Turbulent Layer Research Articles

Exceptional strength-toughness-hardness integrated B4C ceramics with synergistic reinforcement of nano-BN and in-situ ceramic phases

Boron carbide (B4C) ceramics with enhanced mechanical properties were fabricated by incorporating nano boron nitride (nano-BN), obtained through high-energy ball milling (HEBM) using ZrO2 balls as the medium, and utilizing the spark plasma sintering (SPS) technique. During the densification process of B4C/nano-BN composite powders, an in-situ reaction between the B4C matrix and ZrO2 resulted in the formation of ZrB2 ceramic phases at 1200–1300 °C. Additionally, the rapid sintering densification temperature of composites is reduced to 1500–1700 °C, approximately 80 °C lower than that required for pure B4C ceramics. Notably, while maintaining a high relative density (99.5 %), the Vickers hardness, flexural strength, and fracture toughness of B4C ceramics reinforced with synergistic effects of nano-BN and ZrB2 fabricated at 1750 °C are significantly improved to reach values of 36.8 ± 0.15 GPa, 701 ± 12 MPa, and 5.01 ± 0.13 MPa m1/2 respectively; representing an increase of 3.5 GPa (10.5 %), 225 MPa (47.3 %), and 1.72 MPa m1/2 (52.3 %) compared to pure B4C ceramics alone. The multiple reinforcement mechanisms including pinning effects provided by nano-BN and in-situ formed ZrB2 ceramic phases, B4C/ZrB2 grain boundary pressure and intracrystalline pressure within B4C, interlayer dislocations of nano-BN and turbulent layer of B4C/BN boundaries contribute to energy dissipation during fracture processes, such as crack deflection, bridging, propagation hindrance and branching effect; ultimately resulting in exceptional strength-toughness-hardness integrated B4C-based ceramics.

A simple hot wire temperature drift correction based on temperature sensitivity applied to a turbulent shear layer

A procedure is proposed to correct temperature drift for hot wire anemometry measurements in turbulent fields where the facility is not equipped with temperature control. The procedure consists of evaluating the wire sensitivity to the temperature by building a voltage-temperature curve. The voltages of both the calibration points and the measurement points are corrected, shifting the voltage values to an arbitrary reference temperature. The correction can be applied to the instantaneous voltages by performing synced temperature measurements with constant current anemometry or constant voltage anemometry cold wire. The efficacy of the method is tested on a turbulent shear layer that develops on the side of an open jet wind tunnel not equipped with temperature control. The velocity statistics show a good match with respect to reference particle image velocimetry measurements, evidencing the self-similarity of the shear layer in contrast with the non-corrected data and the data corrected using the semi-empirical and analytical relation based on King's law modification. A correction based only on the temperature statistics shows indistinguishable results with respect to the instantaneous correction.

Моделирование суточной вариации атмосферного электрического поля в турбулентном приземном слое

An electrodynamic model of the electric field dynamics behavior in the atmospheric surface layer due to the action of local factors is presented. The model was obtained by reducing the differential equations system of the electrode effect to the so-called total current equation, which is a second-order equation of parabolic type, considered in a two-dimensional space-time region. The total current equation allows us to connect the set of main factors influencing on the atmospheric surface layer electric field state: conduction current, turbulent current and current arising as a result of convective processes in the atmosphere with the so-called total current in the nearground layer, reflecting changes in the ionospheric potential. The described method provides significant advantages in research, since within the framework of one model it allows the formulation of various problems of electrodynamics of the surface layer and a comparative analysis of the influence on the behavior of the electric field in the surface layer of both individual factors and their combinations. Based on meteorological data at the Peak Cheget mountain station in the Elbrus region, a daily variation in the values of the turbulent diffusion coefficient was constructed. The resulting analytical dependence was used to solve the equation for the total current in the surface layer, provided that it is constant at the upper boundary of the turbulent electrode layer. Solutions obtained by the Fourier method describe the daily variation of the electric field strength depending on the degree of turbulent mixing in the atmosphere. The appearance of a time shift in daily extrema, a change in their amplitude, and the appearance of additional extrema depending on the elec-tric field values have been established. All of these effects are comparable to the global unitary variation and increase with increasing electric field.

Carrier-phase direct numerical simulation and flamelet modeling of NOx formation in a pulverized coal/ammonia co-firing flame

A carrier-phase direct numerical simulation (CP-DNS) of a coal/ammonia co-firing flame in a turbulent mixing layer is performed with a detailed chemical reaction mechanism including NOx formation. The combustion characteristics and NOx formation mechanism of the coal/ammonia co-firing flame are investigated in detail through a conditional reaction pathway analysis. A new four-fuel-stream flamelet model is proposed to adapt to the piloted pulverized coal/ammonia co-combustion system, in which the complex mixing among the volatiles, char off-gases, ammonia, and the pilot stream is characterized with four mixture fractions. The flamelet solutions in the fourfold mixture fraction space are transformed into a uniform space to facilitate the access to the flamelet table. The performance of the flamelet model is evaluated through an a priori analysis, a combustion mode analysis, and a chemical timescale analysis. For the turbulent coal/ammonia co-firing flame studied, two distinct flame fronts within the shear layer are observed with the upper part being dominated by ammonia combustion and the lower part being governed by coal combustion. The conditional analyses show that NO species is mainly generated by the lower layer governed by pulverized coal combustion where the nitrogen-containing species from volatile combustion are highly involved in the NO formation. The NO concentration first increases with decreasing the fraction of ammonia in the local computational cell, and then decreases towards pure pulverized coal combustion, which is characterized with a newly introduced manifold coordinate. While the temperature and the major and intermediate species mass fractions in the coal/ammonia co-firing flame can be reasonably predicted by the proposed flamelet model, the NOx species mass fractions are not well predicted in the region where pulverized coal combustion dominates. It is clarified that the inaccurate prediction of the NOx species is not caused by interpolation errors, multiple combustion modes or the kinetics of NOx formation, but mainly attributed to the definition of the progress variable.Novelty and significance statementThe novelty of this research is the first DNS of a coal/ammonia co-firing flame in a turbulent mixing layer, and the proposal of a new flamelet tabulation method for predicting NOx formation in the coal/ammonia co-firing flame. It is significant because• Coal/ammonia co-firing promises to provide continuous, secure power supply at a much reduced carbon footprint compared to pure coal combustion;• The underlying physics governing the coal/ammonia co-firing are analyzed using carrier-phase DNS;• The performance of the newly proposed flamelet model in predicting the NOx species is evaluated based on the DNS dataset.

A Variant of the Local Similarity Theory and Approximations of Vertical Profiles of Turbulent Moments of the Atmospheric Convective Boundary Layer

The approximation of the turbulent moments of the atmospheric convective layer is based on a variant of the local similarity theory using the concepts of the semi-empirical theory of Prandtl turbulence. In the proposed variant of the local similarity theory, the second moment of vertical velocity and the “spectral” Prandtl mixing length are used as basic parameters. This approach allows us to extend Prandtl’s theory to turbulent moments of vertical velocity and buoyancy and additionally offer more than ten new approximations. The comparison of the proposed approximation with other variants of the theory of local similarity is considered. It is shown that the selected basic parameters significantly improve the agreement between the local similarity approximations and experimental data. The approximations are consistent with observations in the turbulent convective layer of the atmosphere, the upper boundary of which nearly corresponds to the lower boundary of the temperature inversion. Analytical approximations of local similarity can find applications in the construction of high-order moment closures in the vortex of resolving numerical turbulence models, as well as in the construction of “mass-flux” parametrization.

Mean-flow structures of the turbulent boundary layers bounding a two-dimensional separation bubble

Understanding the mean-flow structures of a separated turbulent boundary layer (TBL) is crucial for turbulence modeling. This study investigates the spatial scaling properties of the total shear stress and mixing length in the TBLs bounding a two-dimensional (2D) separation bubble, aiming to derive analytical descriptions for the entire mean-velocity profiles of the TBLs. For the adverse pressure gradient (APG) TBL upstream of the separation bubble, the total shear stress possesses a two-layer structure with an inner layer adhering to a linear law and an outer layer conforming to a defect power law. In contrast, the mixing length profile consists of four layers, namely the viscous sublayer, the buffer layer, the overlap layer, and the wake region. Each of the layers exhibits a power law or a defect power law relationship with the spatial coordinate normal to the wall. In the four-layer structure, three parameters are sensitive to the variation of the APG: the buffer-layer thickness, the relative magnitude of the mixing length at the boundary layer edge, and a defect power law exponent quantifying the extent of the wake region. For the reattached TBL downstream of the separation bubble, the total shear stress consists of two parts. One part is induced by the pressure gradient and retains the two-layer structure, while the other, engendered by the intense turbulence advected from the separated shear layer, exhibits a dual-power-law distribution. The advected turbulence also significantly alters the four-layer structure of the mixing length, resulting in an augmented buffer layer, a diminished overlap layer, and a wake region that mimics a turbulent mixing layer. Via a dilation ansatz to describe the scaling transition between adjacent layers, the study formulates the complete profiles of the total shear stress and mixing length. The formulation leads to the derivation of novel analytical expressions for the entire mean-velocity profiles of the TBLs. The expressions are in precise accord with the direct numerical simulations of an incompressible 2D separation-bubble flow and a 2D impinging shock wave/TBL interaction. The elucidation of the mean-flow structures through this study is anticipated to facilitate the analysis of turbulence models, thereby enhancing their performance in simulating separated TBLs. The construction of the mean-flow descriptions by inspecting the spatial scaling properties of turbulence paves a promising way for theoretical exploration of complex nonequilibrium TBLs.

Artificial neural network aided vapor–liquid equilibrium model for multi-component high-pressure transcritical flows with phase change

In this work, an artificial neural network (ANN) aided vapor–liquid equilibrium (VLE) model is developed and coupled with a fully compressible computational fluid dynamics (CFD) solver to simulate the transcritical processes occurring in high-pressure liquid-fueled propulsion systems. The ANN is trained in Python using TensorFlow, optimized for inference using Open Neural Network Exchange Runtime, and coupled with a C++ based CFD solver. This plug-and-play model/methodology can be used to convert any multi-component CFD solver to simulate transcritical processes using only open-source packages, without the need of in-house VLE model development. The solver is then used to study high-pressure transcritical shock-droplet interaction in both two- and four-component systems and a turbulent temporal mixing layer (TML), where both qualitative and quantitative agreement (maximum relative error less than 5%) is shown with respect to results based on both direct evaluation and the state-of-the-art in situ adaptive tabulation (ISAT) method. The ANN method showed a 6 times speed-up over the direct evaluation and a 2.2-time speed-up over the ISAT method for the two-component shock-droplet interaction case. The ANN method is faster than the ISAT method by 12 times for the four-component shock-droplet interaction. A 7 times speed-up is observed for the TML case for the ANN method compared to the ISAT method while achieving a data compression factor of 2881. The ANN method also shows intrinsic load balancing, unlike traditional VLE solvers. A strong parallel scalability of this ANN method with the number of processors was observed for all the three test cases. Code repository for 0D VLE solvers, and C++ ANN interface—https://github.com/UMN-CRFEL/ANN_VLE.git.

Efficient aerodynamic design using BézierGAN and model order reduction: A computational study

Bézier Generative Adversarial Networks (BézierGANs) is one of the most widely used Convolutional Neural Network (CNN) technique-based algorithms for generating smooth curves to analyze and optimize complex shapes and flow patterns, particularly aerodynamics. Airfoils, the basic cross-sectional shape to design air wings, are generated here by selecting the vital parameters wisely after alternating the typical BézierGANs algorithm instead of relying on pre-existing models. When these predicted airfoils are used to develop the physical structure of the adjacent air layer to observe the phenomena, they become the subject of computationally expensive simulations of turbulent airflow. Simulations of turbulent airflow that are computationally expensive are required when these anticipated airfoils are utilized to create the physical structure of the adjacent air layer to monitor the physical events. To prevail over this computational burden, the Model Order Reduction (MOR) technique is applied to develop the best-fitted lower-order model of the original turbulent air layer model around the airfoils by filtering the most effective system's singular values while preserving all the essential characteristics of the original large-scale model. As evidence of the effectiveness of the Reduced Order Model (ROM) of the turbulent air layer regarding the truncation of the design time and computational costs, the comparative analysis of the computational time is occupied by the original and prescribed system to ensure about 99.7660% of less time consumption by the ROM. The regeneration of the reduced-order physical model is also covered in this paper, which analyzes the physical behaviors regarding the air pressure and the velocity patterns of the airflow around the airfoils and compares the similarities to the physical characteristics of the Full Order Model (FOM). It was found that the ROM can be one of the best alternatives to FOM in real-life implementation.

Postfilament-Induced Two-Photon Fluorescence of Dyed Liquid Aerosol Enhanced by Structured Femtosecond Laser Pulse

Laser-induced fluorescence spectroscopy (LIFS) is actively used for remote sensing of atmospheric aerosols and is currently one of the most sensitive and selective techniques for determining small concentrations of substances inside particles. The use of high-power femtosecond laser sources for LIFS-based remote sensing of aerosols contributes to the development of new-generation fluorescence atmospheric lidars since it makes it possible to overcome the energy threshold for the nonlinear-optical effects of multiphoton absorption in particles and receive the emission signal at long distances in the atmosphere. Our study is aimed at the development and experimental demonstration of the technique of nonlinear laser-induced fluorescence spectroscopy (NLIFS) based on the remote excitation of aerosol fluorescent emission stimulated by a spatially structured high-power femtosecond laser pulse. Importantly, for the first time to our knowledge, we demonstrate the advances in using stochastically structured plasma-free intense light channels (postfilaments) specially formed by the propagation of femtosecond laser radiation through a turbulent air layer to improve NLIFS efficiency. A multiple increase in the received signal of two-photon-excited fluorescence of polydisperse-dyed aqueous aerosols by the structured postfilaments is reported.

Detection of the irrotational boundary using machine learning methods

Four machine learning methods, i.e., self-organizing map (SOM), Gaussian mixture model (GMM), eXtreme gradient boosting (XGBoost), and contrastive learning (CL), are used to detect the irrotational boundary (IB), which represents the outer edge of the turbulent and non-turbulent interface layer. To accurately evaluate the detection methods, high-resolution databases from direct numerical simulations of a temporally evolving turbulent plane jet are used. It is found that except for the SOM method, the general contour of the IB appears to be effectively captured using the GMM, XGBoost, and CL methods, which indicate the turbulent and non-turbulent regions can be roughly recognized. Furthermore, the intrinsic features of the detected IB using the GMM, XGBoost, and the CL methods are quantitatively evaluated. Unlike the conventional vorticity norm method, the three machine learning methods do not rely on a single threshold of vorticity magnitude to separate the turbulent and non-turbulent regions. A small part of the detected IB using the three machine learning methods is characterized by the rotational motions, which are expected to be only found inside the turbulent sublayer and turbulent core region. Compared to the vorticity norm and XGBoost methods, the fractal dimensions of the IB detected by the GMM and CL methods are relatively small, which are related to the missing detection of some highly contorted elements. With the three machine learning methods, a large part of the detected IB is characterized by a convex shape, similarly as with the vorticity norm. However, the probability density function profiles of the local curvature of the detected IB differ greatly between the three machine learning methods and the vorticity norm. A mild variation of the mean conditional distributions of the vorticity magnitude can be observed across the detected IB by the three machine learning methods. This study first implies that using the machine learning methods the turbulent and non-turbulent regions can be roughly distinguished, but it is still challenging to obtain the intrinsic features of the detected IB.

Short vertical wavelength gravity waves in the Martian polar lower atmosphere observed by reanalysis of Mars Global Surveyor radio occultation data

This study investigated gravity waves in the Martian polar lower atmosphere using Mars Global Surveyor (MGS) radio occultation data from February 1998 to March 1999. In addition to the conventional geometrical optics method, Full Spectrum Inversion (FSI) was used to achieve a vertical resolution of ∼300 m in terms of the wavelength. In the polar night in the southern high latitude, wavelike structures with vertical wavelengths ranging from ∼1 km to several km extend from the surface to high altitudes. The positive static stability near the surface and the high terrain in the southern high latitude suggest the waves were topographically generated. The near-surface wind speed was estimated to be a few m s−1. In the midnight sun in the northern high latitude, waves show smaller amplitudes up to 10–15 km altitudes and attenuation above, which is attributable to reduced background stability. Near-neutral thin layers were ubiquitously observed in both groups, indicating the generation of turbulent layers by saturated gravity waves. It was shown that high-resolution radio occultations with radio holographic analysis offer a valuable tool for understanding atmosphere-solid planet interactions.

Структура электрического поля в конвективно-турбулентном приземном слое атмосферы

Electrodynamic models of the surface layer of the atmosphere, taking into account turbulent and convective transport, are constructed and studied. The models are based on the so-called total current equation derived from the equations of the theory of the electrode effect in the atmosphere. From the point of view of mathematics, this is a partial differential equation of a parabolic type with variable coefficients. Since in this type of equations the differential operator is not necessarily the Sturm-Liouville operator, in appropriate cases it is necessary to use different approaches to integrating the total current equation. This, in turn, makes it necessary to consider various hypotheses about the ratio of the intensities of local factors that affect the structure of the equation. The paper considers several cases of the model corresponding to the convective turbulent and convective-turbulent electrode layer. Analytical solutions of the stationary equation of the total electric current are obtained. in various approximations. Electric field strength profiles in the surface layer of the atmosphere for various physical conditions are constructed and studied.

Turbulence-enhanced THz generation by multiple chaotically-distributed femtosecond filaments in air

Remote generation of electromagnetic waves in the terahertz (THz) by the volume of air medium gains increasing scientific interest due to the demand for this spectral range in solving various practical problems including those belonging to the nonlinear atmospheric optics. During self-focusing and filamentation of high-power femtosecond laser pulses in air, the source of THz radiation is the plasma of laser filaments. One of the main challenges of THz generation by a laser filament is increasing the value of optical energy conversion to the long-wavelength band. In this paper, we present the results of our studies on DC-biased THz generation during single-color filamentation in air of focused femtosecond Ti:Sapphire-laser pulses (800 nm, pulse energy up to 40 mJ). The distinctive feature of our study is that a femtosecond optical pulse propagates through a spatially-localized heated air layer containing randomly inhomogeneous refractive index perturbations, which mimics strong air turbulence. For the first time to our knowledge, we show, that the turbulent air layer formed at the beginning of the optical path allows increasing the yield of THz radiation up to 1.5 times due to the formation of multiple chaotically-arranged filaments resulting from random perturbations of the optical beam energy profile that reduces the subsequent THz (re)absorption in the filament plasma.

Two-dimensional direct numerical simulation study of multicomponent mixing with phase transition in a transcritical shear layer

In this paper, we investigate two-dimensional direct numerical simulations of a transcritical shear layer. Three configurations are chosen, which are distinguished by the level of presence of two-phase phenomena. The thermodynamic model is based on a cubic equation of state. It was extended for multicomponent mixtures, and it is able to account for vapor–liquid equilibrium. The thermodynamic modeling with phase-transition is validated using experimental data from the literature. Special focus is put on the effect of the density gradient and the density changes caused by phase-transition on the development of the turbulent shear layer and the associated mixing. In addition to this, the vorticity distribution and the components of its transport equation are analyzed and compared for the different configurations.

Features of Adaptive Phase Correction of Optical Wave Distortions under Conditions of Intensity Fluctuations

An analysis of the features of measurements and correction of phase distortions in optical waves propagating in the atmosphere at various levels of turbulence was performed. It is shown that with increasing intensity fluctuations, the limiting capabilities of phase correction decrease, and the phase of an optical wave that has passed through a turbulence layer consists of two components: potential and vortex. It was found that even in the region of weak fluctuations there is an overlap of spectral filtering functions for intensity and phase fluctuations. Areas of turbulence inhomogeneities have been identified that will have mutual influence and negatively affect the operation of the phase meter. It is noted that correlation functions, both phase and intensity, are less susceptible to this compared to structural functions. The results of experimental studies on the reconstruction of the wavefront of laser radiation distorted by atmospheric turbulence using a Shack–Hartmann wavefront sensor during vignetting and central screening of the entrance pupil in the optical system are presented. Studies have been carried out on the propagation of laser radiation along a horizontal atmospheric path for various levels of turbulence. The results are analyzed in terms of Zernike polynomials.

Deep tomography for the three-dimensional atmospheric turbulence wavefront aberration

Multiconjugate adaptive optics (MCAO) can overcome atmospheric anisoplanatism to achieve high-resolution imaging with a large field of view (FOV). Atmospheric tomography is the key technology for MCAO. The commonly used modal tomography approach reconstructs the three-dimensional atmospheric turbulence wavefront aberration based on the wavefront sensor (WFS) detection information from multiple guide star (GS) directions. However, the atmospheric tomography problem is severely ill-posed. The incomplete GS coverage in the FOV coupled with the WFS detection error significantly affects the reconstruction accuracy of the three-dimensional atmospheric turbulence wavefront aberration, leading to a nonuniform aberration detection precision over the whole FOV. We propose an efficient approach for achieving accurate atmospheric tomography to overcome the limitations of the traditional modal tomography approach. We employed a deep-learning-based approach to the tomographic reconstruction of the three-dimensional atmospheric turbulence wavefront aberration. We propose an atmospheric tomography residual network (AT-ResNet) that is specifically designed for this task, which can directly generate wavefronts of multiple turbulence layers based on the Shack-Hartmann (SH) WFS detection images from multiple GS directions. The AT-ResNet was trained under different turbulence intensity conditions to improve its generalization ability. We verified the performance of the proposed approach under different conditions and compared it with the traditional modal tomography approach. The well-trained AT-ResNet demonstrates a superior performance compared to the traditional modal tomography approach under different atmospheric turbulence intensities, various turbulence layer distributions, higher-order turbulence aberrations, detection noise, and reduced GSs conditions. The proposed approach effectively addresses the limitations of the modal tomography approach, leading to a notable improvement in the accuracy of atmospheric tomography. It achieves a highly uniform and high-precision wavefront reconstruction over the whole FOV. This study holds great significance for the development and application of the MCAO technology.

Reinterpretation of the Thorpe Length Scale

Abstract In 1977, S. A. Thorpe proposed a method to estimate the dissipation rate ε of turbulence kinetic energy (TKE) in an overturning turbulent layer in a lake, by sorting the observed (unstable) density profile to render it stable and thus deriving a length scale LT named after him, from the resulting vertical displacements of water parcels. By further proposing that this purely empirical scale (with no a priori physical basis, unlike many other turbulence length scales) is proportional to the Ozmidov scale LO, definable only for stably (not unstably or neutrally) stratified flows, he was able to extract ε. The simplicity of the approach that requires nothing but CTD (Conductivity, Temperature and Depth) casts in water bodies, including lakes and oceans, made it attractive, until microstructure profilers were developed and perfected in later decades to actually make in-situ measurements of ε. Since equivalent microstructure devices are not available for the atmosphere, Thorpe technique has been resurrected in recent years for application to the atmosphere, using potential temperature profiles obtained from high vertical resolution radiosondes. Its popularity and utility have increased lately, in spite of unresolved issues related to the validity of assuming LT is proportional to LO. In this study, we touch upon these issues and offer an alternative interpretation of the Thorpe length scale as indicative of the turbulence velocity scale σK, which allows Thorpe sorting technique to be applied to all turbulent flows, including those generated by convection.

Taming the TuRMoiL: The Temperature Dependence of Turbulence in Cloud–Wind Interactions

Turbulent radiative mixing layers play an important role in many astrophysical contexts where cool (≲104 K) clouds interact with hot flows (e.g., galactic winds, high-velocity clouds, infalling satellites in halos and clusters). The fate of these clouds (as well as many of their observable properties) is dictated by the competition between turbulence and radiative cooling; however, turbulence in these multiphase flows remains poorly understood. We have investigated the emergent turbulence arising in the interaction between clouds and supersonic winds in hydrodynamic enzo-e simulations. In order to obtain robust results, we employed multiple metrics to characterize the turbulent velocity, v turb. We find four primary results when cooling is sufficient for cloud survival. First, v turb manifests clear temperature dependence. Initially, v turb roughly matches the scaling of sound speed on temperature. In gas hotter than the temperature where cooling peaks, this dependence weakens with time until v turb is constant. Second, the relative velocity between the cloud and wind initially drives rapid growth of v turb. As it drops (from entrainment), v turb starts to decay before it stabilizes at roughly half its maximum. At late times, cooling flows appear to support turbulence. Third, the magnitude of v turb scales with the ratio between the hot phase sound-crossing time and the minimum cooling time. Finally, we find tentative evidence for a length scale associated with resolving turbulence. Underresolving this scale may cause violent shattering and affect the cloud’s large-scale morphological properties.

Exploring the daytime boundary layer evolution based on Doppler spectrum width from multiple coplanar wind lidars during CROSSINN

Abstract. Over heterogeneous, mountainous terrain, the determination of spatial heterogeneity of any type of a turbulent layer has been known to pose substantial challenges in mountain meteorology. In addition to the combined effect in which buoyancy and shear contribute to the turbulence intensity of such layers, it is well known that mountains add an additional degree of complexity via non-local transport mechanisms, compared to flatter topography. It is therefore the aim of this study to determine the vertical depths of both daytime convectively and shear-driven boundary layers within a fairly wide and deep Alpine valley during summertime. Specifically, three Doppler lidars deployed during the CROSSINN (Cross-valley flow in the Inn Valley investigated by dual-Doppler lidar measurements) campaign within a single week in August 2019 are used to this end, as they were deployed along a transect nearly perpendicular to the along-valley axis. To achieve this, a bottom-up exceedance threshold method based on turbulent Doppler spectrum width sampled by the three lidars has been developed and validated against a more traditional bulk Richardson number approach applied to radiosonde profiles obtained above the valley floor. The method was found to adequately capture the depths of convective turbulent boundary layers at a 1 min temporal and 50 m spatial resolution across the valley, with the degree of ambiguity increasing once surface convection decayed and upvalley flows gained in intensity over the course of the afternoon and evening hours. Analysis of four intensive observation period (IOP) events elucidated three regimes of the daytime mountain boundary layer in this section of the Inn Valley. Each of the three regimes has been analysed as a function of surface sensible heat flux H, upper-level valley stability Γ, and upper-level subsidence wL estimated with the coplanar retrieval method. Finally, the positioning of the three Doppler lidars in a cross-valley configuration enabled one of the most highly spatially and temporally resolved observational convective boundary layer depth data sets during daytime and over complex terrain to date.

Nonlinear Wave Damping by Kelvin–Helmholtz Instability-induced Turbulence

Magnetohydrodynamic kink waves naturally form as a consequence of perturbations to a structured medium, for example, transverse oscillations of coronal loops. Linear theory has provided many insights into the evolution of linear oscillations, and results from these models are often applied to infer information about the solar corona from observed wave periods and damping times. However, simulations show that nonlinear kink waves can host the Kelvin–Helmholtz instability (KHI), which subsequently creates turbulence in the loop, dynamics that are beyond linear models. In this paper we investigate the evolution of KHI-induced turbulence on the surface of a flux tube where a nonlinear fundamental kink mode has been excited. We control our numerical experiment so that we induce the KHI without exciting resonant absorption. We find two stages in the KHI turbulence dynamics. In the first stage, we show that the classic model of a KHI turbulent layer growing at ∝t is applicable. We adapt this model to make accurate predictions of the damping of the oscillation and turbulent heating as a consequence of the KHI dynamics. In the second stage, the now dominant turbulent motions are undergoing decay. We find that the classic model of energy decay proportional to t −2 approximately holds and provides an accurate prediction of the heating in this phase. Our results show that we can develop simple models for the turbulent evolution of a nonlinear kink wave, but the damping profiles produced are distinct from those of linear theory that are commonly used to confront theory and observations.