谈镐生文集

本文集收入了著名力学家、应用数学家、中国科学院院士谈镐生先生在流体力学、稀薄气体动力学和应用数学研究领域的论文和研究报告26篇，谈镐生先生倡导和支持力学基础研究的有关文章和论述21篇，谈先生的学术活动和生活图片多幅，以及谈镐生先生生平，最后附有谈先生生平年表。

 

 

Aspects of quality control of wind profiler measurements in complex topography

It is well known in the scientific community that some remote sensing instruments assume that sample volumes present homogeneous conditions within a defined meteorological profile. At complex topographic sites and under extreme meteorological conditions, this assumption may be fallible depending on the site, and it is more likely to fail in the lower layers of the atmosphere. This piece of work tests the homogeneity of the wind field over a boundary layer wind profiler radar located in complex terrain on the coast under different meteorological conditions. The results reveal the qualitative importance of being aware of deviations in this homogeneity assumption and evaluate its effect on the final product. Patterns of behavior in data have been identified in order to simplify the analysis of the complex signal registered. The quality information obtained from the homogeneity study under different meteorological conditions provides useful indicators for the best alternatives the system can offer to build wind profiles. Finally, the results are also to be considered in order to integrate them in a quality algorithm implemented at the product level.

Seabed Sensor Technology, Savannah, Georgia, February 1-3, 2006: workshop proceedings

Future coastal management practices require that a holistic, ecosystem management approach be adopted. Coastal ecosystems, however, present a variety of specific and unique challenges relative to open ocean systems. In particular, interactions with the seabed significantly influence the coastal ecosystem. Observing technologies must be developed and employed to incorporate seafloor interactions, processes and habitat diversity into research and management activities. An ACT Workshop on Seabed Sensor Technology was held February 1-3, 2006 in Savannah, Georgia, to summarize the current state of sensor technologies applicable to examining and monitoring the coastal seabed, including the near-bed benthic boundary layer and surface sediment layer. Workshop participants were specifically charged to identify current sensors in use, recommend improvements to these systems and to identify areas for future development and activities that would advance the use of sensor technology in the observation, monitoring and management of the coastal benthic environment. (pdf contains 23 pages)

A Hybrid Scheme Based on Finite Element/Volume Methods for Two Immiscible Fluid Flows

We have successfully extended our implicit hybrid finite element/volume (FE/FV) solver to flows involving two immiscible fluids. The solver is based on the segregated pressure correction or projection method on staggered unstructured hybrid meshes. An intermediate velocity field is first obtained by solving the momentum equations with the matrix-free implicit cell-centered FV method. The pressure Poisson equation is solved by the node-based Galerkin FE method for an auxiliary variable. The auxiliary variable is used to update the velocity field and the pressure field. The pressure field is carefully updated by taking into account the velocity divergence field. This updating strategy can be rigorously proven to be able to eliminate the unphysical pressure boundary layer and is crucial for the correct temporal convergence rate. Our current staggered-mesh scheme is distinct from other conventional ones in that we store the velocity components at cell centers and the auxiliary variable at vertices. The fluid interface is captured by solving an advection equation for the volume fraction of one of the fluids. The same matrix-free FV method, as the one used for momentum equations, is used to solve the advection equation. We will focus on the interface sharpening strategy to minimize the smearing of the interface over time. We have developed and implemented a global mass conservation algorithm that enforces the conservation of the mass for each fluid.

MHD控制激波诱导边界层分离的机理

激波边界层相互作用是高超声速飞行器面临的重大问题,激波入射到平板引起的边界层分离是其中最具代表性的一种.用加权的3阶ENN格式计算了小磁雷诺数近似的MHD方程,研究了 MHD控制层流边界层分离的机理.数值结果显示,通过局部电离空气并施加洛伦兹力,能使分离点向下游移动,分离区尺寸减小,从而抑制和缓解由于激波-边界层相互作用而引起的分离.

Asymptotic analysis of thin plates under normal load and horizontal edge thrust

We consider the radially symmetric nonlinear von Kármán plate equations for circular or annular plates in the limit of small thickness. The loads on the plate consist of a radially symmetric pressure load and a uniform edge load. The dependence of the steady states on the edge load and thickness is studied using asymptotics as well as numerical calculations. The von Kármán plate equations are a singular perturbation of the Fӧppl membrane equation in the asymptotic limit of small thickness. We study the role of compressive membrane solutions in the small thickness asymptotic behavior of the plate solutions.

We give evidence for the existence of a singular compressive solution for the circular membrane and show by a singular perturbation expansion that the nonsingular compressive solution approach this singular solution as the radial stress at the center of the plate vanishes. In this limit, an infinite number of folds occur with respect to the edge load. Similar behavior is observed for the annular membrane with zero edge load at the inner radius in the limit as the circumferential stress vanishes.

We develop multiscale expansions, which are asymptotic to members of this family for plates with edges that are elastically supported against rotation. At some thicknesses this approximation breaks down and a boundary layer appears at the center of the plate. In the limit of small normal load, the points of breakdown approach the bifurcation points corresponding to buckling of the nondeflected state. A uniform asymptotic expansion for small thickness combining the boundary layer with a multiscale approximation of the outer solution is developed for this case. These approximations complement the well known boundary layer expansions based on tensile membrane solutions in describing the bending and stretching of thin plates. The approximation becomes inconsistent as the clamped state is approached by increasing the resistance against rotation at the edge. We prove that such an expansion for the clamped circular plate cannot exist unless the pressure load is self-equilibrating.

I. Singular perturbation problems involving singular points and turning points. II. On the averaged Lagrangian technique for nonlinear dispersive waves

In Part I a class of linear boundary value problems is considered which is a simple model of boundary layer theory. The effect of zeros and singularities of the coefficients of the equations at the point where the boundary layer occurs is considered. The usual boundary layer techniques are still applicable in some cases and are used to derive uniform asymptotic expansions. In other cases it is shown that the inner and outer expansions do not overlap due to the presence of a turning point outside the boundary layer. The region near the turning point is described by a two-variable expansion. In these cases a related initial value problem is solved and then used to show formally that for the boundary value problem either a solution exists, except for a discrete set of eigenvalues, whose asymptotic behaviour is found, or the solution is non-unique. A proof is given of the validity of the two-variable expansion; in a special case this proof also demonstrates the validity of the inner and outer expansions.

Nonlinear dispersive wave equations which are governed by variational principles are considered in Part II. It is shown that the averaged Lagrangian variational principle is in fact exact. This result is used to construct perturbation schemes to enable higher order terms in the equations for the slowly varying quantities to be calculated. A simple scheme applicable to linear or near-linear equations is first derived. The specific form of the first order correction terms is derived for several examples. The stability of constant solutions to these equations is considered and it is shown that the correction terms lead to the instability cut-off found by Benjamin. A general stability criterion is given which explicitly demonstrates the conditions under which this cut-off occurs. The corrected set of equations are nonlinear dispersive equations and their stationary solutions are investigated. A more sophisticated scheme is developed for fully nonlinear equations by using an extension of the Hamiltonian formalism recently introduced by Whitham. Finally the averaged Lagrangian technique is extended to treat slowly varying multiply-periodic solutions. The adiabatic invariants for a separable mechanical system are derived by this method.

Effects of particle size ratio on single particle motion in colloidal dispersions

The motion of a single Brownian particle of arbitrary size through a dilute colloidal dispersion of neutrally buoyant bath spheres of another characteristic size in a Newtonian solvent is examined in two contexts. First, the particle in question, the probe particle, is subject to a constant applied external force drawing it through the suspension as a simple model for active and nonlinear microrheology. The strength of the applied external force, normalized by the restoring forces of Brownian motion, is the Péclet number, Pe. This dimensionless quantity describes how strongly the probe is upsetting the equilibrium distribution of the bath particles. The mean motion and fluctuations in the probe position are related to interpreted quantities of an effective viscosity of the suspension. These interpreted quantities are calculated to first order in the volume fraction of bath particles and are intimately tied to the spatial distribution, or microstructure, of bath particles relative to the probe. For weak Pe, the disturbance to the equilibrium microstructure is dipolar in nature, with accumulation and depletion regions on the front and rear faces of the probe, respectively. With increasing applied force, the accumulation region compresses to form a thin boundary layer whose thickness scales with the inverse of Pe. The depletion region lengthens to form a trailing wake. The magnitude of the microstructural disturbance is found to grow with increasing bath particle size -- small bath particles in the solvent resemble a continuum with effective microviscosity given by Einstein's viscosity correction for a dilute dispersion of spheres. Large bath particles readily advect toward the minimum approach distance possible between the probe and bath particle, and the probe and bath particle pair rotating as a doublet is the primary mechanism by which the probe particle is able to move past; this is a process that slows the motion of the probe by a factor of the size ratio. The intrinsic microviscosity is found to force thin at low Péclet number due to decreasing contributions from Brownian motion, and force thicken at high Péclet number due to the increasing influence of the configuration-averaged reduction in the probe's hydrodynamic self mobility. Nonmonotonicity at finite sizes is evident in the limiting high-Pe intrinsic microviscosity plateau as a function of bath-to-probe particle size ratio. The intrinsic microviscosity is found to grow with the size ratio for very small probes even at large-but-finite Péclet numbers. However, even a small repulsive interparticle potential, that excludes lubrication interactions, can reduce this intrinsic microviscosity back to an order one quantity. The results of this active microrheology study are compared to previous theoretical studies of falling-ball and towed-ball rheometry and sedimentation and diffusion in polydisperse suspensions, and the singular limit of full hydrodynamic interactions is noted.

Second, the probe particle in question is no longer subject to a constant applied external force. Rather, the particle is considered to be a catalytically-active motor, consuming the bath reactant particles on its reactive face while passively colliding with reactant particles on its inert face. By creating an asymmetric distribution of reactant about its surface, the motor is able to diffusiophoretically propel itself with some mean velocity. The effects of finite size of the solute are examined on the leading order diffusive microstructure of reactant about the motor. Brownian and interparticle contributions to the motor velocity are computed for several interparticle interaction potential lengths and finite reactant-to-motor particle size ratios, with the dimensionless motor velocity increasing with decreasing motor size. A discussion on Brownian rotation frames the context in which these results could be applicable, and future directions are proposed which properly incorporate reactant advection at high motor velocities.

Aerosol-cloud-precipitation interactions in marine stratocumulus clouds

Marine stratocumulus clouds are generally optically thick and shallow, exerting a net cooling influence on climate. Changes in atmospheric aerosol levels alter cloud microphysics (e.g., droplet size) and cloud macrophysics (e.g., liquid water path, cloud thickness), thereby affecting cloud albedo and Earth’s radiative balance. To understand the aerosol-cloud-precipitation interactions and to explore the dynamical effects, three-dimensional large-eddy simulations (LES) with detailed bin-resolved microphysics are performed to explore the diurnal variation of marine stratocumulus clouds under different aerosol levels and environmental conditions. It is shown that the marine stratocumulus cloud albedo is sensitive to aerosol perturbation under clean background conditions, and to environmental conditions such as large-scale divergence rate and free tropospheric humidity.

Based on the in-situ Eastern Pacific Emitted Aerosol Cloud Experiment (E-PEACE) during Jul. and Aug. 2011, and A-Train satellite observation of 589 individual ship tracks during Jun. 2006-Dec. 2009, an analysis of cloud albedo responses in ship tracks is presented. It is found that the albedo response in ship tracks depends on the mesoscale cloud structure, the free tropospheric humidity, and cloud top height. Under closed cell structure (i.e., cloud cells ringed by a perimeter of clear air), with sufficiently dry air above cloud tops and/or higher cloud top heights, the cloud albedo can become lower in ship tracks. Based on the satellite data, nearly 25% of ship tracks exhibited a decreased albedo. The cloud macrophysical responses are crucial in determining both the strength and the sign of the cloud albedo response to aerosols.

To understand the aerosol indirect effects on global marine warm clouds, multisensory satellite observations, including CloudSat, MODIS, CALIPSO, AMSR-E, ECMWF, CERES, and NCEP, have been applied to study the sensitivity of cloud properties to aerosol levels and to large scale environmental conditions. With an estimate of anthropogenic aerosol fraction, the global aerosol indirect radiative forcing has been assessed.

As the coupling among aerosol, cloud, precipitation, and meteorological conditions in the marine boundary layer is complex, the integration of LES modeling, in-situ aircraft measurements, and global multisensory satellite data analyses improves our understanding of this complex system.

Planar reflection of gaseous detonations

Pipes containing flammable gaseous mixtures may be subjected to internal detonation. When the detonation normally impinges on a closed end, a reflected shock wave is created to bring the flow back to rest. This study built on the work of Karnesky (2010) and examined deformation of thin-walled stainless steel tubes subjected to internal reflected gaseous detonations. A ripple pattern was observed in the tube wall for certain fill pressures, and a criterion was developed that predicted when the ripple pattern would form. A two-dimensional finite element analysis was performed using Johnson-Cook material properties; the pressure loading created by reflected gaseous detonations was accounted for with a previously developed pressure model. The residual plastic strain between experiments and computations was in good agreement.

During the examination of detonation-driven deformation, discrepancies were discovered in our understanding of reflected gaseous detonation behavior. Previous models did not accurately describe the nature of the reflected shock wave, which motivated further experiments in a detonation tube with optical access. Pressure sensors and schlieren images were used to examine reflected shock behavior, and it was determined that the discrepancies were related to the reaction zone thickness extant behind the detonation front. During these experiments reflected shock bifurcation did not appear to occur, but the unfocused visualization system made certainty impossible. This prompted construction of a focused schlieren system that investigated possible shock wave-boundary layer interaction, and heat-flux gauges analyzed the boundary layer behind the detonation front. Using these data with an analytical boundary layer solution, it was determined that the strong thermal boundary layer present behind the detonation front inhibits the development of reflected shock wave bifurcation.

Large-eddy simulations of fully developed turbulent channel and pipe flows with smooth and rough walls

Studies in turbulence often focus on two flow conditions, both of which occur frequently in real-world flows and are sought-after for their value in advancing turbulence theory. These are the high Reynolds number regime and the effect of wall surface roughness. In this dissertation, a Large-Eddy Simulation (LES) recreates both conditions over a wide range of Reynolds numbers Re_τ = O(10²)-O(10⁸) and accounts for roughness by locally modeling the statistical effects of near-wall anisotropic fine scales in a thin layer immediately above the rough surface. A subgrid, roughness-corrected wall model is introduced to dynamically transmit this modeled information from the wall to the outer LES, which uses a stretched-vortex subgrid-scale model operating in the bulk of the flow. Of primary interest is the Reynolds number and roughness dependence of these flows in terms of first and second order statistics. The LES is first applied to a fully turbulent uniformly-smooth/rough channel flow to capture the flow dynamics over smooth, transitionally rough and fully rough regimes. Results include a Moody-like diagram for the wall averaged friction factor, believed to be the first of its kind obtained from LES. Confirmation is found for experimentally observed logarithmic behavior in the normalized stream-wise turbulent intensities. Tight logarithmic collapse, scaled on the wall friction velocity, is found for smooth-wall flows when Re_τ ≥ O(10⁶) and in fully rough cases. Since the wall model operates locally and dynamically, the framework is used to investigate non-uniform roughness distribution cases in a channel, where the flow adjustments to sudden surface changes are investigated. Recovery of mean quantities and turbulent statistics after transitions are discussed qualitatively and quantitatively at various roughness and Reynolds number levels. The internal boundary layer, which is defined as the border between the flow affected by the new surface condition and the unaffected part, is computed, and a collapse of the profiles on a length scale containing the logarithm of friction Reynolds number is presented. Finally, we turn to the possibility of expanding the present framework to accommodate more general geometries. As a first step, the whole LES framework is modified for use in the curvilinear geometry of a fully-developed turbulent pipe flow, with implementation carried out in a spectral element solver capable of handling complex wall profiles. The friction factors have shown favorable agreement with the superpipe data, and the LES estimates of the Karman constant and additive constant of the log-law closely match values obtained from experiment.

The influence of freestream turbulence, freestream nuclei populations and a drag-reducing polymer on cavitation inception on two axisymmetric bodies

The influence upon the basic viscous flow about two axisymmetric bodies of (i) freestream turbulence level and (ii) the injection of small amounts of a drag-reducing polymer (Polyox WSR 301) into the test model boundary layer was investigated by the schlieren flow visualization technique. The changes in the type and occurrence of cavitation inception caused by the subsequent modifications in the viscous flow were studied. A nuclei counter using the holographic technique was built to monitor freestream nuclei populations and a few preliminary tests investigating the consequences of different populations on cavitation inception were carried out.

Both test models were observed to have a laminar separation over their respective test Reynolds number ranges. The separation on one test model was found to be insensitive to freestream turbulence levels of up to 3.75 percent. The second model was found to be very susceptible having its critical velocity reduced from 30 feet per second at a 0.04 percent turbulence level to 10 feet per second at a 3.75 percent turbulence level. Cavitation tests on both models at the lowest turbulence level showed the value of the incipient cavitation number and the type of cavitation were controlled by the presence of the laminar separation. Cavitation tests on the second model at 0.65 percent turbulence level showed no change in the inception index, but the appearance of the developed cavitation was altered.

The presence of Polyox in the boundary layer resulted in a cavitation suppression comparable to that found by other investigators. The elimination of the normally occurring laminar separation on these bodies by a polymer-induced instability in the laminar boundary layer was found to be responsible for the suppression of inception.

Freestream nuclei populations at test conditions were measured and it was found that if there were many freestream gas bubbles the normally present laminar separation was elminated and travelling bubble type cavitation occurred - the value of the inception index then depended upon the nuclei population. In cases where the laminar separation was present it was found that the value of the inception index was insensitive to the free stream nuclei populations.