Variable Boundary Layer Research Articles

Second Law Analysis for Variable Viscosity Hydromagnetic Boundary Layer Flow with Thermal Radiation and Newtonian Heating

The present paper is concerned with the analysis of inherent irreversibility in hydromagnetic boundary layer flow of variable viscosity fluid over a semi-infinite flat plate under the influence of thermal radiation and Newtonian heating. Using local similarity solution technique and shooting quadrature, the velocity and temperature profiles are obtained numerically and utilized to compute the entropy generation number. The effects of magnetic field parameter, Brinkmann number, the Prandtl number, variable viscosity parameter, radiation parameter and local Biot number on the fluid velocity profiles, temperature profiles, local skin friction and local Nusselt number are presented. The influences of the same parameters and the dimensionless group parameter on the entropy generation rate in the flow regime and Bejan number are calculated, depicted graphically and discussed quantitatively. It is observed that the peak of entropy generation rate is attained within the boundary layer region and plate surface act as a strong source of entropy generation and heat transfer irreversibility.

Modeling and controller design of an industrial hydraulic actuator system in the presence of friction and internal leakage

This paper presents a robust controller scheme and its capabilities to control the position tracking performance of an electro-hydraulic actuator system. Sliding mode control with fixed and varying boundary layer is proposed in the scheme. It is aimed to compensate nonlinearities and uncertainties caused by the presence of friction and internal leakage. Its capabilities are verified through simulations in Matlab Simulink environment. The friction was represented by the LuGre model and the internal leakage was assumed to change. The results indicate that the scheme successfully improves the robustness and the tracking accuracy of the system. This improvement offers a significant contribution in the control of modern equipment positioning applications.

Saturn's low-latitude boundary layer: 1. Properties and variability

[1] Transport of solar wind plasma into a planetary magnetosphere produces an internal boundary layer adjacent to the magnetopause that contains a mixture of solar wind and magnetospheric plasma. The potential processes responsible for this transport are varied, and their relative importance remains unclear, as well as how their competition varies between the magnetized planets. In this paper we examine the properties and variability of Saturn's low-latitude boundary layer (LLBL) using observations made by the Cassini spacecraft; the electron structure of Saturn's LLBL is examined in a companion paper. The duration of spacecraft excursions into the LLBL was generally between ∼3 and ∼23 min, and the electron environment of Saturn's LLBL was intermediate between that of the magnetosheath and that of the magnetosphere, as expected. Estimates of the speed of the magnetopause current layer are of the order of 100 km s−1, and the estimated thickness of the LLBL is of the order of 1 Saturn radius. Our results do not reveal a strong influence of the orientation of the interplanetary magnetic field on the thickness of Saturn's LLBL, which is unlike its terrestrial counterpart. There is also no clear dawn-dusk asymmetry in the thickness of Saturn's LLBL, which might be expected on the basis of our understanding of the growth of the Kelvin-Helmholtz instability at Saturn's magnetopause. We discuss the implications of these findings for the physics of Saturn's magnetospheric boundary and what this could mean for our understanding of how boundary layers are formed in planetary magnetospheres.

Modeling short-term variability of semivolatile organic chemicals in air at a local scale: An integrated modeling approach

Monitoring campaigns from different locations have recently shown how air concentrations of persistent semivolatile contaminants such as polychlorinated biphenyls (PCBs) often exhibit short-term (less than 24 h) variations. The observed patterns have been ascribed to different factors, such as temperature-mediated air–surface exchange and variability of planetary boundary layer (PBL) height and dynamics. Here, we present a new modeling approach developed in order to investigate the short-term variability in air concentrations of organic pollutants at a local scale. A new dynamic multimedia box model is supplied by a meteorological preprocessor (AERMET) with hourly values of air compartment height and wind speed. The resulting model is tested against an existing dataset of PCB air concentrations measured in Zurich, Switzerland. Results show the importance of such modeling approach in elucidating the short- and long-term behavior of semivolatile contaminants in the air/soil system.

An Analytical Model of Evaporation Efficiency for Unsaturated Soil Surfaces with an Arbitrary Thickness

Abstract Analytical expressions of evaporative efficiency over bare soil (defined as the ratio of actual to potential soil evaporation) have been limited to soil layers with a fixed depth and/or to specific atmospheric conditions. To fill the gap, a new analytical model is developed for arbitrary soil thicknesses and varying boundary layer conditions. The soil evaporative efficiency is written [0.5 − 0.5 cos(πθL/θmax)]P with θL being the water content in the soil layer of thickness L, θmax being the soil moisture at saturation, and P being a function of L and potential soil evaporation. This formulation predicts soil evaporative efficiency in both energy-driven and moisture-driven conditions, which correspond to P < 0.5 and P > 0.5, respectively. For P = 0.5, an equilibrium state is identified when retention forces in the soil compensate the evaporative demand above the soil surface. The approach is applied to in situ measurements of actual evaporation, potential evaporation, and soil moisture at five different depths (5, 10, 30, 60, and 100 cm) collected in summer at two sites in southwestern France. It is found that (i) soil evaporative efficiency cannot be considered as a function of soil moisture only because it also depends on potential evaporation, (ii) retention forces in the soil increase in reaction to an increase of potential evaporation, and (iii) the model is able to accurately predict the soil evaporation process for soil layers with an arbitrary thickness up to 100 cm. This new model representation is expected to facilitate the coupling of land surface models with multisensor (multisensing depth) remote sensing data.

The Probability Distribution of Sea Surface Wind Speeds: Effects of Variable Surface Stratification and Boundary Layer Thickness

Abstract Air–sea exchanges of momentum, energy, and material substances of fundamental importance to the variability of the climate system are mediated by the character of the turbulence in the atmospheric and oceanic boundary layers. Sea surface winds influence, and are influenced by, these fluxes. The probability density function (pdf) of sea surface wind speeds p(w) is a mathematical object describing the variability of surface winds that arises from the physics of the turbulent atmospheric planetary boundary layer. Previous mechanistic models of the pdf of sea surface wind speeds have considered the momentum budget of an atmospheric layer of fixed thickness and neutral stratification. The present study extends this analysis, using an idealized model to consider the influence of boundary layer thickness variations and nonneutral surface stratification on p(w). It is found that surface stratification has little direct influence on p(w), while variations in boundary layer thickness bring the predictions of the model into closer agreement with the observations. Boundary layer thickness variability influences the shape of p(w) in two ways: through episodic downward mixing of momentum into the boundary layer from the free atmosphere and through modulation of the importance (relative to other tendencies) of turbulent momentum fluxes at the surface and the boundary layer top. It is shown that the second of these influences dominates over the first.

Marine boundary layer over the subtropical southeast Pacific during VOCALS-REx – Part 2: Synoptic variability

Abstract. In the second part of this work we study the day-to-day variability of the marine atmospheric boundary layer (MBL) over the subtropical southeast Pacific using primarily results from a numerical simulation that covered the whole VOCALS-REx period (October–November 2008). In situ and satellite-derived observations of the MBL height in the offshore region indicate rapid, significant variations (from 500 m to 1700 m a.s.l. over a few days) during October. These MBL changes are connected with the passage of midlatitude troughs that altered the large-scale environment over the VOCALS-REx region. In contrast, the synoptic forcing and MBL changes were less prominent during November. Modelled and observed MBL depth at Point Omega (20° S, 85° W) compare quite well during October (but the simulation is on average 200 m lower) while in November the simulation does not perform as well. In the prognostic local MBL height equation the height change, the horizontal MBL height advection, and the large scale vertical velocity at MBL top are calculated explicitly from the simulation. The entrainment velocity is calculated as the residual of the other terms in the equation. While the vertical velocity and residual terms are opposing and generally have the largest magnitude on average, it is the variability in the advection that explains most of the large changes in the MBL depth. Examination of several cases during VOCALS-REx suggests that the advective term is in turn largely controlled by changes in wind direction, driven by midlatitude activity, acting on a MBL that generally slopes down toward the coast. In one phase, the subtropical anticyclone is reinforced and extends toward the Chilean coast, leading to easterly wind that advects low MBL heights from the coast as far as Point Omega. The opposite phase occurs after the passage of an extratropical cyclone over southern Chile, leading to southwesterly wind that advects a deeper MBL towards subtropical latitudes.

Combined Effects of Wind-Driven Upwelling and Internal Tide on the Continental Shelf

Abstract Internal tides on the continental shelf can be intermittent as a result of changing hydrographic conditions associated with wind-driven upwelling. In turn, the internal tide can affect transports associated with upwelling. To study these processes, simulations in an idealized, alongshore uniform setup are performed utilizing the hydrostatic Regional Ocean Modeling System (ROMS) with conditions corresponding, as closely as possible, to the central Oregon shelf. “Wind only” (WO), “tide only” (TO), and “tide and wind” (TW) solutions are compared, utilizing cases with constant upwelling-favorable wind stress as well as with time-variable observed stress. The tide is forced by applying cross-shore barotropic flow at the offshore boundary with intensity sufficient to generate an internal tide with horizontal velocity amplitudes near 0.15 m s−1, corresponding to observed levels. The internal tide affects the subinertial circulation, mostly through the changes in the bottom boundary layer variability, resulting in a larger bottom stress and a weaker depth-averaged alongshore current in the TW case compared to WO. The spatial variability of the cross-shore and vertical volume transport is also affected. Divergence in the Reynolds stress associated with the baroclinic tidal flow contributes to the tidally averaged cross-shore momentum balance. Internal waves cause high-frequency variability in the turbulent kinetic energy in both the bottom and surface boundary layers, causing periodic restratification of the inner shelf in the area of the upwelling front. Increased vertical shear in the horizontal velocity resulting from the superposition of the upwelling jet and the internal tide results in intermittent patches of intensified turbulence in the mid–water column. Variability in stratification associated with upwelling can affect not only the propagation of the internal tide on the shelf, but also the barotropic-to-baroclinic energy conversion on the continental slope, in this case changing the classification of the slope from nearly critical to supercritical such that less barotropic tidal energy is converted to baroclinic and a larger fraction of the baroclinic energy is radiated into the open ocean.

고속 슬라이딩모드 관측기를 이용한 PMSM 센서리스 속도제어

The paper proposes a sensorless speed control strategy for a PMSM (Permanent Magnet Synchronous Motor) based on a new SMO (Sliding Mode Observer), which substitutes a signum function with a sigmoid function. To apply robust sensorless control of PMSM against parameter fluctuations and disturbance, the high speed SMO is proposed, which estimates the rotor position and angular velocity from the back EMF. The low-pass filter and additional position compensation of the rotor are used to reduce the chattering problem commonly found in sliding mode observer with signum function, which becomes possible by applying the sigmoid function with the control of a switching function. Also the proposed sliding mode observer with the sigmoid function has better efficiency than the conventional sliding mode observer since it adjusts the observer gain by variable boundary layer and estimates the stator resistance. The stability of the proposed sliding mode observer is verified by the Lyapunov second method in determining the observer gain. The validity of the proposed high speed PMSM sensorless velocity control has been demonstrated by real experiments.

Comparison between Non-Gaussian Puff Model and a Model Based on a Time-Dependent Solution of Advection-Diffusion Equation

A comparison between a non-Gaussian puff model and an advanced time-dependent model to simulate the pollutant dispersion in the Planetary Boundary Layer is presented. The puff model is based on a general technique for solving the K-equation, using the truncated Gram-Charlier expansion (type A) of the concentration field and finite set equations for the corresponding moments. The other model (named ADMM: Analytical Dispersion Multilayers Model) is an semi- analytical solution to the time-dependent two-dimensional advection-diffusion equation based on a discretization of the PBL in N sub-layers; in each sub-layers the advection-diffusion equation is solved by the Laplace transform technique, considering an average value for eddy diffusivity and the wind speed. A preliminary performance evaluation is shown in the case of continuous emission from an elevated source in a variable boundary layer. Both models were able to correctly reproduce the concentration field measured and so to be used as operative air pollution models.

Structural ensemble dynamics based closure model for wall-bounded turbulent flow

Wall-bounded turbulent flow involves the development of multi-scale turbulent eddies, as well as a sharply varying boundary layer. Its theoretical descriptions are yet phenomenological. We present here a new framework called structural ensemble dynamics (SED), which aims at using systematically all relevant statistical properties of turbulent structures for a quantitative description of ensemble means. A new set of closure equations based on the SED approach for a turbulent channel flow is presented. SED order functions are defined, and numerically determined from data of direct numerical simulations (DNS). Computational results show that the new closure model reproduces accurately the solution of the original Navier–Stokes simulation, including the mean velocity profile, the kinetic energy of the streamwise velocity component, and every term in the energy budget equation. It is suggested that the SED-based studies of turbulent structure builds a bridge between the studies of physical mechanisms of turbulence and the development of accurate model equations for engineering predictions.

Moisture Vertical Structure, Column Water Vapor, and Tropical Deep Convection

AbstractThe vertical structure of the relationship between water vapor and precipitation is analyzed in 5 yr of radiosonde and precipitation gauge data from the Nauru Atmospheric Radiation Measurement (ARM) site. The first vertical principal component of specific humidity is very highly correlated with column water vapor (CWV) and has a maximum of both total and fractional variance captured in the lower free troposphere (around 800 hPa). Moisture profiles conditionally averaged on precipitation show a strong association between rainfall and moisture variability in the free troposphere and little boundary layer variability. A sharp pickup in precipitation occurs near a critical value of CWV, confirming satellite-based studies. A lag–lead analysis suggests it is unlikely that the increase in water vapor is just a result of the falling precipitation. To investigate mechanisms for the CWV–precipitation relationship, entraining plume buoyancy is examined in sonde data and simplified cases. For several different mixing schemes, higher CWV results in progressively greater plume buoyancies, particularly in the upper troposphere, indicating conditions favorable for deep convection. All other things being equal, higher values of lower-tropospheric humidity, via entrainment, play a major role in this buoyancy increase. A small but significant increase in subcloud layer moisture with increasing CWV also contributes to buoyancy. Entrainment coefficients inversely proportional to distance from the surface, associated with mass flux increase through a deep lower-tropospheric layer, appear promising. These yield a relatively even weighting through the lower troposphere for the contribution of environmental water vapor to midtropospheric buoyancy, explaining the association of CWV and buoyancy available for deep convection.

Seasonal and diurnal variations of ambient PM 2.5 concentration in urban and rural environments in Beijing

Three years of measurement of PM 2.5 with 5-min time resolution was conducted from 2005 to 2007 in urban and rural environments in Beijing to study the seasonal and diurnal variations in PM 2.5 concentration. Pronounced seasonal variation was observed in the urban area, with the highest concentrations typically observed in the winter and the lowest concentrations generally found in the summer. In the rural area, the maximum in PM 2.5 concentration usually appeared during the spring, followed by a second maximum in the summer, while the minimum generally occurred in the winter. Significant diurnal variations in PM 2.5 concentration were observed in both urban and rural areas. In the urban area, the PM 2.5 concentration displays a bimodal pattern, with peaks between 7:00 and 8:00 a.m. and between 7:00 and 11:00 p.m. The minimum generally appears around noon. The morning peak is attributed to enhanced anthropogenic activity during rush hours. The decreases of boundary layer height and wind speed in the afternoon companying with increased source activity during the afternoon rush hour result in the highest PM 2.5 concentration during evening hours. In the rural area, the PM 2.5 concentration shows a unimodal pattern with a significant peak between 5:00 and 11:00 p.m. The seasonal and diurnal variations in PM 2.5 concentration in the urban area are mostly dominated by the seasonal and diurnal variability of boundary layer and source emissions. The year-to-year variability of rainfall also has an important influence on the seasonal variation of PM 2.5 in the urban area. The seasonal and diurnal wind patterns are more important factors for PM 2.5 variation in the rural area. Southerly winds carry pollutants emitted in southern urban areas northward and significantly enhance the PM 2.5 concentration level in the rural area.

Boundary Layer, Cloud, and Drizzle Variability in the Southeast Pacific Stratocumulus Regime

Abstract The southeast Pacific stratocumulus regime is an important component of the earth’s climate system because of its substantial impact on albedo. Observational studies of this cloud regime have been limited, but during the past 5 yr, a series of cruises with research vessels equipped with in situ and remote sensing systems have provided unprecedented observations of boundary layer cloud and drizzle structures. These cruises started with the East Pacific Investigation of Climate (EPIC) 2001 field experiment, followed by cruises in a similar area in 2003 and 2004 [Pan-American Climate Studies (PACS) Stratus cruises]. The sampling from these three cruises provides a sufficient dataset to study the variability occurring over this region. This study compares observations from the 2004 cruise with those obtained during the previous two cruises. Observations from the ship provide information about boundary layer structure, fractional cloudiness, cloud depth, and drizzle characteristics. This study indicates more strongly decoupled boundary layers during the 2004 cruise than the well-mixed conditions that dominated the cloud and boundary layer structures during the EPIC cruise, and the highly variable conditions—sharp transitions from a solid stratus deck to broken-cloud and clear-sky periods—encountered during PACS Stratus 2003. Diurnal forcing and synoptic conditions are considered to be factors affecting these variations. A statistical evaluation of the macrophysical boundary layer, cloud, and drizzle properties is performed using the 5–6-day periods for which the research vessels remained stationed at the location of 20°S, 85°W during each cruise.

Chattering Reduction Using Variable Boundary Layer Solution in a Class of Nonlinear Variable Structure Systems

A new method,variable boundary layer solution,is proposed in this paper for a class of nonlinear variable structure systems to restrain the chattering.The mathemat- ical relationship between the static errors and the width of saturating property is presented. The saturating property with time-varying boundary layer width can be designed through the specification of the static errors,which can not only reduce the chattering in the system but also simultaneously satisfy the specification of the static errors.The simulation results show the validity of the method.

Accounting for atmospheric boundary layer variability on flux estimation from RS observations

A Large Eddy Simulation (LES) model is coupled to a remote‐sensing‐based SVAT that accounts for soil and vegetation in order to study the feedback effects between surface state and spatial variability in fluxes, through the induction of spatial variability in the lower atmosphere. As such, this study focuses on sensible heat flux exchange. The simulations indicated that changes are introduced to the flux distributions mainly at higher surface temperatures. A scale‐dependent method is presented to account for feedback effects. This showed the most significant correlation between surface and air temperature at scales from 500 to 1000 m and modulated the spatial variance of sensible heat flux. This suggests that feedback effects act to limit the spatial variability in fluxes, and ignoring them will cause the largest errors at the extremes.

The Impact of Rapid Wind Variability upon Air–Sea Thermal Coupling

Abstract The basic effect of extratropical atmosphere–ocean thermal coupling is to enhance the variance of both anomalous sea surface temperatures (SSTs) and air temperatures (AIRT) due to a decreased energy flux between the atmosphere and ocean, called reduced thermal damping. In this paper it is shown that rapidly varying surface winds, through their influence upon the turbulent surface heat fluxes that drive this coupling, act to effectively weaken the coupling and thus partially counteract the reduced thermal damping. In effect, rapid fluctuations in wind speed somewhat insulate the atmosphere and ocean from each other. The nonlinear relationship between the rapidly varying wind speed anomalies and SST and AIRT anomalies results in a rapidly varying component of the surface heat fluxes. The clear separation between the dynamical time scales of the ocean and atmosphere allows this rapidly varying flux to be simply approximated by a stochastic process in which rapidly varying wind speed is represented as Gaussian white noise whose amplitude is modulated by the more slowly evolving thermal anomalies. Such state-dependent (multiplicative) noise can alter the dynamics of atmosphere–ocean coupling because it induces an additional heat flux term, the noise-induced drift, that effectively acts to weaken both coupling and dissipation. Another key implication of the outlined theory is that air–sea coupling includes both deterministic and stochastic components. The theory is tested by examining daily observations during extended winter (November–April) at several ocean weather stations (OWSs). Two important results are found. First, multiplicative noise at OWS P effectively decreases the coupling by about one-third, with about a 10% (20%) decrease in the damping of SST (AIRT). This suggests that multiplicative noise may be responsible for roughly half of the AIRT variability at OWS P on subseasonal time scales. Second, OWS observations reveal that joint probability distribution functions of daily averaged SST and AIRT anomalies are significantly non-Gaussian. It is shown that treating the rapidly varying boundary layer heat fluxes as state-dependent noise can reproduce this observed non-Gaussianity. It is concluded that the effect of state-dependent noise is crucial to understand and model atmosphere–ocean coupling.

Carbon isotope fractionation in species of the torrenticolous families Podostemaceae and Hydrostachyaceae

Carbon isotope ratios of herbarium material from members of the fresh-water families Podostemaceae and Hydrostachyaceae (Rosidae) were analyzed. The levels of 13C were highly variable (Podostemaceae −12.8‰ to −38.55‰; Hydrostachyaceae −10.78‰ to −30.42‰), across as well as within species and across a wide geographic range. We suggest that the high variance observed is due neither to a constant attribute of the species like the photosynthetic CO 2-carboxylase (in water plants with very high discrimination of the 13CO 2 probably Rubisco) nor to the constant structural peculiarities of these species. Rather, it is likely due to the ‘diffusional resistance’ for the CO 2-flux from the turbulent and/or fast flowing water, causing a very variable boundary layer on the plant surface.

Approximate heat transfer coefficients based on variable thermophysical properties for laminar flow over a uniformly heated flat plate

New heat transfer coefficient approximations are developed for forced laminar flow over a uniformly heated flat plate at zero incidence angle. The development is based on solving the variable property boundary layer equations using a variable property similarity transform that incorporates an adjustable similarity scaling constant. The scaling constants value is iteratively adjusted until the scaled temperature gradient-at-the-wall value is equal to the small temperature difference value. The resulting scaled profiles are nearly congruent. The congruency scaling constant is then approximated in terms of simple functions of the kinematic viscosity and the Prandlt number evaluated at the plate and free stream temperatures. The approximate scaling constants are used to form new approximations for the heat transfer coefficient. The new approximate coefficients are compared to traditional coefficients for four gases and six liquid flows covering the range 0.5 < Pr < 3,000 with large temperature differences.

Surface boundary-layer variability off Northern California, USA, during upwelling

Abstract A five-element mooring array is used to study surface boundary-layer transport over the Northern California shelf from May to August 2001. In this region, upwelling favorable winds increase in strength offshore, leading to a strong positive wind stress curl. We examine the cross-shelf variation in surface Ekman transport calculated from the wind stress and the actual surface boundary-layer transport estimated from oceanic observations. The two quantities are highly correlated with a regression slope near one. Both the Ekman transport and surface boundary layer transport imply curl-driven upwelling rates of about 3×10 −4 m s −1 between the 40 and 90 m isobaths (1.5 and 11.0 km from the coast, respectively) and curl-driven upwelling rates about 1.5×10 −4 m s −1 between the 90 and 130 m isobaths (11.0 and 28.4 km from the coast, respectively). Thus curl-driven upwelling extends to at least 25 km from the coast. In contrast, upwelling driven by the adjustment to the coastal boundary condition occurs primarily inshore of the 40-m isobath. The upwelling rates implied by the differentiating the 40-m transport observations with the coastal boundary condition are up to 8×10 −4 m s −1 . The estimated upwelling rates and the temperature–nitrate relationship imply curl-driven vertical nitrate flux divergences are about half of those driven by coastal boundary upwelling.