Pulsed Doppler lidars are powerful tools for long-range, high-resolution measurements of radial wind velocities. With the development of commercial Doppler lidars and the reduction of acquisition costs, dualDoppler lidar systems will be become increasingly accessible in upcoming years. This study reviews the most common dual-Doppler techniques, describes the setup of a highly synchronized long-range dual-Doppler lidar system, and discusses extensively the different kinds of errors connected with this complex measurement technique. Sources of errors and their interactions are traced through the retrieval algorithm, including errors from single-Doppler lidar and those occurring from a combination of instruments related to various parameters, such as relative beam angles, time and spatial scales of the scan pattern, and atmospheric conditions.
Organized structures in turbulent flow fields are a well-known and still fascinating phenomenon. Although these so-called coherent structures are obvious from visual inspection, quantitative assessment is a challenge and many aspects e.g., formation mechanisms and contribution to turbulent fluxes, are discussed controversially. During the "High Definition Clouds and Precipitation for Advancing Climate Prediction" Observational Prototype Experiment (HOPE) from April to May 2013, an advanced dual Doppler lidar technique was used to image the horizontal wind field near the surface for approximately 300 h. A visual inspection method, as well as a two-dimensional integral length scale analysis, were performed to characterize the observations qualitatively and quantitatively. During situations with forcing due to shear, the wind fields showed characteristic patterns in the form of clearly bordered, elongated areas of enhanced or reduced wind speed, which can be associated with near-surface streaks. During calm situations with strong buoyancy forcing, open cell patterns in the horizontal divergence field were observed. The measurement technique used enables the calculation of integral length scales of both horizontal wind components in the streamwise and cross-stream directions. The individual length scales varied considerably during the observation period but were on average shorter during situations with z/L < 0 compared to strongly stable situations. During unstable situations, which were dominated by wind fields with structures, the streamwise length scales increased with increasing wind speed, whereas the cross-stream length scales decreased. Consequently, the anisotropy increased from 1 for calm situations to values of 2-3 for wind speeds of 8-10 m s −1 . During neutral to stable situations, the eddies were on average quite isotropic in the horizontal plane.
Dual-Doppler lidar has become a useful tool to investigate the wind-field structure in two-dimensional planes. However, lidar pulse width and scan duration entail significant and complex averaging in the resulting retrieved wind-field components. The effects of these processes on the wind-field structure remain difficult to investigate with in situ measurements. Based on high resolution large-eddy simulation (LES) data for the surface layer, we performed virtual dual-Doppler lidar measurements and two-dimensional data retrievals. Applying common techniques (integral length scale computation, wavelet analysis, twodimensional clustering of low-speed streaks) to detect and quantify the length scales of the occurring coherent structures in both the LES and the virtual lidar wind fields, we found that, (i) dual-Doppler lidar measurements overestimate the correlation length due to inherent averaging processes, (ii) the wavelet analysis of lidar data produces reliable results, provided the length scales exceed a lower threshold as a function of the lidar resolution, and (iii) the low-speed streak clusters are too small to be detected directly by the dual-Doppler lidar. Furthermore, we developed and tested a method to correct the integral scale overestimation that, in addition to the dual-Doppler lidar, only requires high-resolution wind-speed variance measurements, e.g. at a tower or energy balance station.
We present a quantum-field-theoretical framework based on path integrals and Feynman diagrams for the investigation of the quantum-optical properties of one-dimensional waveguiding structures with embedded quantum impurities. In particular, we obtain the Green's functions for a waveguide with an embedded two-level system in the single-and two-excitation sector for arbitrary dispersion relations both in the time and the frequency domain. In the single excitation sector, we show how to sum the diagrammatic perturbation series to all orders and thus obtain explicit expressions for physical quantities such as the spectral density and the scattering matrix. In the two-excitation sector, we show that strictly linear dispersion relations exhibit the special property that the corresponding diagrammatic perturbation series terminates after two terms, again allowing for closed-form expressions for physical quantities. In the case of general dispersion relations, notably those exhibiting a band edge or waveguide cut-off frequencies, the perturbation series cannot be summed explicitly. Instead, we derive a self-consistent T -matrix equation that reduces the computational effort to that of a single-excitation computation. This analysis allows us to identify a Fano resonance between the occupied quantum impurity and a free photon in the waveguide as a unique signature of the fewphoton nonlinearity inherent in such systems. In addition, our diagrammatic approach allows for the classification of different physical processes such as the creation of photon-photon correlations and interaction-induced radiation trapping -the latter being absent for strictly linear dispersion relations. Our framework can serve as the basis for further studies that involve more complex scenarios such as several and many-level quantum impurities, networks of coupled waveguides, disordered systems, and non-equilibrium effects.
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