力学与湍流重点实验室学术报告 (8月27日--主持：佘振苏）
发布时间: 2009-08-19 10:36:00
SEMINAR SERIES
北京大学工学院 
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力学与空天技术系
湍流与复杂系统国家重点实验室
报告人 Paolo Orlandi
Dip. Mecc. e Aer.,
Università “La Sapienza”
Rome, Italy
题目一：Energy spectra power laws and vortical structures
内容摘要：In fluid dynamics the equations describing the flow physics are known, these are derived on solid principles and have been confirmed by reproducing laboratory experiments. Even if the model is true still in fluid mechanics several aspects are not completely understood. These equations generate energy spectra with a wide distribution in wave numbers, whose origin is related to the non-linearity of the Euler and Navier-Stokes equations. In real flows a wide power law is achieved when the Reynolds number is large, for instance in turbulent flows, where, the Kolmogorov theory for Re→∞ predicts a k-5/3 power law. The aim of the present work is to continue the effort that promoted several studies to investigate whether it is possible to relate the exponents of the power law to the shape of the vortical structures. In turbulent flows the inertial range is followed by an exponential decay range. In these circumstances the large scales are immersed in a sea of small scales, and the structures can be rod- or ribbon-like . To have fully turbulent flows the number of
ribbon must overcome the rod-like structures. To investigate whether the power law exponent is linked to the shape of the structures, it is necessary to find other flows with well defined and wide power laws. In particular flows without the exponential decay region, in large part due to the rod-like structures, which modify the structures in the power law region. These flows can be generated by solving the Euler equations, and by analyzing the field at a time of the the evolution when the fully resolved simulation produces a spectrum with a long power law. For inviscid simulations there is the constrain to start the simulations with smooth initial conditions, and with negligible energy at small scales. Orlandi & Carnevale solved the Euler equations to get insights on the vorticity dynamics before the occurrence of the hypothetical finite time singularity (FTS). They claimed that, at the present time, is impossible to have a definite
and clear proof of the FTS existence for the Euler equations. They demonstrated, By a well resolved DNS, a model equations can be derived having a FTS, in addition, for a short time before the supposed FTS, the energy spectrum has a rather wide range k-3 power law. The simulations started with two Lamb dipoles, having a k-6 power law energy spectrum. The Taylor-Green vortex can be used as the initial condition to verify whether the Euler equations have a FTS. In this flow at t = 0 the energy is concentrated at k = 1, and in time is transfered at high k. It can be speculated, that a reason of the controversial arguments on the FTS singularity, for this flow, could be related to the lack of well defined power laws during the evolution. The present Kmax = 256 is sufficient to demonstrate that, at a certain time, a satisfactory long k-3 is achieved, permitting to investigate the shape of the vertical structures and their relationship with statistics. These two inviscid flows have been compared with isotropic forced turbulence to quantify the relation between structures and power law.
题目二：An efficient 2nd order finite difference method for parallel
computers to understand the physics of wall turbulent flows
内容摘要：In the fluid dynamics community is believed that the flow physics numerically should be studied by the Direct Numerical Simulation of the Navier-Stokes equations by pseudospectral methods. These methods for linear equations have a spectral accuracy, but for non-linear equations, to be efficient, require a pseudospectral procedure, based on the evaluation of the non-linear terms in physical space. Different kind of dealiasing procedures are necessary and the results depend strongly on these. In these circumstances the spectral accuracy cannot be any more proved. In this study it is shown that second order accurate finite difference methods are appropriate to study the flow physics. Several flows in Cartesian and cylindrical coordinates are investigated. The necessary requirement is that these numerical schemes are energy conserving for inviscid ideal flows. Particular emphasis is given to wall bounded flows in circular pipes and in channels where the drag is modified by changing the velocity boundary conditions, or by modifying the shape of the wall.
主持人：佘振苏 教授
时 间：8月27日（周四）下午
3:00~4:00 (报告一)
4:00~5:00 (报告二)
地 点：北大资源西楼2210会议室
欢迎广大师生光临！
附：报告人（Paolo Orlandi）简介：
Paolo Orlandi in the last ten years was invited to visit, until 2002, the Center of Turbulence Research at Stanford NASA-Ames to do research and to attend the summer schools. He was visiting for two periods of one month (2002 and 2004) the University of Newcastle in Australia to collaborate with Prof. Antonia on the DNS of turbulent flows past rough surfaces and on the statistics of the passive scalar in turbulent flows. He spent a short period at SCRIPPS in 2002
to work with Carnevale on the instability of trailing vortices.
P.Orlandi was invited in 1999 to give a plenary talk at the EUROMECH Colloquium 396 on Vortical Structures in Rotating and Stratified Fluids and in 2004 to give an invited talk to the 13th Drag Reduction meeting in Aussois. He gave a talk in 2007 at the Symposium on The International Center for Renewable Energy & Turbulence/Aerospace in Portorico. He participated to two workshops on the solution of the Euler equations at the University of Warwick(17 march 2008) and at the Newton institute in Cambridge (31 october 2008).
In the year 2000 P.O. wrote a book for Kluwer “Flow physical phenomena: a numerical toolkit”, in this book numerical methods for two- and three-dimensional flows were described and the relevant Fortran codes were furnished.
P. Orlandi is in the Advisory committee of the Turbulent Shear Flow Phenomena conference series. He organised in the year 2006 the 14th Drag Reduction meeting in Ischia and in 2007 the WALLTURB ERCOFTAC meeting in Viterbo.