Demonstration of the refined three-dimensional structure of mesoscale eddies and computational error estimates via Lagrangian analysis

In previous studies,Lagrangian analyses were used to assess large-scale ocean circulation,and the Lagrangian coherent structure could also reveal the evolution of the two-dimensional structure of the mesoscale eddies.However,few studies have demonstrated the three-dimensional structure of the mesoscale eddies via Lagrangian analysis.Compared with previous studies,which investigated the eddy structure via a Eulerian view,we used a Lagrangian view to provide a different perspective to study the eddy structure.An idealized cyclonic mesoscale eddy is built up over a seamount,and it presents downwelling inside the eddy and upwelling alongside the eddy formed within a closed circulation system.This structure is difficult to display via a Eulerian analysis.However,the trajectories of particles can well demonstrate the full cycle:the fluid sank and rotated inside the eddies,converged to the upwelling zone of the bottom layer and returned to the surface through upwelling.We also applied a Lagrangian analysis to a realistic simulation.As a significant phenomenon in the South China Sea,the dipole structure of the anticyclonic eddy(AE)/cyclonic eddy(CE)pair off of central Vietnam has been well studied but mainly at the sea surface.With a Lagrangian analysis,we illustrate the three-dimensional structure of the eddy pair:the fluid sank(rose)and rotated inside the AE(CE).More importantly,the trajectories of the particles suggested that there was no fluid exchange between the two eddies since the strong boundary jet separates them from each other.All the conclusions above have been verified and are supported by the computational error estimate.With a selected time step and integral period,the computational errors always present small values,although they increase with strong divergent and vertical diffusive flow.

Lagrangian coherent structure analysis on transport of Acetes chinensis along coast of Lianyungang,China

Spatial heterogeneity or“patchiness”of plankton distributions in the ocean has always been an attractive and challenging scientific issue to oceanographers.We focused on the accumulation and dynamic mechanism of the Acetes chinensis in the Lianyungang nearshore licensed fishing area.The Lagrangian frame approaches including the Lagrangian coherent structures theory,Lagrangian residual current,and Lagrangian particle-tracking model were applied to find the transport pathways and aggregation characteristics of Acetes chinensis.There exist some material transport pathways for Acetes chinensis passing through the licensed fishing area,and Acetes chinensis is easy to accumulate in the licensed fishing area.The main mechanism forming this distribution pattern is the local circulation induced by the nonlinear interaction of topography and tidal flow.Both the Lagrangian coherent structure analysis and the particle trajectory tracking indicate that Acetes chinensis in the licensed fishing area come from the nearshore estuary.This work contributed to the adjustment of licensed fishing area and the efficient utilization of fishery resources.

An efficient formulation based on the Lagrangian method for contact–impact analysis of flexible multi-body system

In this paper,an efficien formulation based on the Lagrangian method is presented to investigate the contact–impact problems of f exible multi-body systems.Generally,the penalty method and the Hertz contact law are the most commonly used methods in engineering applications.However,these methods are highly dependent on various non-physical parameters,which have great effects on the simulation results.Moreover,a tremendous number of degrees of freedom in the contact–impact problems will influenc thenumericalefficien ysignificantl.Withtheconsideration of these two problems,a formulation combining the component mode synthesis method and the Lagrangian method is presented to investigate the contact–impact problems in fl xible multi-body system numerically.Meanwhile,the finit element meshing laws of the contact bodies will be studied preliminarily.A numerical example with experimental verificatio will certify the reliability of the presented formulationincontact–impactanalysis.Furthermore,aseries of numerical investigations explain how great the influenc of the finit element meshing has on the simulation results.Finally the limitations of the element size in different regions are summarized to satisfy both the accuracy and efficien y.

Identification, characterization and evolution of non-local quasi-Lagrangian structures in turbulence

The recent progress on non-local Lagrangian and quasi-Lagrangian structures in turbulence is reviewed.The quasi-Lagrangian structures, e.g., vortex surfaces in viscous flow, gas-liquid interfaces in multi-phase flow, and flame fronts in premixed combustion, can show essential Lagrangian following properties, but they are able to have topological changes in the temporal evolution. In addition,they can represent or influence the turbulent flow field. The challenges for the investigation of the non-local structures include their identification, characterization, and evolution.The improving understanding of the quasi-Lagrangian structures is expected to be helpful to elucidate crucial dynamics and develop structure-based predictive models in turbulence.

On the stress–strain states of cellular materials under high loading rates

A virtual Taylor impact of cellular materials is analyzed with a wave propagation technique, i.e. the Lagrangian analysis method, of which the main advantage is that no pre-assumed constitutive relationship is required. Time histories of particle velocity, local strain, and stress profiles are calculated to present the local stress-strain history curves, from which the dynamic stress-strain states are obtained. The present results reveal that the dynamic-rigid-plastic hardening （D-R-PH） material model introduced in a previous study of our group is in good agreement with the dynamic stress-strain states under high loading rates obtained by the Lagrangian analysis method. It directly reflects the effectiveness and feasibility of the D-R-PH material model for the cellular materials under high loading rates.

Analysis of shock wave unsteadiness using space and time correlations applied to shadowgraph flow visualization data

Unsteady flow characteristics of a normal shock wave,a lambda foot,and a separated turbulent boundary layer are investigated within a unique test section with supersonic inlet flow.The supersonic wind tunnel facility,containing this test section,provides a Mach number of approximately 1.54 at the test section entrance.Digitized shadowgraph flow visualization data are employed to visualize shock wave structure within the test section.These data are analyzed to determine shock wave unsteadiness characteristics,including grayscale spectral energy variations with frequency,as well as time and space correlations,which give coherence and time lag properties associated with perturbations associated with different flow regions.Results illustrate the complexity and unsteadiness of shock-wave-boundary-layerinteractions,including event frequencies from grayscale spectral energy distributions determined using a Lagrangian approach applied to shock wave location,and by grayscale spectral energy distributions determined using ensemble-averaging applied to multiple closely-located stationary pixel locations.Auto-correlation function results and two-point correlation functions(in the form of magnitude squared coherence)quantify the time-scales of periodic events,as well as the coherence of flow perturbations associated with different locations,over a range of frequencies.Associated time lag data provide information on the originating location of perturbation events,as well as the propagation direction and event sequence associated with different flow locations.Additional insight into spatial variations of time lag and flow coherence is provided by application of magnitude squared coherence analysis to multiple locations,relative to a single location associated with the normal shock wave.

DEVELOPMENT OF EXPERIMENTAL METHODS FOR IMPACT TESTING BY COMBINING HOPKINSON PRESSURE BAR WITH OTHER TECHNIQUES

The split Hopkinson pressure bar（SHPB） technique and the wave propagation inverse analysis（WPIA） technique are both extensively used to experimentally investigate the impact behavior of materials, although neither of them alone provides a fully satisfactory analysis. In the present paper, attention is given to new experimental techniques by incorporating a damagemodified constitutive model into the SHPB technique and combining the Hopkinson pressure bar（HPB） technique with WPIA. First, to distinguish the response due to dynamic constitutive behavior and the response due to dynamic damage evolution, the SHPB method incorporating a damage-modified constitutive model is developed, including an explicit damage-modified Zhu–Wang–Tang model and an implicit damage-modified constitutive model. Second, when the SHPB results become invalid, a method of combining new Lagrange inverse analyses with the HPB technique is developed, including cases of the HPB arranged in front of a long specimen and behind the specimen. As examples of these new methods, typical results are given for nonlinear viscoelastic polymers and concretes considering damage evolution, a super-elastic Ti–Ni alloy with phase transformation and an aluminum foam with shock waves propagating within it.

Experimental Study on the Dynamic Mechanical Properties of Reinforced Concrete under Shock Loading

A simple experimental method was introduced to study the mechanical properties of reinforced concrete under shock loading. The one-stage light gas gun was used to test the me- chanical properties of reinforced concrete with different reinforcement ratios under various impact velocities. Three Mn-Cu piezoresistive pressure gauges embedded in the target were used to record the voltage-time signals, from which the stress-strain curves of reinforced concrete were obtained using Lagrangian analysis. Experimental results indicated that the load-bearing capacities of re- inforced concrete increased greatly with the impact velocity and the reinforcement ratio. The peak stress of the shock wave decreased exponentially with the propagation distance.

SHOCK INITIATION OF EXPLOSIVES INVESTIGATED WITH SMALL PARTITION EXPERIMENT AND NUMERICAL SIMULATION

In order to investigate the shock ignition of high energy solid explosives by shock waves,we carry out Lagrangian experiments with 2-D Lagrangian technique which uses composite manganin-constantan （CMC）.The effects of the shock sensitivity of pressed solid high explosives,TNT,and the effect of the lateral rarefaction wave were studied.Based on the measured pressure histories and the radial displacements,we formulate the Ignition and Growth reactive flow models for the pressed TNT.The shock initiation process simulated by Ignition and Growth model agreed well with experimental data.This pressed TNT model can be applied to shock initiation scenarios which are highly unpredictable and have not been or cannot be tested experimentally.

Dynamic Testing Technique Based on Multi-channel Photonic Doppler Velocimetry for Investigating the Dynamic Behavior of Materials

In the present paper,more attention is paid to develop a new optical measurement approach of split-Hopkinson pressure bar(SHPB)and wave propagation inverse analysis(WPIA)by using multi-channel photonic Doppler velocimetry(PDV).Based on the particle velocities measured by PDV,the dynamic stress-strain curve of material is obtained in SHPB tests.The strain is determined by the radial particle velocity of specimen,and the stress is determined by the free surface particle velocity of the transmit ted bar.The results obtained by the new method coincide with those obtained by the conventional strain gauge measurements.The new method is non-intrusive and insensitive to electrical noise,making it significantly more reliable than strain gauges.Using the oblique incidence of laser beam,a series of particle velocity wave propagation signals for long rod specimen are measured simultaneously.Based on the measurements of particle velocity profile,the dynamic constitutive response of polymethyl methacrylate(PMMA)is det ermined by WPIA method.The comparison bet ween the dynamic st ress-s train curve and the quasi-static one indicates that the strain-rate effect must be taken into account for PMMA.