The Effect of the Oceanic Boundary Layer on the Mean Drift of Pack Ice: Application of a Simple Model

1979 ◽  
Vol 9 (2) ◽  
pp. 388-400 ◽  
Author(s):  
Miles G. McPhee
Keyword(s):  
Boundary Layer ◽  
Simple Model ◽  
Pack Ice ◽  
The Mean ◽  
Oceanic Boundary Layer

scholarly journals Large-Eddy Simulation of Wind Turbine Flows: A New Evaluation of Actuator Disk Models

Energies ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 3745
Author(s):  
Tristan Revaz ◽  
Fernando Porté-Agel
Keyword(s):  
Boundary Layer ◽  
Simple Model ◽  
Wind Turbine ◽  
Wake Flow ◽  
Test Case ◽  
Flow Solver ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Layer Flow ◽  
Advanced Model

Large-eddy simulation (LES) with actuator models has become the state-of-the-art numerical tool to study the complex interaction between the atmospheric boundary layer (ABL) and wind turbines. In this paper, a new evaluation of actuator disk models (ADMs) for LES of wind turbine flows is presented. Several details of the implementation of such models are evaluated based on a test case studied experimentally. In contrast to other test cases used in previous similar studies, the present test case consists of a wind turbine immersed in a realistic turbulent boundary-layer flow, for which accurate data for the turbine, the flow, the thrust and the power are available. It is found that the projection of the forces generated by the turbine into the flow solver grid is crucial for rotor predictions, especially for the power, and less important for the wake flow prediction. In this context, the projection of the forces into the flow solver grid should be as accurate as possible, in order to conserve the consistency between the computed axial velocity and the projected axial force. Also, the projection of the force is found to be much more important in the rotor plane directions than in the streamwise direction. It is found that for the case of a wind turbine immersed in a realistic turbulent boundary-layer flow, the potential spurious numerical oscillations originating from sharp force projections are not harmful to the results. By comparing an advanced model which computes the non-uniform distribution of the turbine forces over the rotor with a simple model which assumes uniform effects of the turbine forces, it is found that both can lead to accurate results for the far wake flow and the thrust and power predictions. However, the comparison shows that the advanced model leads to better results for the near wake flow. In addition, it is found that the simple model overestimates the rotor velocity prediction in comparison to the advanced model. These elements are explained by the lack of local feedback between the axial velocity and the axial force in the simple model. By comparing simulations with and without including the effects of the nacelle and tower, it is found that the consideration of the nacelle and tower is relatively important both for the near wake and the power prediction, due to the shadow effects. The grid resolution is not found to be critical once a reasonable resolution is used, i.e. in the order of 10 grid points along each direction across the rotor. The comparison with the experimental data shows that an accurate prediction of the flow, thrust, and power is possible with a very reasonable computational cost. Overall, the results give important guidelines for the implementation of ADMs for LES.

Data Analysis Methods for Stereo PIV of a High Aspect Ratio Flexible Cylinder

2007 ◽  
Author(s):  
D. Furey ◽  
P. Atsavapranee ◽  
K. Cipolla
Keyword(s):  
Boundary Layer ◽  
Data Analysis ◽  
Aspect Ratio ◽  
High Aspect Ratio ◽  
Particle Image Velocimetry Data ◽  
Flow Fields ◽  
Mean Flow ◽  
Boundary Flow ◽  
The Mean ◽  
Cylinder Flow

Stereo Particle Image velocimetry data was collected over high aspect ratio flexible cylinders (L/a = 1.5 to 3 × 105) to evaluate the axial development of the turbulent boundary layer where the boundary layer thickness becomes significantly larger than the cylinder diameter (δ/a>>1). The flexible cylinders are approximately neutrally buoyant and have an initial length of 152 m and radii of 0.45 mm and 1.25 mm. The cylinders were towed at speeds ranging from 3.8 to 15.4 m/sec in the David Taylor Model Basin. The analysis of the SPIV data required a several step procedure to evaluate the cylinder boundary flow. First, the characterization of the flow field from the towing strut is required. This evaluation provides the residual mean velocities and turbulence levels caused by the towing hardware at each speed and axial location. These values, called tare values, are necessary for comparing to the cylinder flow results. Second, the cylinder flow fields are averaged together and the averaged tare fields are subtracted out to remove strut-induced ambient flow effects. Prior to averaging, the cylinder flow fields are shifted to collocate the cylinder within the field. Since the boundary layer develops slowly, all planes of data occurring within each 10 meter increment of the cylinder length are averaged together to produce the mean boundary layer flow. Corresponding fields from multiple runs executed using the same experimental parameters are also averaged. This flow is analyzed to evaluate the level of axisymmetry in the data and determine if small changes in cylinder angle affect the mean flow development. With axisymmetry verified, the boundary flow is further averaged azimuthally around the cylinder to produce mean boundary layer profiles. Finally, the fluctuating velocity levels are evaluated for the flow with the cylinder and compared to the fluctuating velocity levels in the tare data. This paper will first discuss the data analysis techniques for the tare data and the averaging methods implemented. Second, the data analysis considerations will be presented for the cylinder data and the averaging and cylinder tracking techniques. These results are used to extract relevant boundary layer parameters including δ, δ* and θ. Combining these results with wall shear and momentum thickness values extracted from averaged cylinder drag data, the boundary layer can be well characterized.

scholarly journals Diurnal Coupling in the Tropical Oceans of CCSM3

2006 ◽  
Vol 19 (11) ◽  
pp. 2347-2365 ◽  
Author(s):  
Gokhan Danabasoglu ◽  
William G. Large ◽  
Joseph J. Tribbia ◽  
Peter R. Gent ◽  
Bruce P. Briegleb ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Diurnal Cycle ◽  
Upper Ocean ◽  
Solar Forcing ◽  
Layer Depth ◽  
Climate System Model ◽  
Tropical Oceans ◽  
Ocean Coupling ◽  
Coupling Interval ◽  
The Mean

Abstract New features that may affect the behavior of the upper ocean in the Community Climate System Model version 3 (CCSM3) are described. In particular, the addition of an idealized diurnal cycle of solar forcing where the daily mean solar radiation received in each daily coupling interval is distributed over 12 daylight hours is evaluated. The motivation for this simple diurnal cycle is to improve the behavior of the upper ocean, relative to the constant forcing over each day of previous CCSM versions. Both 1- and 3-h coupling intervals are also considered as possible alternatives that explicitly resolve the diurnal cycle of solar forcing. The most prominent and robust effects of all these diurnal cycles are found in the tropical oceans, especially in the Pacific. Here, the mean equatorial sea surface temperature (SST) is warmed by as much as 1°C, in better agreement with observations, and the mean boundary layer depth is reduced. Simple rectification of the diurnal cycle explains about half of the shallowing, but less than 0.1°C of the warming. The atmospheric response to prescribed warm SST anomalies of about 1°C displays a very different heat flux signature. The implication, yet to be verified, is that large-scale air–sea coupling is a prime mechanism for amplifying the rectified, daily averaged SST signals seen by the atmosphere. Although the use of upper-layer temperature for SST in CCSM3 underestimates the diurnal cycle of SST, many of the essential characteristics of diurnal cycling within the equatorial ocean are reproduced, including boundary layer depth, currents, and the parameterized vertical heat and momentum fluxes associated with deep-cycle turbulence. The conclusion is that the implementation of an idealized diurnal cycle of solar forcing may make more frequent ocean coupling and its computational complications unnecessary as improvements to the air–sea coupling in CCSM3 continue. A caveat here is that more frequent ocean coupling tends to reduce the long-term cooling trends typical of CCSM3 by heating already too warm ocean depths, but longer integrations are needed to determine robust features. A clear result is that the absence of diurnal solar forcing of the ocean has several undesirable consequences in CCSM3, including too large ENSO variability, much too cold Pacific equatorial SST, and no deep-cycle turbulence.

Skin friction and surface temperature of an insulated flat plate fixed in a fluctuating stream

1971 ◽  
Vol 46 (1) ◽  
pp. 165-175 ◽  
Author(s):  
Hiroshi Ishigaki
Keyword(s):  
Boundary Layer ◽  
Surface Temperature ◽  
Flat Plate ◽  
Skin Friction ◽  
High Frequency ◽  
Energy Equation ◽  
Oscillation Amplitude ◽  
Flow Oscillation ◽  
Velocity Amplitude ◽  
The Mean

The time-mean skin friction of the laminar boundary layer on a flat plate which is fixed at zero incidence in a fluctuating stream is investigated analytically. Flow oscillation amplitude outside the boundary layer is assumed constant along the surface. First, the small velocity-amplitude case is treated, and approximate formulae are obtained in the extreme cases when the frequency is low and high. Next, the finite velocity-amplitude case is treated under the condition of high frequency, and it is found that the formula obtained for the small-amplitude and high-frequency case is also valid. These results show that the increase of the mean skin friction reduces with frequency and is ultimately inversely proportional to the square of frequency.The corresponding energy equation is also studied simultaneously under the condition of zero heat transfer between the fluid and the surface. It is confirmed that the time-mean surface temperature increases with frequency and tends to be proportional to the square root of frequency. Moreover, it is shown that the timemean recovery factor can be several times as large as that without flow oscillation.

scholarly journals Large-Eddy Simulations of a Drizzling, Stratocumulus-Topped Marine Boundary Layer

2009 ◽  
Vol 137 (3) ◽  
pp. 1083-1110 ◽  
Author(s):  
Andrew S. Ackerman ◽  
Margreet C. vanZanten ◽  
Bjorn Stevens ◽  
Verica Savic-Jovcic ◽  
Christopher S. Bretherton ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Marine Boundary Layer ◽  
Cloud Water ◽  
Large Eddy Simulations ◽  
Cloud Base ◽  
Entrainment Rate ◽  
Liquid Water Path ◽  
Average Maximum ◽  
Large Eddy ◽  
The Mean

Abstract Cloud water sedimentation and drizzle in a stratocumulus-topped boundary layer are the focus of an intercomparison of large-eddy simulations. The context is an idealized case study of nocturnal stratocumulus under a dry inversion, with embedded pockets of heavily drizzling open cellular convection. Results from 11 groups are used. Two models resolve the size distributions of cloud particles, and the others parameterize cloud water sedimentation and drizzle. For the ensemble of simulations with drizzle and cloud water sedimentation, the mean liquid water path (LWP) is remarkably steady and consistent with the measurements, the mean entrainment rate is at the low end of the measured range, and the ensemble-average maximum vertical wind variance is roughly half that measured. On average, precipitation at the surface and at cloud base is smaller, and the rate of precipitation evaporation greater, than measured. Including drizzle in the simulations reduces convective intensity, increases boundary layer stratification, and decreases LWP for nearly all models. Including cloud water sedimentation substantially decreases entrainment, decreases convective intensity, and increases LWP for most models. In nearly all cases, LWP responds more strongly to cloud water sedimentation than to drizzle. The omission of cloud water sedimentation in simulations is strongly discouraged, regardless of whether or not precipitation is present below cloud base.

The structure of a highly decelerated axisymmetric turbulent boundary layer

2021 ◽  
Vol 929 ◽  
Author(s):  
N. Agastya Balantrapu ◽  
Christopher Hickling ◽  
W. Nathan Alexander ◽  
William Devenport
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Shear Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Large Scale ◽  
Convection Velocity ◽  
Mean Flow ◽  
Mean Velocity ◽  
The Mean

Experiments were performed over a body of revolution at a length-based Reynolds number of 1.9 million. While the lateral curvature parameters are moderate ( $\delta /r_s < 2, r_s^+>500$ , where $\delta$ is the boundary layer thickness and r s is the radius of curvature), the pressure gradient is increasingly adverse ( $\beta _{C} \in [5 \text {--} 18]$ where $\beta_{C}$ is Clauser’s pressure gradient parameter), representative of vehicle-relevant conditions. The mean flow in the outer regions of this fully attached boundary layer displays some properties of a free-shear layer, with the mean-velocity and turbulence intensity profiles attaining self-similarity with the ‘embedded shear layer’ scaling (Schatzman & Thomas, J. Fluid Mech., vol. 815, 2017, pp. 592–642). Spectral analysis of the streamwise turbulence revealed that, as the mean flow decelerates, the large-scale motions energize across the boundary layer, growing proportionally with the boundary layer thickness. When scaled with the shear layer parameters, the distribution of the energy in the low-frequency region is approximately self-similar, emphasizing the role of the embedded shear layer in the large-scale motions. The correlation structure of the boundary layer is discussed at length to supply information towards the development of turbulence and aeroacoustic models. One major finding is that the estimation of integral turbulence length scales from single-point measurements, via Taylor's hypothesis, requires significant corrections to the convection velocity in the inner 50 % of the boundary layer. The apparent convection velocity (estimated from the ratio of integral length scale to the time scale), is approximately 40 % greater than the local mean velocity, suggesting the turbulence is convected much faster than previously thought. Closer to the wall even higher corrections are required.

scholarly journals Diurnal variability of the atmospheric boundary layer height over a tropical station in the Indian monsoon region

2017 ◽  
Vol 17 (1) ◽  
pp. 531-549 ◽  
Author(s):  
Sanjay Kumar Mehta ◽  
Madineni Venkat Ratnam ◽  
Sukumarapillai V. Sunilkumar ◽  
Daggumati Narayana Rao ◽  
Boddapaty V. Krishna Murthy
Keyword(s):  
Boundary Layer ◽  
Atmospheric Boundary Layer ◽  
Diurnal Variation ◽  
Indian Monsoon ◽  
Winter Season ◽  
Monsoon Region ◽  
Diurnal Variability ◽  
The Mean ◽  
Indian Monsoon Region ◽  
Tropical Station

Abstract. The diurnal variation of atmospheric boundary layer (ABL) height is studied using high-resolution radiosonde observations available at 3 h intervals for 3 days continuously from 34 intensive campaigns conducted during the period December 2010–March 2014 over a tropical station Gadanki (13.5° N, 79.2° E; 375 m), in the Indian monsoon region. The heights of the ABL during the different stages of its diurnal evolution, namely, the convective boundary layer (CBL), the stable boundary layer (SBL), and the residual layer (RL) are obtained to study the diurnal variabilities. A clear diurnal variation is observed in 9 campaigns out of the 34 campaigns. In 7 campaigns the SBL did not form in the entire day and in the remaining 18 campaigns the SBL formed intermittently. The SBL forms for 33–55 % of the time during nighttime and 9 and 25 % during the evening and morning hours, respectively. The mean SBL height is within 0.3 km above the surface which increases slightly just after midnight (02:00 IST) and remains almost constant until the morning. The mean CBL height is within 3.0 km above the surface, which generally increases from morning to evening. The mean RL height is within 2 km above the surface which generally decreases slowly as the night progresses. The diurnal variation of the ABL height over the Indian region is stronger during the pre-monsoon and weaker during winter season. The CBL is higher during the summer monsoon and lower during the winter season while the RL is higher during the winter season and lower during the summer season. During all the seasons, the ABL height peaks during the afternoon (∼ 14:00 IST) and remains elevated until evening (∼ 17:00 IST). The ABL suddenly collapses at 20:00 IST and increases slightly in the night. Interestingly, it is found that the low level clouds have an effect on the ABL height variability, but the deep convective clouds do not. The lifting condensation level (LCL) is generally found to occur below the ABL for the majority of the database and they are randomly related.

A theory of turbulence in stratified fluids

1970 ◽  
Vol 42 (2) ◽  
pp. 349-365 ◽  
Author(s):  
Robert R. Long
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Density Profile ◽  
Richardson Number ◽  
Mixed Volume ◽  
Volume Of Fluid ◽  
Velocity Shear ◽  
Mean Velocity ◽  
Large Wave ◽  
The Mean

An effort is made to understand turbulence in fluid systems like the oceans and atmosphere in which the Richardson number is generally large. Toward this end, a theory is developed for turbulent flow over a flat plate which is moved and cooled in such a way as to produce constant vertical fluxes of momentum and heat. The theory indicates that in a co-ordinate system fixed in the plate the mean velocity increases linearly with heightzabove a turbulent boundary layer and the mean density decreases asz3, so that the Richardson number is large far from the plate. Near the plate, the results reduce to those of Monin & Obukhov.Thecurvatureof the density profile is essential in the formulation of the theory. When the curvature is negative, a volume of fluid, thoroughly mixed by turbulence, will tend to flatten out at a new level well above the original centre of mass, thereby transporting heat downward. When the curvature is positive a mixed volume of fluid will tend to fall a similar distance, again transporting heat downward. A well-mixed volume of fluid will also tend to rise when the density profile is linear, but this rise is negligible on the basis of the Boussinesq approximation. The interchange of fluid of different, mean horizontal speeds in the formation of the turbulent patch transfers momentum. As the mixing in the patch destroys the mean velocity shear locally, kinetic energy is transferred from mean motion to disturbed motion. The turbulence can arise in spite of the high Richardson number because the precise variations of mean density and mean velocity mentioned above permit wave energy to propagate from the turbulent boundary layer to the whole region above the plate. At the levels of reflexion, where the amplitudes become large, wave-breaking and turbulence will tend to develop.The relationship between the curvature of the density profile and the transfer of heat suggests that the density gradient near the level of a point of inflexion of the density curve (in general cases of stratified, shearing flow) will increase locally as time goes on. There will also be a tendency to increase the shear through the action of local wave stresses. If this results in a progressive reduction in Richardson number, an ultimate outbreak of Kelvin–Helmholtz instability will occur. The resulting sporadic turbulence will transfer heat (and momentum) through the level of the inflexion point. This mechanism for the appearance of regions of low Richardson number is offered as a possible explanation for the formation of the surfaces of strong density and velocity differences observed in the oceans and atmosphere, and for the turbulence that appears on these surfaces.

Viscous boundary layers in reversing flow

1976 ◽  
Vol 74 (1) ◽  
pp. 59-79 ◽  
Author(s):  
T. J. Pedley
Keyword(s):  
Boundary Layer ◽  
Shear Rate ◽  
Leading Edge ◽  
Wall Shear Rate ◽  
Viscous Boundary Layer ◽  
Large Molecules ◽  
Displacement Thickness ◽  
The Mean ◽  
Wall Shear ◽  
Viscous Boundary

The viscous boundary layer on a finite flat plate in a stream which reverses its direction once (at t = 0) is analysed using an improved version of the approximate method described earlier (Pedley 1975). Long before reversal (t < −t1), the flow at a point on the plate will be quasi-steady; long after reversal (t > t2), the flow will again be quasi-steady, but with the leading edge at the other end of the plate. In between (−t1 < t < t2) the flow is governed approximately by the diffusion equation, and we choose a simple solution of that equation which ensures that the displacement thickness of the boundary layer remains constant at t = −t1. The results of the theory, in the form of the wall shear rate at a point as a function of time, are given both for a uniformly decelerating stream, and for a sinusoidally oscillating stream which reverses its direction twice every cycle. The theory is further modified to cover streams which do not reverse, but for which the quasi-steady solution breaks down because the velocity becomes very small. The analysis is also applied to predict the wall shear rate at the entrance to a straight pipe when the core velocity varies with time as in a dog's aorta. The results show positive and negative peak values of shear very much larger than the mean. They suggest that, if wall shear is implicated in the generation of atherosclerosis because it alters the permeability of the wall to large molecules, then an appropriate index of wall shear at a point is more likely to be the r.m.s. value than the mean.

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