Near-wall model for boundary layer turbulence

The evolution of an intermittently created isolated three-dimensional turbulent eddy near a wall is followed in space and time on the assumption that its structure evolves on three separate time scales, a shear interaction one, a viscous one, and a nonlinear one. The large-time limit of the solution for the shear interaction stage shows many of the observed features of the near-wall turbulence structure such as the formation of shear layers, of streaks, and of streamwise vortices. It also provides initial conditions for the viscous and nonlinear stages showing viscous decay of convected structures and the possibility of a singularity in the nonlinear development. The eddy model is also used to construct a new model for the turbulent shear stress showing strong similarity to Prandtl's mixing-length model.     

Wavelet spectrum analysis on energy transfer of multi-scale structures in wall turbulence

The streamwise velocity components at different vertical heights in wall turbulence were measured. Wavelet transform was used to study the turbulent energy spectra, indicating that the global spectrum results from the weighted average of Fourier spectrum based on wavelet scales. W＇avelet transform with more vanishing moments can express the declining of turbulent spectrum. The local wavelet spectrum shows that the physical phenomena such as deformation position in the boundary layer, and the or breakup of eddies are related to the vertical energy-containing eddies exist in a multi-scale form. Moreover, the size of these eddies increases with the measured points moving out of the wall. In the buffer region, the small scale energy-containing eddies with higher frequency are excited. In the outer region, the maximal energy is concentrated in the low-frequency large-scale eddies, and the frequency domain of energy-containing eddies becomes narrower.     

Experimental study on the local similarity scaling of the turbulence spectrum in the turbulent boundary layer

The streamwise fluctuating velocity in the turbulent boundary layer is measured under approximately medium Reynolds Number by hot wire in order to investigate the scaling properties of the overlapped turbulent spectrum among energy-containing area, inertial subrange and dissipation range based on FFT analysis. The experiment indicates that the high Reynolds flow reported before is not indispensable to produce −1 scaling. So far as the measured position is provided with much higher spatial resolution and enough closing to the wall, −1 scaling is determinate to exist when approaching medium Reynolds. The scaling ranges are supposed to begin at inner scale and end in outer scale, which reveals the local similarity of the energy spectrum over the energy-containing eddies near the wall. In the logarithmic area (y ⁺ > 130), −5/3 scaling occurs in the energy spectrum, while moving away from the wall with Reynolds numbers increasing, the inertial subrange extends to the lower wavenumbers. On the condition k ₁ η ≫ 0.1, the curves of the turbulence spectrum in the logarithmic layer are superposed, which expresses the similarity of turbulence energy distributed in Komogorov scaling area and exhibits local isotropy characteristics by virtue of the viscous dissipation. Supported by the National Natural Science Foundation of China (Grant Nos. 10832001 and 10872145), the Program for New Century Excellent Talents in Universities of Education Ministry of China, and the Plan of Tianjin Science and Technology Development (Grant No. 06TXTJJC13800)     

A meshless numerical method for solving slow mixed convections in containers with discontinuous boundary data

This paper describes the formulations of the method of fundamental solutions (MFS), which is a famous meshless numerical method representing a sought solution by a series of fundamental solutions to solve slow mixed convections in containers with discontinuous boundary data. In the derivations, the fundamental solutions were obtained by using the Hörmander operator decomposition technique. All the velocities, temperatures, pressures, stresses and thermal fluxes corresponding to the fundamental solutions were addressed explicitly in tensor forms. Although the MFS is highly accurate for smooth boundary data, its convergence becomes poor when it is applied to problems with discontinuous boundary data. To compensate for this drawback, we enriched the MFS by adding the local discontinuous solutions to the series of fundamental solutions. This enriched MFS was applied to solve the benchmark problems of a lid‐driven cavity and natural convection in rectangular containers. In addition, the numerical solutions were compared with the analytical solutions. Then, the meshless numerical method was further utilized to solve mixed convections in a triangular cavity and a cavity with a cosine‐shaped bottom. These numerical results demonstrated the applicability of the enriched MFS to two‐dimensional mixed convections in containers with discontinuous boundary data. Copyright © 2010 John Wiley & Sons, Ltd.     

Dynamics of large turbulent structures in a steady breaker

The flow near the leading edge of a steady breaker has been studied experimentally using Bubble Image Velocimetry (BIV) with the aim of characterizing the dynamics of the large eddies responsible for air entrainment. It is well reported in the literature, and confirmed by our measurements of the instantaneous velocity field, that this flow shares some important features with the turbulent shear-layer formed between two parallel semi-infinite streams with different velocities. Namely, the formation of a periodic array of coherent vortices, the constant convective velocity of those vortices, the linear relation between their size and their downstream position and the self-similar structure of both mean velocity profiles and Reynolds shear stresses. Nonetheless, important differences exists between the dynamics of the large eddies in a steady breaker and those in a free shear-layer. Particularly, the convective velocity of these large structures is slower in a steady breaker and, consistent with this, their growth rates are larger. A physical interpretation of these differences is provided together with a discussion of their implications. To support our measurements and conclusions, we present a careful analysis of the accuracy of the BIV technique in turbulent flows with large bubbles.     

The simulation of offshore turbulent dispersion using seeded eddies

A way of representing turbulence in a two-dimensional situation is introduced appropriate to depth-independent offshore fluid mechanics. The turbulence is simulated by a collection of eddies, each of which has an analytically simple form but whose size, strength and position is governed by stochastically assigned variables. The problem addressed here is how contaminant is dispersed in such an eddy field. A number of experiments are performed whereby the eddies are seeded with marked particles that move with the fluid. The variance of these particles is monitored as time varies, and the results are compared with an assumed power law distribution. Although not a perfect fit, the results are in general accord with a power law with index between 1.5 and 2.5, which is in agreement with the observed power law of 2.34 due to Okubo, and a marked improvement on random walk models which give a variance directly proportional to time. Some further applications of this technique are discussed, namely the simulation of turbulent boundary layers and the simulation of the cascade of energy up turbulent length scales.     

On a class of three-dimensional corner eddies

Consider Stokes flow in a viscous fluid filling a corner, of angle 2α, bounded by two infinite plane walls. Assume that the flow is symmetrical about some plane which is normal to the walls bounding the corner. Since superposition is valid we may consider flows that are symmetrical about the plane bisecting the comer and those that are antisymmetrical about this plane. In either case it is shown that for a class of corner eddies, the corner flow is made up of an infinite sequence of eddies asr → 0, wherer is the radial distance from the corner. Moreover, the eigenvalues λ which determine the structure of the corner eddy fields satisfy the same equation, sin λα = ± λ sin 2α, that arises in the corresponding plane case. The three-dimensional velocity fields are, however, quite different from those seen in the plane case. In particular, in the symmetric case the streamlines are not closed and foci, rather than elliptic stagnation points, are the centres of the eddies in the plane of symmetry. These results represent, in this special context, a generalization to three-dimensions of Moffatt’s classical result for planar corner eddies.     

Inversion transformation of Stokes flows bounded by parallel planes

The positive inversion transformation applied to a two-dimensional Stokes flow around bodies leads alike to a Stokes flow. This fact can be exploited to find new two-dimensional Stokes flow solutions around inverse bodies. Some features of this method, such as the relations between the reference and inverse fluid velocity fields, are presented followed by an application to examples of cellular flow between two parallel plates induced by rotating or translating cylinder. Thus hydrodynamic characteristics of flow around circular bodies obtained by inversion of the plates are straightforward deduced. Typical fluid flow patterns around two circular cylinders in contact placed in the centre of a rotating or a translating circular cylinder are thus illustrated.     

表示湍流场的一种新设想

本文仿照量子场论中描述基本粒子产生湮灭的方法来描述湍流中涡旋的产生和消灭.因为当某一基本粒子存在的时候,我们可以认为它是一个不变实体,而湍流中涡旋则在时间过程中不断变化和耗散,所以在类比应用量子场论方法时首先要解决怎样的湍流涡旋可认为是同一个涡旋.根据线性化理论的特点,我们认为在时间过程中按相似性规律变化时湍流涡旋才算是同一个涡旋,而把不具有相似性的涡旋出现或消失,看成是方程(2.6)中相互作用项φ_i所引起的湮火和产生的结果.然后,我们采用和量子场论相类似的产生算符和消灭算符来描述湍流涡旋系统所处的状态.最后,我们利用原N-S方程中相互作用项来构成涡旋相互作用的“Schr?dinger”方程以描述其状态的变化.这样就得类似于量子场论的湍流涡旋相互作用理论.     

The computation of the eddy along the upper wall in the three‐dimensional flow over a backward‐facing step

A three‐dimensional laminar flow over a backward‐facing step is studied as a numerical experiment by solving the steady‐state, isothermal and incompressible Navier–Stokes equations using two different finite element codes. The Reynolds number ranges from 100 to 1050. The expansion ratio is 1:1.94, and the aspect ratio is 1:36.7. The numerical experiment reveals both eddies along the lower and upper walls downstream of the step. Results of computations regarding positions of detachment of the eddy along the upper wall and positions of reattachments of the eddies along both the lower and upper walls are tabulated along with positions and magnitudes of global extrema of shear rate within the eddies. The wall effects are shown by calculating streamlines along planes parallel/normal to the lateral walls of the domain and depicting how the streamlines are distorted close to the walls and how they assume a two‐dimensional configuration in the plane of symmetry. Comparisons are made with available numerical results and laboratory measurements. Copyright © 2011 John Wiley & Sons, Ltd.