimulate us to work in the field of oscillatory fluid flows. In general, the unsteady Navier-Stokes equations in a reference frame fixed to the oscillating plane describe fluid flows on an oscillating plane. Hence, the fluid velocity components at the oscillating plane must satisfy no-slip and no-penetration boundary conditions with respect to the oscillatory reference frame. However, due to the oscillatory effect with respect to the oscillatory reference frame, the D’Alembert body force must be included in the momentum equations. In addition, hydrodynamic stress boundary conditions at the fluid surface are required to close the oscillatory flow system. The main motivation is to decipher the transition from laminar to turbulence caused by the oscillatory modes in a fluid flow when the bottom plane oscillates in both streamwise and cross-stream directions. Due to the oscillation of the bottom plane, the oscillatory modes, the so-called subharmonic and harmonic modes, emerge along with the usual surface and shear modes of a fluid flow with a free surface. In particular, the subharmonic and harmonic resonances alternately occur in separate unstable ranges of wavenumber when the forcing amplitude exceeds the respective critical amplitudes for the subharmonic and harmonic resonances. However, the subharmonic resonance occurs before the harmonic resonance in the finite wavenumber regime. As this is a theory based computational project, the outcome of the proposed project will provide the physical mechanism for the onset of the oscillatory instability under the framework of the time-dependent Orr-Sommerfeld type boundary value problem (OS BVP). The numerical solution of the unsteady OS BVP will be based on the Chebyshev spectral collocation method and the complex Floquet theory for infinitesimal disturbances of arbitrary wavenumbers.