Viscous fingering in a modified Hele-Shaw cell is numerically investigated. The cell allows periodic variation of depth in the lateral direction. The wavenumber n of the depth perturbation has great influence on fingering patterns. For n = 1, the fingering pattern due to the interface instability remains the same as that in the conventional Hele- Shaw cell, while the depth variation causes the steady finger to be a little narrower. For n = 2, four different fingering patterns are captured, similar to the available experimental observations in a modified Hele-Shaw cell containing a centered step-like occlusion. It is found that new fingering patterns appear as n further increases, among which, two patterns with spatial oscillation along both edges of the finger are particularly interesting. One is a symmetric oscillatory finger for n = 3, and the other is an asymmetric one for n = 4. The influence of capillary number on fingering patterns is studied for n = 3 and 4. We find that spatial oscillation of the finger nearly ceases at moderate capillary numbers and occurs again as the capillary number increases further. Meanwhile, the wide finger shifts to the narrow one. It is accompanied by a sudden decrease in the finger width which otherwise decreases continuously as the capillary number increases. The wavenumber and the amplitude of depth perturbation have little effect on the finger width.
Independent component analysis(ICA)is used to study the multiscale localised modes of streamwise velocity fluctuations in turbulent channel flows.ICA aims to decompose signals into independent modes,which may induce spatially localised objects.The height and size are defined to quantify the spatial position and extension of these ICA modes,respectively.In contrast to spatially extended proper orthogonal decomposition(POD)modes,ICA modes are typically localised in space,and the energy of some modes is distributed across the near-wall region.The sizes of ICA modes are multiscale and are approximately proportional to their heights.ICA modes can also help to reconstruct the statistics of turbulence,particularly the third-order moment of velocity fluctuations,which is related to the strongest Reynolds shear-stressproducing events.The results reported in this paper indicate that the ICA method may connect statistical descriptions and structural descriptions of turbulence.
This letter describes numerical simulation of the unsteady flow over a slow-flying bat by using the immersed boundary method based on the measured bat wing geometry and kinematics. The main vortical structures around the bat flapping wings are identified, illuminating the lift-generating role of the leading- edge vortices generated mainly in the downstroke. Furthermore, the lift decomposition indicates that the vortex lift has the dominant contribution to the time-averaged lift and the lift associated with the fluid acceleration has the relatively moderate effect.
We find an asymptotic expression for the characteristic timescales of decorrelation processes in weakly compressible and isothermal turbulence. This result is used in the Eddy-Damped Quasi-Normal Markovian equation to derive the scalings of compressible energy spectra: (1) if the acoustic waves are dominant, the compressible energy spectra exhibit \(-7/3\) scaling; (2) if local eddy straining is dominant, the compressible energy spectra are scaled as \(-3\). Meanwhile, the energy spectra of incompressible components display the same scaling of \(-5/3\) as those in incompressible turbulence. The direct numerical simulations of weakly compressible turbulence are used to examine the scaling.
A novel method is proposed to combine the wall-modeled large-eddy simulation(LES) with the diffuse-interface direct-forcing immersed boundary(IB) method.The new developments in this method include:(i) the momentum equation is integrated along the wall-normal direction to link the tangential component of the effective body force for the IB method to the wall shear stress predicted by the wall model;(ii) a set of Lagrangian points near the wall are introduced to compute the normal component of the effective body force for the IB method by reconstructing the normal component of the velocity. This novel method will be a classical direct-forcing IB method if the grid is fine enough to resolve the flow near the wall. The method is used to simulate the flows around the DARPA SUBOFF model. The results obtained are well comparable to the measured experimental data and wall-resolved LES results.
Beiji SHIXiaolei YANGGuodong JINGuowei HEShizhao WANG
