Boundary Layer Parameters Research Articles

Comparison between temporal and spatial direct numerical simulations for bypass transition flows

ABSTRACT Temporally developing direct numerical simulations (T-DNS) are performed for free-stream turbulence induced bypass transition flow over a flat-plate under zero-pressure gradient, and results are validated using experimental data and spatially developing DNS (S-DNS) results. The temporal simulations predict the growth of near-wall Klebanoff modes in the pre-transition regime and their subsequent breakdown due to the sinuous-like instability, where the increase in free-stream turbulence intensity and length scale enhanced the instability. A formulation for the domain translation velocity is developed using the momentum integral boundary layer equation, to estimate the translation of the domain along the plate. The formulation was found to be robust for a range of free-stream turbulence intensities, and both the boundary layer growth and free-stream decay compared well with spatial simulations, confirming that the same translation velocity can be used for the entire domain. The optimal domain size for a temporal simulation is dictated by the length scale of the turbulent spots and errors due to streamwise periodicity, and is estimated to be to , where is the boundary layer thickness at the transition onset. The T-DNS prediction of the integral boundary layer parameters, mean flow, second and higher-order statistics, stress budgets, and free-stream decay were comparable to those of S-DNS, even though they were obtained on ten times smaller streamwise domain and numerical grid. However, T-DNS are limited for bypass transtion flows for which leading-edge effects are unimportant, and may have limitations for the accurate predictions of the near-wall Klebanoff modes that extend up to breakdown. Nonetheless, temporal approach is identified to be a viable inexpensive alternative to the spatial approach for canonical test cases for transition flow physics analysis.

The Effects of Different Planetary Boundary Layer Schemes on the Meteorological and Environmental Elements in winter stable weather of Shenyang

Two planetary boundary layer schemes (YUS and MYJ) in the WRF-CMAQ model, are selected for sensitivity simulation, and the simulation capabilities of different planetary boundary layer schemes to meteorological elements and PM2.5 concentration distribution are analyzed from December 17th to December 20th in 2016. The results show that using the YSU and MYJ schemes can well simulate the spatial distribution and diurnal variation characteristics of temperature, wind speed and PM2.5 concentration on the ground under the background of stable weather in winter. It is sensitive to temperature, wind speed and PM2.5 concentration on the ground using different planetary boundary layer parameterization schemes. The simulated wind speed is relatively large, and the maximum deviation can reach about 2m/s. The deviation of wind speed using the MYJ scheme is relatively small than YSU, which is closer to the real value. There has a lower PM2.5 concentration value using YSU than MYJ at night, however the daytime (mainly from 11:00 to 18: 00) YSU scheme is relatively higher than MYJ. The deviation of PM2.5 concentration on the ground using the MYJ scheme is relatively smaller than YSU, and the characteristics of daily variation is closer to the real situation. Overall, the MYJ scheme is better than YSU in air pollution simulation.

Evaluation of CMAQ modeling sensitivity to planetary boundary layer parameterizations for gaseous and particulate pollutants over a fjord valley

Abstract Three-dimensional chemical transport models are useful for spatial and temporal analyses of outdoor air quality. However, the suitability of boundary-layer parameterizations for air pollution modeling over deep, coastal valleys has seldom been tested. An evaluation of the Community Multiscale Air Quality (CMAQ) model performance for five planetary boundary-layer schemes (PBL) with the Weather Research and Forecasting (WRF) meteorological driver was conducted at 1-km horizontal resolution for fine particulate matter (PM2.5), sulfur dioxide (SO2) and nitrogen dioxide (NO2) over the Terrace-Kitimat valley of northwestern British Columbia, Canada. The top-ranked schemes were Mellor-Yamada-Nakanishi-Niino Level 3 (MYNN3) for PM2.5 and Mellor-Yamada-Janjic for NO2. Both schemes ranked high for absolute SO2 levels, but the MYJ and Asymmetric Convective Model, version 2 (ACM2) schemes qualitatively emulated peak summertime diurnal concentrations in the near field of elevated point sources. Greater nighttime SO2 concentrations with MYNN3 and Yonsei University PBL schemes, in less agreement with station monitoring 8 km downwind of emissions from tall stacks, suggested sustained pollutant mixing and downward transport within the nocturnal boundary layer. Consequently, for these two schemes with representations of nonlocal mass flux transfers between model layers, inland penetrations of pollutant plumes were farther than those of ACM2, MYJ, and University of Washington schemes. For NO2 and PM2.5 that mainly discharged passively from fugitive, ground-level sources, hence are less accurately quantified than SO2 emissions, the fully local MYJ, and semi-local MYNN3 PBL schemes more reasonably reproduced peak season concentrations than other schemes. It is concluded that for air pollution modeling in rugged, remote areas, the mode of pollutant emissions is important for the choice of a PBL scheme. PM2.5 was consistently underestimated by the various PBL schemes, and aspects for improving CMAQ simulations for a complex environment are discussed.

Simulating Real Atmospheric Boundary Layers at Gray-Zone Resolutions: How Do Currently Available Turbulence Parameterizations Perform?

Recent computational and modeling advances have led a diverse modeling community to experiment with atmospheric boundary layer (ABL) simulations at subkilometer horizontal scales. Accurately parameterizing turbulence at these scales is a complex problem. The modeling solutions proposed to date are still in the development phase and remain largely unvalidated. This work assesses the performance of methods currently available in the Weather Research and Forecasting (WRF) model to represent ABL turbulence at a gray-zone grid spacing of 333 m. We consider three one-dimensional boundary layer parameterizations (MYNN, YSU and Shin-Hong) and coarse large-eddy simulations (LES). The reference dataset consists of five real-case simulations performed with WRF-LES nested down to 25 m. Results reveal that users should refrain from coarse LES and favor the scale-aware, Shin-Hong parameterization over traditional one-dimensional schemes. Overall, the spread in model performance is large for the cellular convection regime corresponding to the majority of our cases, with coarse LES overestimating turbulent energy across scales and YSU underestimating it and failing to reproduce its horizontal structure. Despite yielding the best results, the Shin-Hong scheme overestimates the effect of grid dependence on turbulent transport, highlighting the outstanding need for improved solutions to seamlessly parameterize turbulence across scales.

Numerical study of 3-D finlets using Reynolds-averaged Navier–Stokes computational fluid dynamics for trailing edge noise reduction

This paper uses Reynolds-averaged Navier–Stokes computational fluid dynamics to study trailing edge noise reduction with 3-D finlets. Reynolds-averaged Navier–Stokes computational fluid dynamics provides boundary layer parameters near a trailing edge for an empirical wall pressure spectrum model, and then an acoustic model predicts far-field noise based on pressure fluctuations obtained from the wall pressure spectrum model. First, this numerical approach is validated against experiments. Second, a comprehensive trend analysis is conducted to give insight into the design of 3-D finlets under different flow conditions. A data-driven turbulence spanwise length scale model is developed to tackle finlets with small spacing. Combined with acoustic results, detailed computational flow field results are analyzed to understand the physical mechanism of noise reduction. While the major part of the proposed mechanism is the same as prior work, several new observations are shown which better understand the physical mechanism of noise reduction with 3-D finlets. The goals of the current paper are to provide an efficient Reynolds-averaged Navier–Stokes-based approach to predict trailing edge noise of 3-D finlets, to give complete trend analysis results with various finlets under different flow conditions, and to advance an understanding of the underlying physics.

A Numerical Study of a Sea Breeze at Fuerteventura Island, Canary Islands, Spain

The genesis and evolution of a sea-breeze front associated with a shallow convection episode at Fuerteventura Island (Canaries archipelago) are investigated using the Weather Research and Forecasting (WRF) numerical model. Three local and two non-local planetary boundary layer (PBL) parametrization schemes are used, and results of the numerical simulations are compared with observations from the local meteorological surface station network. Statistical analysis shows a good agreement between simulations and measurements, in particular for the 2-m temperature. These results are used in choosing the final PBL scheme and its coupled surface-layer scheme, which is used to simulate the daytime period of the sea-breeze development and weakening. During this episode, a sea-breeze front moved inland against a prevailing offshore flow 3 h after sunrise, colliding with a downslope flow near the centre of the island. The convergence of both flows from opposing directions produced a strong updraft, forming shallow convection a few hours later.

Evaluation of an E–ε and Three Other Boundary Layer Parameterization Schemes in the WRF Model over the Southeast Pacific and the Southern Great Plains

Abstract To accurately simulate the atmospheric state within the planetary boundary layer (PBL) by PBL parameterization scheme in different regions with their dominant weather/climate regimes is important for global/regional atmospheric models. In this study, we introduce the turbulence kinetic energy (TKE) and TKE dissipation rate (ε) based 1.5-order closure PBL parameterization (E–ε, EEPS) in the Weather Research and Forecasting (WRF) Model. The performances of the newly implemented EEPS scheme and the existing Yonsei University (YSU) scheme, the University of Washington (UW) scheme, and Mellor–Yamada–Nakanishi–Niino (MYNN) scheme are evaluated over the stratocumulus dominated southeast Pacific (SEP) and over the Southern Great Plains (SGP) where strong PBL diurnal variation is common. The simulations by these PBL parameterizations are compared with various observations from two field campaigns: the Variability of American Monsoon Systems Project (VAMOS) Ocean–Cloud–Atmosphere–Land Study (VOCALS) in 2008 over the SEP and the Land–Atmosphere Feedback Experiment (LAFE) in 2017 over the SGP. Results show that the EEPS and YSU schemes perform comparably over both regions, while the MYNN scheme performs differently in many aspects, especially over the SEP. The EEPS (MYNN) scheme slightly (significantly) underestimates liquid water path over the SEP. Compared with observations, the UW scheme produces the best PBL height over the SEP. The MYNN produces too high PBL height over the western part of the SEP while both the YSU and EEPS schemes produce too low PBL and cloud-top heights. The differences among the PBL schemes in simulating the PBL features over the SGP are relatively small.

Simulation of Atmospheric Microbursts Using a Numerical Mesoscale Model at High Spatiotemporal Resolution

AbstractAtmospheric microbursts are low‐level meteorological events that can produce significant damage on the surface and pose a major risk to aircraft flying close to the ground. Studies and ad hoc numerical models have been developed to understand the origin and dynamics of the microburst; nevertheless, there are few researches of the phenomenon using global and mesoscale models. This is mainly due to the limitations in resolution, as microbursts normally span for less than 4 km and 20 min. In this paper, the Weather Research and Forecasting model is used at resolutions of 400 m and 3 min to test if it can properly capture the variables and dynamics of high‐reflectivity microbursts. Several microphysics and planetary boundary layer parametrizations are tested to find the best model configuration for the simulation of this kind of episodes. General conditions are evaluated by using thermodynamic diagrams. Surface and vertical wind speed, reflectivity, precipitation, and other variables for each simulated event are compared with observations, and the model's sensitivity to the variables is assessed. The dynamics and evolution of the microburst is evaluated using different plots of a chosen event. The results show that the model is able to reproduce high‐reflectivity microbursts in accordance with observations, although there is a tendency to underestimate the intensity of variables, most markedly on the wind vertical velocity. Regarding the microphysics schemes, the Morrison parametrization performs better than the WRF single‐moment 6‐class scheme. No major differences are found between the Mellor‐Yamada‐Janjic and the Mellor‐Yamada‐Nakanishi‐Niino planetary boundary layer parametrizations.

Sub-kilometer dispersion simulation of a CO tracer for an inter-Andean urban valley

Air quality planning and management can benefit from the ability of numerical models to produce skillful forecasts. However, obtaining these forecasts is a continuing challenge, particularly in complex terrain. Here we examine the dispersion of traffic emissions in the Aburrá valley (located in the Colombian Andes) during an episode of severe air pollution, using the WRF-Chem and a Lagrangian model at sub-kilometer resolution. We focus on the identification of areas with higher CO concentrations (the pollutant analyzed), and examine the role of local and regional airflows in the distribution of CO inside the valley. The meteorological model performance, considering different planetary boundary layer parameterizations and grid sizes, is evaluated using available observations. Overall, the meteorological model performance is within recommended benchmarks for complex terrain. Model performance improves with increasing grid resolution for surface temperature and wind direction, but not for wind speed. Both dispersion models reproduce important features of the spatial and diurnal variability of CO in the valley, but underestimate CO concentrations throughout the simulation period. The south and southeast areas of the valley present the largest CO concentrations, associated with a prevalent northerly transport along the valley axis and reduced transport on the eastern slope. The representation of CO improves when the model adequately reproduces observed rainfall, due to effects of rainfall on boundary layer height and stability, which condition dispersion. Better simulation of transport processes is crucial for informing decisions on air quality management in critical areas such as urban valleys.

The role of the planetary boundary layer parameterization schemes on the meteorological and aerosol pollution simulations: A review

In the past decades, various planetary boundary layer (PBL) parameterization schemes have been developed. The PBL schemes play an essential role in the simulation of meteorological parameters and PBL structures of the model. This review is aimed at presenting the contemporary state of simulation of the meteorological parameters and PBL structures through different PBL schemes over the world, as well as at identifying the main gaps in the simulation capability of PBL schemes and the impact of PBL schemes on the aerosol pollution. To date, there are a total of twelve PBL schemes embedded in the WRF model. Theoretically, the nonlocal closure schemes (MRF, YSU and SH schemes) are more suitable for unstable stratifications. Due to the nonlocal effects, these schemes will produce stronger turbulent mixing. While the local closure schemes (e.g., MY series schemes) are applicable to stable stratifications and produce smaller turbulent mixing. In general, serious PM 2.5 -haze events are accompanied by calm surface winds, higher relative humidity, stronger anomalous temperature inversion and weaker turbulent diffusion within the PBL. Therefore, the results of different PBL schemes on the meteorological parameters, PBL structures, turbulent diffusion were summarized. In summary, to further understand the shortcoming of PBL schemes during the severe haze periods and simulate influence on pollutants by the PBL schemes, and then to improve them in the future. • Multiple planetary boundary layer parameterization schemes are reviewed. • The influence of these schemes on the meteorological and aerosol pollution is discussed. • The main gaps between these schemes and aerosol pollution are presented. • We suggest that further improve the simulation capability of these schemes during the severe haze periods.

The Community Earth System Model Version 2 (CESM2)

AbstractAn overview of the Community Earth System Model Version 2 (CESM2) is provided, including a discussion of the challenges encountered during its development and how they were addressed. In addition, an evaluation of a pair of CESM2 long preindustrial control and historical ensemble simulations is presented. These simulations were performed using the nominal 1° horizontal resolution configuration of the coupled model with both the “low‐top” (40 km, with limited chemistry) and “high‐top” (130 km, with comprehensive chemistry) versions of the atmospheric component. CESM2 contains many substantial science and infrastructure improvements and new capabilities since its previous major release, CESM1, resulting in improved historical simulations in comparison to CESM1 and available observations. These include major reductions in low‐latitude precipitation and shortwave cloud forcing biases; better representation of the Madden‐Julian Oscillation; better El Niño‐Southern Oscillation‐related teleconnections; and a global land carbon accumulation trend that agrees well with observationally based estimates. Most tropospheric and surface features of the low‐ and high‐top simulations are very similar to each other, so these improvements are present in both configurations. CESM2 has an equilibrium climate sensitivity of 5.1–5.3 °C, larger than in CESM1, primarily due to a combination of relatively small changes to cloud microphysics and boundary layer parameters. In contrast, CESM2's transient climate response of 1.9–2.0 °C is comparable to that of CESM1. The model outputs from these and many other simulations are available to the research community, and they represent CESM2's contributions to the Coupled Model Intercomparison Project Phase 6.

Anisotropy of Langmuir turbulence and the Langmuir-enhanced mixed layer entrainment

Surface waves in the ocean surface boundary layer can create Langmuir turbulence which has structure distinct from shear turbulence in a conventional boundary layer. We show that the distinctive structure of Langmuir turbulence is quickly lost away from the surface, so that near the boundary layer base it becomes indistinguishable from turbulence in the absence of surface waves. This has important implications for modeling the effect of ocean surface waves on the boundary layer entrainment and improving ocean surface boundary layer parameterizations in Earth system models.

Configuration and hindcast quality assessment of a Brazilian global sub‐seasonal prediction system

AbstractThis article presents the Centre for Weather Forecast and Climate Studies (CPTEC) developments for configuring a global sub‐seasonal prediction system and assessing its ability in producing retrospective predictions (hindcasts) for meteorological conditions of the following 4 weeks. Six Brazilian Global Atmospheric Model version 1.2 (BAM‐1.2) configurations were tested in terms of vertical resolution, deep convection and boundary‐layer parametrizations, as well as soil moisture initialization. The aim was to identify the configuration with best performance when predicting weekly accumulated precipitation, weekly mean 2 m temperature (T2M) and the Madden–Julian Oscillation (MJO) daily evolution. Hindcasts assessment was performed for 12 extended austral summers (November–March, 1999/2000– 2010/2011) with two start dates for each month for the six configurations and two ensemble approaches. The first approach, referred to as Multiple Configurations Ensemble (MCEN), was formed of one ensemble member from each of the six configurations. The second, referred to as Initial Condition Ensemble (ICEN), was composed of six ensemble members produced with the chosen configuration as the best using an empirical orthogonal function (EOF) perturbation methodology. The chosen configuration presented high correlation and low root‐mean‐squared error (RMSE) for precipitation and T2M anomaly predictions at the first week and these indices degraded as lead time increased, maintaining moderate performance up to week‐4 over the tropical Pacific and northern South America. For MJO predictions, this configuration crossed the 0.5 bivariate correlation threshold in 18 days. The ensemble approaches improved the correlation and RMSE of precipitation and T2M anomalies. ICEN improved precipitation and T2M predictions performance over eastern South America at week‐3 and over northern South America at week‐4. Improvements were also noticed for MJO predictions. The time to cross the above‐mentioned threshold increased to 21 days for MCEN and to 20 days for ICEN.

Toward the GMF for Wind Speed and Surface Stress Retrieval in Hurricanes Based on the Collocated GPS-Dropsonde and Remote Sensing Data

This article describes the first step toward the development of the geophysical model function (GMF) for the retrieval of wind speed and wind stress in hurricanes, based on developing a relation between the cross-polarized satellite SAR data from Sentinel-1 and winds/stress observed from collocated NOAA GPS-dropsondes data. Field measurements and remote sensing data for tropical cyclones in the Atlantic Ocean were analyzed. Using the data measured by GPS-dropsondes, average wind velocity profiles were obtained, while the parameters of the wind boundary layer (drag coefficient and friction velocity) were restored from the “wake” part of the velocity profiles using the self-similarity property. The self-similarity of the velocity profile “defect” in the boundary layer, known from the fluid dynamics, was used to retrieve the parameters of the atmospheric boundary layer (the surface wind velocity, drag coefficient, and friction velocity) from the dropsonde wind velocity profiles in ten major hurricanes. Based on the processing of the measurements in the hurricanes Irma 2017/09/07 and Maria 2017/09/21 and 2017/09/23 at a time close to the time of acquisition of the Sentinel-1 images, the dependencies of the cross-polarized normalized radar cross section on the wind speed and wind friction velocity were obtained and used for constructing the GMFs.

Numerical simulation of supersonic flow past a plate with surface material sublimation

A method of direct numerical simulation and a method of solving the boundary-layer equations were applied to parameters of a supersonic boundary layer for a flow past a flat plate (Mach number M = 2) for the case of a plate coated with a sublimation material. The sublimating material is naphthalene (C10 H8). Comparison of results from these two approaches — numerical simulation and solution of a boundary layer under the assumption on the local self-similarity — demonstrated a satisfactory agreement between them. Calculations demonstrated that a higher surface temperature produces a higher mass rate of evaporation. Meanwhile, the total heat flux to the solid wall decreases and the wall temperature is lower than for the case of zero sublimation. Since the molecular mass of naphthalene is by several times higher than the molecular mass of air and due to evaporation-induced wall cooling, we observe a higher density of the mixture of air with the sublimating substance vapor near the wall. This may facilitate a higher stability of the supersonic boundary layer and delays the flow transition to the turbulent state.

Three-Dimensional Planetary Boundary Layer Parameterization for High-Resolution Mesoscale Simulations

Wind energy applications including wind resource assessment, wind power forecasting, and wind plant optimization require high-resolution mesoscale simulations. High resolution mesoscale simulations are essential for accurate characterization of atmospheric flows over heterogeneous land use and complex terrain. Under such conditions, the assumption of grid-cell homogeneity, used in one-dimensional planetary boundary layer (1D PBL) parameterizations, breaks down. However, in most numerical weather prediction (NWP) models, boundary layer turbulence is parameterized using 1D PBL parameterizations. We have therefore developed a three-dimensional (3D) PBL parameterization to better account for horizontal flow heterogeneities. We have implemented and tested the 3D PBL parameterization in the Weather Research and Forecasting (WRF) numerical weather prediction model. The new parameterization is validated using observations from the Wind Forecast Improvement 2 (WFIP 2) project and compared to 1D PBL results.

Sensitivity study of the planetary boundary layer and microphysical schemes to the initialization of convection over the Arabian Peninsula

AbstractIn this study, we present a five‐member Weather Research and Forecasting (WRF) physics ensemble over the Arabian Peninsula on the convection‐permitting (CP) scale and investigate the ability to simulate convection and precipitation by varying the applied cloud microphysics and planetary boundary layer (PBL) parametrizations. The study covers a typical precipitation event ocurring during summertime over the eastern part of the United Arab Emirates (UAE). Our results show that the best results are obtained by using water‐ and ice‐friendly aerosols combined with aerosol‐aware Thompson cloud microphysics and the Mellor‐Yamada‐Nakanishi‐Niino (MYNN) PBL parametrization. The diurnal cycle of 2‐m temperature over the desert is well captured by all members, although a cold bias is present during the morning and evening transition. All members are capable of simulating the correct timing of the onset of convection. Simulations with the MYNN PBL and Thompson scheme produce the highest convective available potential energy (CAPE) and convective inhibition (CIN), associated with stronger mixing inside the PBL, leading to the formation of more dense liquid water clouds. The WDM6 microphysics scheme is not a suitable option, as there are hardly any liquid water clouds; mainly ice clouds are simulated. Precipitation is best captured by applying the MYNN and Thomspon scheme. Although the ensemble size is relatively small, this allows for the provision of cloud probability maps suitable for cloud‐seeding applications.

LiDAR measurements for an onshore wind farm: Wake variability for different incoming wind speeds and atmospheric stability regimes

AbstractWind measurements were performed with the UTD mobile LiDAR station for an onshore wind farm located in Texas with the aim of characterizing evolution of wind‐turbine wakes for different hub‐height wind speeds and regimes of the static atmospheric stability. The wind velocity field was measured by means of a scanning Doppler wind LiDAR, while atmospheric boundary layer and turbine parameters were monitored through a met‐tower and SCADA, respectively. The wake measurements are clustered and their ensemble statistics retrieved as functions of the hub‐height wind speed and the atmospheric stability regime, which is characterized either with the Bulk Richardson number or wind turbulence intensity at hub height. The cluster analysis of the LiDAR measurements has singled out that the turbine thrust coefficient is the main parameter driving the variability of the velocity deficit in the near wake. In contrast, atmospheric stability has negligible influence on the near‐wake velocity field, while it affects noticeably the far‐wake evolution and recovery. A secondary effect on wake‐recovery rate is observed as a function of the rotor thrust coefficient. For higher thrust coefficients, the enhanced wake‐generated turbulence fosters wake recovery. A semi‐empirical model is formulated to predict the maximum wake velocity deficit as a function of the downstream distance using the rotor thrust coefficient and the incoming turbulence intensity at hub height as input. The cluster analysis of the LiDAR measurements and the ensemble statistics calculated through the Barnes scheme have enabled to generate a valuable dataset for development and assessment of wind farm models.

Modeling Arctic Boundary Layer Cloud Streets at Grey-zone Resolutions

To better understand how model resolution affects the formation of Arctic boundary layer clouds, we investigated the influence of grid spacing on simulating cloud streets that occurred near Utqiagvik (formerly Barrow), Alaska, on 2 May 2013 and were observed by MODIS (the Moderate Resolution Imaging Spectroradiometer). The Weather Research and Forecasting model was used to simulate the clouds using nested domains with increasingly fine resolution ranging from a horizontal grid spacing of 27 km in the boundary-layer-parameterized mesoscale domain to a grid spacing of 0.111 km in the large-eddy-permitting domain. We investigated the model-simulated mesoscale environment, horizontal and vertical cloud structures, boundary layer stability, and cloud properties, all of which were subsequently used to interpret the observed roll-cloud case. Increasing model resolution led to a transition from a more buoyant boundary layer to a more shear-driven turbulent boundary layer. The clouds were stratiform-like in the mesoscale domain, but as the model resolution increased, roll-like structures, aligned along the wind field, appeared with ever smaller wavelengths. A stronger vertical water vapor gradient occurred above the cloud layers with decreasing grid spacing. With fixed model grid spacing at 0.333 km, changing the model configuration from a boundary layer parameterization to a large-eddy-permitting scheme produced a more shear-driven and less unstable environment, a stronger vertical water vapor gradient below the cloud layers, and the wavelengths of the rolls decreased slightly. In this study, only the large-eddy-permitting simulation with gird spacing of 0.111 km was sufficient to model the observed roll clouds.

Simulation of boundary layer under laminar and turbulent modes of newtonian fluid motion in a flexible pipeline

The article deals with the modeling of boundary layer parameters for Newtonian fluids under laminar and turbulent modes of motion. Based on the system of Prandtl equations and initial boundary conditions under laminar motion, using the Gallorkin method, a tri-diagonal system of equations is formed, which connects the values of functions at the node of nets n+1 across the boundary layer. The numerical method uses the Thomas algorithm to calculate values Ujn+. The velocity value Vjn+1 is determined from the continuity equation by integration across the boundary layer. The Navier-Stokes equation in dimensionless form was used to model the turbulent boundary layer, given the velocity U is an independent variable. The differential equation system was solved using the numerical Dorodnicin method. The results of modeling the velocity distribution in the boundary layer, the thickness of the boundary layer in the section of the flexible pipeline 0.8-1.5 m from the beginning of the fluid entering the pipeline at the expense up to 0.1 kg/s are presented. Keywords: boundary layer, turbulent mode, velocity, Prandtl equation