STABILITY OF 3-D DISTURBANCE WAVES ON BOUNDARY LAYER WITH DISTRIBUTED LOCAL ROUGHNESS

The numerical solution of the stable basic flow on a 3-D boundary layer is obtained by using local ejection, local suction, and combination of local ejection and suction to simulate the local rough wall. The evolution of 3-D disturbance T-S wave is studied in the spatial processes, and the effects of form and distribution structure of local roughness on the growth rate of the 3-D disturbance wave and the flow stability are discussed. Numerical results show that the growth of the disturbance wave and the form of vortices are accelerated by the 3-D local roughness. The modification of basic flow owing to the evolvement of the finite amplitude disturbance wave and the existence of spanwise velocity induced by the 3-D local roughness affects the stability of boundary layer. Propagation direction and phase of the disturbance wave shift obviously for the 3-D local roughness of the wall. The flow stability characteristics change if the form of the 2-D local roughness varies.

Boundary-layer receptivity under interaction of free-stream turbulence and localized wall roughness

The boundary-layer receptivity under the interaction of free-stream turbu- lence （FST） and localized wall roughness is studied by the direct numerical simulation （DNS） and the fast Fourier transform. The results show that the Tollmien-Schlichting （T-S） wave packets superposed by a group of stability, neutral, and instability T-S waves are generated in the boundary layer. The propagation speeds of the T-S wave packets are calculated. The relation among the boundary-layer receptivity response, the amplitude of the FST, the roughness height, and the roughness width is determined. The results agree well with Dietz＇s experiments. The effect of the roughness geometries on the receptivity is also studied.

Analysis of a time-dependent fluid-solid interaction problem above a local rough surface

This paper is concerned with the mathematical analysis of a time-dependent fluid-solid interaction problem associated with a bounded elastic body immersed in a homogeneous air or fluid above a local rough surface. We reformulate the unbounded scattering problem into an equivalent initial-boundary value problem defined in a bounded domain by proposing a transparent boundary condition(TBC) on a hemisphere. Analyzing the reduced problem with the Lax-Milgram lemma and the abstract inversion theorem of the Laplace transform,we prove the well-posedness and stability for the reduced problem. Moreover, an a priori estimate is established directly in the time domain for the acoustic wave and elastic displacement by using the energy method.

Numerical Reconstruction of Locally Rough Surfaces with a Newton Iterative Algorithm

In this paper,we propose a Newton iterative algorithm to numerically reconstruct a locally rough surface with Dirichlet and impedance boundary conditions by near-field measurements of acoustic waves.The algorithm relies on the Frechet differentiability analysis of the locally rough surface scattering problem,which is established by reducing the original model into an equivalent boundary value problem with compactly supported boundary data.With a slight modification,the algorithm can be also extended to reconstruct the local perturbation of a non-local rough surface.Finally,numerical results are presented to illustrate the effectiveness of the inversion algorithm with the multi-frequency data.