Complex-amplitude Fourier single-pixel imaging via coherent structured illumination

We propose a method of complex-amplitude Fourier single-pixel imaging(CFSI)with coherent structured illumination to acquire both the amplitude and phase of an object.In the proposed method,an object is illustrated by a series of coherent structured light fields,which are generated by a phase-only spatial light modulator,the complex Fourier spectrum of the object can be acquired sequentially by a single-pixel photodetector.Then the desired complex-amplitude image can be retrieved directly by applying an inverse Fourier transform.We experimentally implemented this CFSI with several different types of objects.The experimental results show that the proposed method provides a promising complex-amplitude imaging approach with high quality and a stable configuration.Thus,it might find broad applications in optical metrology and biomedical science.

Tomographic PIV investigation of coherent structures in a turbulent boundary layer flow

Tomographic particle image velocimetry was used to quantitatively visualize the three-dimensional co- herent structures in the logarithmic region of the turbulent boundary layer in a water tunnel. The Reynolds number based on momentum thickness is Reo = 2 460. The in- stantaneous velocity fields give evidence of hairpin vortices aligned in the streamwise direction forming very long zones of low speed fluid, which is flanked on either side by high- speed ones. Statistical support for the existence of hairpins is given by conditional averaged eddy within an increasing spanwise width as the distance from the wall increases, and the main vortex characteristic in different wall-normal re- gions can be reflected by comparing the proportion of ejec- tion and its contribution to Reynolds stress with that of sweep event. The pre-multiplied power spectra and two-point cor- relations indicate the presence of large-scale motions in the boundary layer, which are consistent with what have been termed very large scale motions （VLSMs）. The three dimen-sional spatial correlations of three components of veloc- ity further indicate that the elongated low-speed and high- speed regions will be accompanied by a counter-rotating roll modes, as the statistical imprint of hairpin packet structures, all of which together make up the characteristic of coherent structures in the logarithmic region of the turbulent boundary layer （TBL）.

Gustiness and Coherent Structure of Strong Winds and Their Role in Dust Emission and Entrainment

After the passage of a cold front, spring in northern China, the outbreak of strong wind is often accompanied by dust emissions. Through analyses of data in the atmospheric boundary layer during a typical case, it is revealed there are rather regular gust wave packets superimposed on the basic strong wind flow. The gust-wind wave packets have a period equal to around 3 6 rains and possess coherent structure. As the vertical transport of momentum is decomposed into separate parts by （a） basic flow, （b） gust-wind, and （c） turbulence, they are all in a downwards direction at the lower levels of the atmospheric boundary layer during strong wind periods. However, （a） is the largest, while （b） and （c） are comparable. All these are very different from the case of normal weather. Besides, the friction velocity at the ground surface is also much larger than that of normal weather and should be corrected by taking the contributions of the basic flow and gust-wind into account.The strong basic flow with descending motion is very favorable for soil erosion and sand/dust emissions, but suppresses the entrainment of dust particles by keeping them within the bottom levels of the atmospheric boundary layer. Owing to the coherent structure of gust-wind, dust particles can effectively overcome the systematic descending air motion and penetrate into the middle and upper levels of the atmospheric boundary layer, and then propagate further and diffuse into the troposphere where ascending air motion prevails.

Coherent structures and wavepackets in subsonic transitional turbulent jets

A large eddy simulation (LES) is performed for two subsonic jets with a Reynolds number of , which have different core temperatures, i.e., the cold and hot jet. The far-field overall sound pressure levels (OASPL) and noise spectra are well validated against previous experimental results. It is found that the OASPL is raised by heating at shallow angles. The most energetic coherent structures are extracted with specified frequencies using the filter based on the frequency domain variant of the snapshot method of proper orthogonal decomposition (POD). The modes have high coherence of near-field pressure for both jets, while the coherence of modes is enhanced greatly by heating. Based on the coherent structures, spatial wavepackets are educed and the characteristics of growth, saturation and decay are analyzed and compared between the two jets in detail. The results show that heating would enhance the linear growth rate for high frequency components, and nonlinear growth rates for low frequency components in general, which are responsible for higher OASPL in the hot jet. The far-field sound generated by wavepackets is computed using the Kirchhoff extrapolation, which matches well with that of LES at shallow angles. This indicates that the wavepackets associated with coherent structures are dominant sound sources in forced transitional turbulent jets. Additionally, the present POD method is proven to be a robust tool to extract the salient features of the wavepackets in turbulent flows.

WAVELET ANALYSIS OF COHERENT STRUCTURES IN A THREE-DIMENSIONAL MIXING LAYER

Wavelet analysis is applied to the results obtained by the direct numerical simulation of a three-dimensional (3D) mixing layer in order to investigate coherent structures in dimension of scale. First, 3D orthonormal wavelet bases are constructed, and the corresponding decomposition algorithm is developed. Then the Navier-Stokes equations are transformed into the wavelet space and the architecture for multi-scale analysis is established. From this architecture, the coarse field images in different scales are obtained and some local statistical quantities are calculated. The results show that, with the development of a mixing layer, the energy spectrum densities for different wavenumbers increase and the energy is transferred from the average flow to vortex structures in different scales. Due to the non-linear interactions between different scales, cascade processes of energy are very complex. Because vortices always roll and pair at special areas, for a definite scale, the energy is obtained from other scales at some areas while it is transferred to other scales at other areas. In addition, energy dissipation and transfer always occur where an intense interaction between vortices exists.

The spatial-temporal evolution of coherent structures in log law region of turbulent boundary layer

The spatial-temporal evolution of coherent structures （CS） is significant for turbulence control and drag re- duction. Among the CS, low and high speed streak structures show typical burst phenomena. The analysis was based on a time series of three-dimensional and three-component （3D-3C） velocity fields of the flat plate turbulent boundary layer （TBL） measured by a Tomographic and Time-resolved PIV （Tomo TRPIV） system. Using multi-resolution wavelet transform and conditional sampling method, we extracted the intrinsic topologies and found that the streak structures appear in bar-like patterns. Furthermore, we seized locations and velocity information of transient CS, and then calculated the propagation velocity of CS based on spatial-temporal cross-correlation scanning. This laid a foundation for further studies on relevant dynamics properties.

THE EFFECT OF COMPLIANT COATINGS ON COHERENT STRUCTURE IN TURBULENT BOUNDARY LAYERS

The velocity profile,turbulence intensity profile,streaky structure and bursting frequency in turbulent boundary layers over a flat plate with compliant coatings were investigated by Laser Doppler Anemometry and condi- tional sampling techniques.This experiment led to the conclusions that in boundary layer flows on a compliant wall,as compared with that on a rigid wall,the log law region was extended further away from the wall,and that the maximum value of each turbulence intensity profile in the near wall region was reduced and the bursting frequency obviously decreased with the compliant coatings.One point worthy of notice was that the above results were very much like those of polymer drag reduction experiments.

A KIND OF FAST CHANGING COHERENT STRUCTURE IN A TURBULENT BOUNDARY LAYER

Coherent structures of a turbulent boundary layer were investigated by hydrogen bubble method. A kind of fast changing structure was observed. That is a spot in which all the hydrogen bubbles vanish much faster than in other regions. This investigation verified that dark-spot is formed by a strong sweep from outer layer. Inside a dark-spot the local instantaneous flow speed might be four times of its neighboring high-speed streaks. Comparing with the low/high speed streaks, both dark-spot and the vortical structures around it are changing very fast. Around dark-spot intensive shear layers are formed and indications of the generation of small-scale structures could be observed.

AN EXPERIMENTAL STUDY ON TURBULENT COHERENT STRUCTURES NEAR A SHEARED AIR-WATER INTERFACE

The turbulence structures near a sheared air-water interface were experimentally investigated with the hydrogen bubble visualization technique. Surface shear was imposed by an airflow over the water flow which was kept free from surface waves. Results show that the wind shear has the main influence on coherent structures under air-water interfaces. Low- and high- speed streaks form in the region close to the interface as a result of the imposed shear stress. When a certain airflow velocity is reached, “turbulent spots” appear randomly at low-speed streaks with some characteristics of hairpin vortices. At even higher shear rates, the flow near the interface is dominated primarily by intermittent bursting events. The coherent structures observed near sheared air-water interfaces show qualitative similarities with those occurring in near-wall turbulence. However, a few distinctive phenomena were also observed, including the fluctuating thickness of the instantaneous boundary layer and vertical vortices in bursting processes, which appear to be associated with the characteristics of air-water interfaces.

A MECHANISM FOR EXCITATION OF COHERENT STRUCTURES IN WALL REGION OF A TURBULENT BOUNDARY LAYER

The problem of how the coherent structures in the wall region of a turbulent boundary layer could be excited by the disturbances from the outer region was investigated by using direct numerical simulation (DNS) method. The results show that velocity disturbances at the upper boundary of the wall region could excite coherent structures in the wall region, thus offering a more comprehensive model for individual coherent structures.

Detecting Near-Surface Coherent Structure Characteristics Using Wavelet Transform with Different Meteorological Elements

In the present study, three wavelet basis functions, i.e., Mexican-hat, Morlet, and Wave, were used to analyze the atmospheric turbulence data obtained from an eddy covariance system in order to determine the effect of six meteorological elements including three-dimensional wind speed, temperature, and CO2and H2O concentrations on the time scale of coherent structures. First, we used the degree of correlation between original and reconstructed waveforms to test the three wavelets’performance when determining the time scale of coherent structures. The Wave wavelet’s reconstructed coherent structure signal best matched the original signal;thus, it was used to further analyze the time scale, number, and time cover of the meteorological elements. We found similar results for all elements, though there was some internal variation, suggesting that coherent structures are not inherently dependent on these elements. Our results provide a basis for proper coherent structure detection in atmospheric turbulence and improve the understanding of similarities and differences between coherent structure characteristics of different meteorological elements, which is helpful for further research into atmospheric turbulence and boundary layers.

Surface water exchanges in the Luzon Strait as inferred from Lagrangian coherent structures

This study presents a Lagrangian view of upper water exchanges across the Luzon Strait based on the finite-time Lyapunov exponents(FTLE)fields computed from the surface geostrophic current.The Lagrangian coherent structures(LCSs)extracted from the FTLE fields well identify the typical flow patterns and eddy activities around the Luzon Strait.In addition,they reveal the intricate transport paths and fluid domains,which are validated by the tracks of satellite-tracked surface drifters and cannot be visually recognized in the velocity maps.The FTLE fields indicate that there are mainly four types of transport patterns near the Luzon Strait;among them,the Kuroshio northward-flowing"leaping"pattern and the clockwise rotating"looping"pattern occur more frequently than the"leaking"pattern of the direct Kuroshio branch into the SCS and the"outflowing"pattern from the SCS to the Pacific.The eddy shedding events of the Kuroshio at the Luzon Strait are further analyzed,and the importance of considering LCSs in estimating transport by eddies is highlighted.The anticyclonic eddy(ACE)shedding cases reveal that ACEs mainly originate from the looping paths of Kuroshio and thus could effectively trap the Kuroshio water before eddy detachments.LCSs provide useful information to predict the positions of the upstream waters that finally enter the ACEs.In contrast,LCS snapshots indicate that during the formation of cyclonic eddies(CEs),most CEs are not connected with the pathways of Kuroshio water.Hence,the contribution of CEs to the surface water exchanges from the Pacific into the SCS is tiny.

Impact of typhoon Lekima(2019)on material transport in Laizhou Bay using Lagrangian coherent structures

Typhoon has an impact on an estuary and coastal environment.However,the present research lacks the detailed description of material transport processes during typhoon passage,such as the transport channels and barriers in the course of material transport and material accumulation area,etc.Therefore,Lagrangian coherent structures(a method developed for describing the transport structure of fluids in recent years)was introduced to investigate and predict the floating material and debris transport process in the Laizhou Bay,Bohai Sea,during typhoon Lekima in 2019.Results show that the Lagrangian coherent structure could well explain the complex flow phenomena in the bay.During the typhoon,the general direction of floating material transport in the Laizhou Bay was anticlockwise.There was a channel for material transport in the northwest and south of the bay,and there are transportation obstacles in the northeast-southwest direction in the middle of the bay.Therefore,the typhoon might worsen the water quality.These results provide references for precise countermeasures to control the formulation of pollution in the Laizhou Bay.

AN EXPERIMENTAL STUDY OF THE LARGE SCALE COHERENT STRUCTURES IN A FORCED FREE SHEAR LAYER

The dynamic characteristics of the large scale coherent structures in a forced free shear layer are experi- mentally studied by means of flow visualization. The quantitative measurements are acquired by the use of a LDV. It is shown that the development of the coherent structures can be greatly influenced by upstream artificial perturbations and as a result the mixing in the layer can be controlled. Like vortex merging, vortex splitting is also a common evolu- tion pattern in the development of the coherent structures.

A study on coherent structures and drag-reduction in the wall turbulence with polymer additives by TRPIV

An experimental measurement was performed us- ing time-resolved particle image velocimetry （TRPIV） to in- vestigate the spatial topological character of coherent struc- tures in wall-bounded turbulence of polymer additive solu- tion. The fully developed near-wall turbulent flow fields with and without polymer additives at the same Reynolds number were measured by TRPIV in a water channel. The compar- isons of turbulent statistics confirm that due to viscoelastic structure of long-chain polymers, the wall-normal velocity fluctuation and Reynolds shear stress in the near-wall region are suppressed significantly. Furthermore, it is noted that such a behavior of polymers is closely related to the decease of the motion of the second and forth quadrants, i.e., the ejection and sweep events, in the near-wall region. The spa- tial topological mode of coherent structures during bursts has been extracted by the new mu-level criteria based on locally averaged velocity structure function. Although the general shapes of coherent structures are unchanged by polymer additives, the fluctuating velocity, velocity gradient, velocity strain rate and vorticity of coherent structures during burst events are suppressed in the polymer additive solution com- pared with that in water. The results show that due to the polymer additives the occurrence and intensity of coherent structures are suppressed, leading to drag reduction.

SOME NEW RESULTS OF THE OBSERVATION ON THE COHERENT STRUCTURES OF TURBULENT BOUNDARY LAYER IN FLOW WITH ADVERSE PRESSURE GRADIENT

By a suitable manipulation of hydrogen bubble generation,some new results were obtained: (1)The long-streaks arc generated along the interfaces between low and high-speed streaks.The long-streaks are generally stretching and are moving faster than its neighboring high-speed streaks.The hydrogen bubbles in long-streaks have longer life.(2)The stream-wise vortices are also generated along the interfaces.

EFFECTS OF TURBULENT COHERENT STRUCTURE ON PLUME DIFFUSION IN ATMOSPHERE BOUNDARY LAYER

The simulation tests of plume diffusion have been carried out in an open water channel,in which a Laser Doppler Velocitymeter,optical concentration measurement and flow visualization technology have been used.Through experiments and theoretical analyses,the effects of environmental wind field,surface roughness and discharge condition of elevated source on plume diffusion have been investigated.The plume dif- fusion mechanism has been elucidated reasonably,based on the turbulent coherent structure theory.

MULTI-SCALE COHERENT STRUCTURES IN TURBULENT BOUNDARY LAYER DETECTED BY LOCALLY AVERAGED VELOCITY STRUCTURE FUNCTIONS

The time sequence of longitudinal velocity component at different vertical locations in turbulent boundary layer was finely measured in a wind tunnel. The concept of coarse_grained velocity structure functions, which describes the relative motions of straining and compressing for multi_scale eddy structures in turbulent flows, was put forward based on the theory of locally multi_scale average. Based on the consistency between coarse_grained velocity structure function and Harr wavelet transformation,detecting method was presented, by which the coherent structures and their intermittency was identified by multi_scale flatness factor calculated by locally average structure function. Phase_averaged evolution course for multi_scale coherent eddy structures in wall turbulence were extracted by this conditional sampling to educe scheme. The dynamics course of multi_scale coherent eddy structures and their effects on statistics of turbulent flows were studied.

Extraction and verification of coherent structures in near-wall turbulence

According to the characteristics of coherent structures in near-wall turbulence, an accurate extraction and verification method is developed based on wavelet transform （WT） and correlation analysis in this paper. At first, the fluid field of a turbulent boundary layer is measured precisely in a gravitational low-speed water tunnel. On the basis of the distribution of the coherent structures, velocity data of three test points are selected and analyzed, whose dimensionless heights are 20.8, 33.5, and 42.6. According to the frequency range of power spectrum density （PSD）, coherent and incoherent structures are both extracted from the original signals using continuous and orthogonal wavelet transforms. To confirm the validity of the extracted signals, the probability density function （PDF） of each extracted signal is calculated. The result demonstrates that the incoherent structures obey the Gaussian distribution, while the coherent structures deviate from the Gaussian distribution. The PDFs of the coherent structures and the original signals are similar, which shows that the coherent structures make most contributions to the turbulence. For further verification, a correlation parameter between coherent and incoherent structures is defined, which evidently proves the validity of the extraction method in this paper.

NUMERICAL RESEARCH ON THE COHERENT STRUCTURE IN THE VISCOELASTIC SECOND-ORDER MIXING LAYERS

Numerical simulations have been performed in time-developing plane mixing layers of the viscoelastic second-order fluids with pseudo-spectral method. Roll-up, pairing and merging of large eddies were examined at high Reynolds numbers and low Deborah numbers. The effect of viscoelastics on the evolution of the large coherent structure was shown by making a comparison between the second-order and Newtonian fluids at the same Reynolds numbers.