Helicity in the Ekman boundary layer

2014 ◽  
Vol 755 ◽  
pp. 654-671 ◽  
Author(s):  
Enrico Deusebio ◽  
Erik Lindborg
Keyword(s):  
Boundary Layer ◽  
Atmospheric Boundary Layer ◽  
Ekman Layer ◽  
Mean Flow ◽  
Left Handed ◽  
Ekman Boundary Layer ◽  
Taylor’S Hypothesis ◽  
Wide Range ◽  
The Mean ◽  
Turbulent Helicity

AbstractHelicity, which is defined as the scalar product of velocity and vorticity, $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}{\mathcal{H}} = {\boldsymbol {u}} \boldsymbol {\cdot }\boldsymbol{\omega}$, is an inviscidly conserved quantity in a barotropic fluid. Mean helicity is zero in flows that are parity invariant. System rotation breaks parity invariance and has therefore the potential of giving rise to non-zero mean helicity. In this paper we study the helicity dynamics in the incompressible Ekman boundary layer. Evolution equations for the mean field helicity and the mean turbulent helicity are derived and it is shown that pressure flux injects helicity at a rate $ 2 \varOmega G^2 $ over the total depth of the Ekman layer, where $ G $ is the geostrophic wind far from the wall and $ {\boldsymbol{\Omega}} = \varOmega {\boldsymbol {e}}_y $ is the rotation vector and $ {\boldsymbol {e}}_y $ is the wall-normal unit vector. Thus right-handed/left-handed helicity will be injected if $ \varOmega $ is positive/negative. We also show that in the uppermost part of the boundary layer there is a net helicity injection with opposite sign as compared with the totally integrated injection. Isotropic relations for the helicity dissipation and the helicity spectrum are derived and it is shown that it is sufficient to measure two transverse velocity components and use Taylor’s hypothesis in the mean flow direction in order to measure the isotropic helicity spectrum. We compare the theoretical predictions with a direct numerical simulation of an Ekman boundary layer and confirm that there is a preference for right-handed helicity in the lower part of the Ekman layer and left-handed helicity in the uppermost part when $ \varOmega > 0 $. In the logarithmic range, the helicity dissipation conforms to isotropic relations. On the other hand, spectra show significant departures from isotropic conditions, suggesting that the Reynolds number considered in the study is not sufficiently large for isotropy to be valid in a wide range of scales. Our analytical and numerical results strongly suggest that there is a turbulent helicity cascade of right-handed helicity in the logarithmic range of the atmospheric boundary layer when $\varOmega >0$, consistent with recent measurements by Koprov, Koprov, Ponomarev & Chkhetiani (Dokl. Phys., vol. 50, 2005, pp. 419–422). The isotropic relations which are derived may facilitate future measurements of the helicity spectrum in the atmospheric boundary layer as well as in controlled wind tunnel experiments.

Further space-time correlations of velocity in a turbulent boundary layer

1958 ◽  
Vol 3 (4) ◽  
pp. 344-356 ◽  
Author(s):  
A. J. Favre ◽  
J. J. Gaviglio ◽  
R. J. Dumas
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Large Scale ◽  
Flow Direction ◽  
Space Time ◽  
Mean Flow ◽  
Taylor’S Hypothesis ◽  
Time Correlations ◽  
The Mean ◽  
Hot Wires

This paper describes the results of further experimental investigation of the turbulent boundary layer with zero pressure gradient. Measurements of autocorrelation and of space-time double correlation have been made respectively with single hot-wires and with two hot-wires with the separation vector in any direction. Space-time correlations reach a maximum for some optimum delay. In the case of two points set on a line orthogonal to the plate, the optimum delay Ti is not zero. In the general case it is equal to the corresponding delay Ti, increased by compensating delay for translation with the mean flow. Taylor's hypothesis may be applied to the boundary layer at distances from the wall greater than 3% of the layer thickness. Space-time isocorrelation surfaces obtained with optimum delay have a large aspect ratio in the mean flow direction, even if they are relative to a point close to the wall (0·03δ); the correlations along the mean flow then retain high values on account of the large scale of the turbulence.

The flat plate boundary layer. Part 1. Numerical integration of the Orr–-Sommerfeld equation

1970 ◽  
Vol 43 (4) ◽  
pp. 801-811 ◽  
Author(s):  
R. Jordinson
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Plate Boundary ◽  
Mean Flow ◽  
Comparison With Experiment ◽  
Wide Range ◽  
The Mean ◽  
Sommerfeld Equation ◽  
Range Of Values ◽  
Flat Plate Boundary Layer

Numerical space-amplified solutions of the Orr-Sommerfeld equation for the case of a boundary layer on a flat plate have been calculated for a wide range of values of frequency and Reynolds number. The mean flow is assumed to be parallel and given by the appropriate component of the Blasius solution. The results are presented in a form suitable for comparison with experiment and are also compared with calculations of earlier authors.

scholarly journals Advances and limitations of atmospheric boundary layer observations with GPS occultation over southeast Pacific Ocean

2012 ◽  
Vol 12 (2) ◽  
pp. 903-918 ◽  
Author(s):  
F. Xie ◽  
D. L. Wu ◽  
C. O. Ao ◽  
A. J. Mannucci ◽  
E. R. Kursinski
Keyword(s):  
Boundary Layer ◽  
Pacific Ocean ◽  
Atmospheric Boundary Layer ◽  
Temperature Inversion ◽  
Lower Percentage ◽  
Trade Wind ◽  
Sampling Errors ◽  
Wide Range ◽  
The Mean ◽  
The Difference

Abstract. The typical atmospheric boundary layer (ABL) over the southeast (SE) Pacific Ocean is featured with a strong temperature inversion and a sharp moisture gradient across the ABL top. The strong moisture and temperature gradients result in a sharp refractivity gradient that can be precisely detected by the Global Positioning System (GPS) radio occultation (RO) measurements. In this paper, the Constellation Observing System for Meteorology, Ionosphere & Climate (COSMIC) GPS RO soundings, radiosondes and the high-resolution ECMWF analysis over the SE Pacific are analyzed. COSMIC RO is able to detect a wide range of ABL height variations (1–2 km) as observed from the radiosondes. However, the ECMWF analysis systematically underestimates the ABL heights. The sharp refractivity gradient at the ABL top frequently exceeds the critical refraction (e.g., −157 N-unit km−1) and becomes the so-called ducting condition, which results in a systematic RO refractivity bias (or called N-bias) inside the ABL. Simulation study based on radiosonde profiles reveals the magnitudes of the N-biases are vertical resolution dependent. The $N$-bias is also the primary cause of the systematically smaller refractivity gradient (rarely exceeding −110 N-unit km−1) at the ABL top from RO measurement. However, the N-bias seems not affect the ABL height detection. Instead, the very large RO bending angle and the sharp refractivity gradient due to ducting allow reliable detection of the ABL height from GPS RO. The seasonal mean climatology of ABL heights derived from a nine-month composite of COSMIC RO soundings over the SE Pacific reveals significant differences from the ECMWF analysis. Both show an increase of ABL height from the shallow stratocumulus near the coast to a much higher trade wind inversion further off the coast. However, COSMIC RO shows an overall deeper ABL and reveals different locations of the minimum and maximum ABL heights as compared to the ECMWF analysis. At low latitudes, despite the decreasing number of COSMIC RO soundings and the lower percentage of soundings that penetrate into the lowest 500-m above the mean-sea-level, there are small sampling errors in the mean ABL height climatology. The difference of ABL height climatology between COSMIC RO and ECMWF analysis over SE Pacific is significant and requires further studies.

scholarly journals Advances and limitations of atmospheric boundary layer observations with GPS occultation over Southeast Pacific Ocean

2011 ◽  
Vol 11 (8) ◽  
pp. 22857-22891
Author(s):  
F. Xie ◽  
D. L. Wu ◽  
C. O. Ao ◽  
A. J. Mannucci ◽  
E. R. Kursinski
Keyword(s):  
Boundary Layer ◽  
Pacific Ocean ◽  
Atmospheric Boundary Layer ◽  
Temperature Inversion ◽  
Lower Percentage ◽  
Trade Wind ◽  
Sampling Errors ◽  
Wide Range ◽  
The Mean ◽  
The Difference

Abstract. The typical atmospheric boundary layer (ABL) over the southeast (SE) Pacific Ocean is featured with a strong temperature inversion and a sharp moisture gradient across the ABL top. The strong moisture and temperature gradients result in a sharp refractivity gradient that can be precisely detected by the Global Positioning System (GPS) radio occultation (RO) measurements. In this paper, the Constellation Observing System for Meteorology, Ionosphere and Climate (COSMIC) GPS RO soundings, radiosondes and the high-resolution ECMWF analysis over the SE Pacific are analyzed. COSMIC RO is able to detect a wide range of ABL height variations (1–2 km) as observed from the radiosondes. Whereas, the ECMWF analyses systematically underestimate ABL heights. The sharp refractivity gradient at the ABL top frequently exceeds the critical refraction (e.g., −157 N-unit km−1) and becomes the so-called ducting condition, which results in systematic RO refractivity bias (or called N-bias) inside the ABL. Simulation study using refractivity profiles based on radiosondes reveals that the N-biases are significant and the magnitudes of biases are vertical resolution dependent. The N-bias is also the primary cause of the systematically smaller refractivity gradient (rarely exceeding −110 N-unit km−1) at the ABL top from RO measurement. However, the N-bias seems not affect the ABL height detection. Instead, the very sharp refractivity gradient and the large RO bending angle due to ducting allow reliable detection of ABL height from GPS RO. The seasonal mean climatology of ABL heights derived from a nine-month composite of COSMIC RO soundings over the SE Pacific reveals significant differences from the ECMWF analysis. Both show the deepening of ABL height from the shallow stratocumulus near the coast to a much higher trade wind inversion further off the coast. However, COSMIC RO shows systematically higher ABL heights overall and reveals different locations of the minimum and maximum ABL heights as compared to the ECMWF analysis. The significantly decreasing number of COSMIC RO soundings at lower latitudes along with the lower percentage of RO soundings penetrating into the lowest 500 m above mean-sea-level (a.m.s.l.), result in generally small sampling errors in the mean ABL climatology and will not affect the morphology of RO ABL height climatology. The difference of ABL height climatology between COSMIC RO and ECMWF analysis over SE Pacific is significant and requires further studies.

Fine-scale turbulent bursts in stable atmospheric boundary layer in complex terrain

2017 ◽  
Vol 833 ◽  
pp. 745-772 ◽  
Author(s):  
E. Kit ◽  
C. M. Hocut ◽  
D. Liberzon ◽  
H. J. S. Fernando
Keyword(s):  
Boundary Layer ◽  
Atmospheric Boundary Layer ◽  
Dissipation Rate ◽  
Atmospheric Modeling ◽  
Simultaneous Increase ◽  
Fine Scale ◽  
Mean Flow ◽  
Tke Dissipation Rate ◽  
The Mean ◽  
Hot Film

Turbulence in the atmospheric boundary layer (ABL) is usually measured using sonic anemometers (sonics), but coarse spatial (${\sim}10$  cm) and temporal (${\sim}32$  Hz) resolutions of sonics preclude direct measurement of fine-scale parameters such as the turbulent kinetic energy (TKE) dissipation rate $\unicode[STIX]{x1D700}$. Instead, $\unicode[STIX]{x1D700}$ is estimated using techniques based on Kolmogorov theory. Fine-scale measurements of ABL turbulence down to Kolmogorov scale were made with a sonic and hot-film anemometer dyad (a ‘combo’ probe) during the field campaigns of the Mountain Terrain Atmospheric Modeling and Observations (MATERHORN) programme. The hot-film probe was located on a gimbal within the sonic probe volume, and was automated to rotate in the horizontal plane to align with the mean flow measured by sonic. This procedure not only helped satisfy the requirement of hot-film alignment with the mean flow, but also allowed in situ calibration of hot-film probes. This paper analyses a period of nocturnal flow that was similar to a stratified parallel shear flow. The combo-probe measurements showed an interesting phenomenon – the occurrence of strong bursts, characterized by short-term increase of velocity fluctuations and simultaneous increase of TKE dissipation rate by orders of magnitude. These bursts were indicative of unusual turbulence activity at finer (${\sim}0.1$–0.4 m) scales that are not captured by sonics since the smallest scales resolved by the latter are greater than 0.6 m. With bursting present, the spectra exhibited bumps at scales intermediate to inertial and dissipation subranges, resembling a bottleneck phenomenon. Its manifestation, although unequivocally related to bursts, may not convincingly fit into the framework of previous bottleneck-effect theories that allude to either viscous effects or buoyancy effects modifying the local energy cascade via non-local effects. The origins of burst are yet to be identified. Stratified ABL with bursts exhibits non-Kolmogorov behaviour, and hence should be modelled with caution.

On laminar boundary layers in oscillatory flow

1975 ◽  
Vol 347 (1648) ◽  
pp. 99-123 ◽  
Keyword(s):  
Boundary Layer ◽  
Laminar Boundary Layer ◽  
Oscillatory Flow ◽  
Travelling Wave ◽  
Convection Velocity ◽  
Mean Flow ◽  
Mean Velocity ◽  
Freestream Velocity ◽  
Wide Range ◽  
The Mean

This paper describes an experimental and theoretical investigation of laminar boundary layer response to harmonic oscillations in velocity associated with a travelling wave imposed on an otherwise constant freestream velocity and convected in the freestream direction. An oscillatory flow wind tunnel and recording system were set up to produce and measure laminar boundary layer velocity profiles over frequencies of 2–10 H z for freestream amplitudes of up to 14 % of the mean velocity. An analysis on the lines of Lighthill’s theory but applying for any travelling wave convection velocity has been developed for both the low and high frequency cases. The experiments show that for a wide range of amplitude and frequency of oscillation the mean flow characteristics are the same as those of steady flow. This supports a major assumption of the theory which is linear in terms of the oscillating perturbations. Comparisons between theory and experiment show satisfactory agreement although the experimental results are largely for frequencies between the extreme ranges of the theories and they display features which are special to that intermediate frequency range. It is found that the boundary layer response is predominantly affected by the travelling wave convection velocity and frequency. In the experiments the freestream oscillation amplitudes increased with downstream distance but the effects of this increase are shown to be negligible.

The structure of the turbulent atmospheric boundary layer

1983 ◽  
Vol 308 (1503) ◽  
pp. 291-309 ◽  
Keyword(s):  
Boundary Layer ◽  
Atmospheric Boundary Layer ◽  
Ekman Layer ◽  
Momentum Balance ◽  
Small Scale ◽  
Mean Flow ◽  
Vertical Fluxes ◽  
Research Aircraft ◽  
Interaction Experiment ◽  
Representative Area

During the Joint Air-Sea Interaction Experiment (JASIN), mean flow and turbulent fluctuations were measured throughout the depth of the atmospheric boundary layer by shipborne surface instrumentation, multiple-instrument packages suspended from tethered balloons and research aircraft flying in low level formation. These enabled both individual localized events and representative area-average (70 km x 70 km) measurements to be investigated. The results are summarized and show that continuous small-scale turbulent mixing was generally confined to an Ekman layer a few hundred metres deep. The structure of this layer is examined in detail, particularly the momentum balance. Spectral analysis reveals two energy-containing regions, one of which, at higher wavenumbers, scales with the Ekman layer depth and carries most of the vertical fluxes. Direct coupling between the Ekman layer and the overlying atmosphere is weak and appears to be strongly dependent on cloud processes, which are intermittent and irregularly distributed on the scale of these measurements.

scholarly journals Rough-wall boundary layers: mean flow universality

2007 ◽  
Vol 585 ◽  
pp. 469-485 ◽  
Author(s):  
IAN P. CASTRO
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Roughness Element ◽  
Momentum Thickness ◽  
Mean Flow ◽  
Layer Depth ◽  
Mean Velocity ◽  
Wide Range ◽  
The Mean ◽  
Two Parameter

Mean flow profiles, skin friction, and integral parameters for boundary layers developing naturally over a wide variety of fully aerodynamically rough surfaces are presented and discussed. The momentum thickness Reynolds number Reθ extends to values in excess of 47000 and, unlike previous work, a very wide range of the ratio of roughness element height to boundary-layer depth is covered (0.03 < h/δ > 0.5). Comparisons are made with some classical formulations based on the assumption of a universal two-parameter form for the mean velocity profile, and also with other recent measurements. It is shown that appropriately re-written versions of the former can be used to collapse all the data, irrespective of the nature of the roughness, unless the surface is very rough, meaning that the typical roughness element height exceeds some 50% of the boundary-layer momentum thickness, corresponding to about $h/\delta\,{\widetilde{>}}\,0.2$.

scholarly journals Heat transfer in rotating Rayleigh–Bénard convection with rough plates

2017 ◽  
Vol 830 ◽  
Author(s):  
Pranav Joshi ◽  
Hadi Rajaei ◽  
Rudie P. J. Kunnen ◽  
Herman J. H. Clercx
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Ekman Layer ◽  
Ekman Pumping ◽  
Ekman Boundary Layer ◽  
Bénard Convection ◽  
Roughness Elements ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

This experimental study focuses on the effect of horizontal boundaries with pyramid-shaped roughness elements on the heat transfer in rotating Rayleigh–Bénard convection. It is shown that the Ekman pumping mechanism, which is responsible for the heat transfer enhancement under rotation in the case of smooth top and bottom surfaces, is unaffected by the roughness as long as the Ekman layer thickness $\unicode[STIX]{x1D6FF}_{E}$ is significantly larger than the roughness height $k$. As the rotation rate increases, and thus $\unicode[STIX]{x1D6FF}_{E}$ decreases, the roughness elements penetrate the radially inward flow in the interior of the Ekman boundary layer that feeds the columnar Ekman vortices. This perturbation generates additional thermal disturbances which are found to increase the heat transfer efficiency even further. However, when $\unicode[STIX]{x1D6FF}_{E}\approx k$, the Ekman boundary layer is strongly perturbed by the roughness elements and the Ekman pumping mechanism is suppressed. The results suggest that the Ekman pumping is re-established for $\unicode[STIX]{x1D6FF}_{E}\ll k$ as the faces of the pyramidal roughness elements then act locally as a sloping boundary on which an Ekman layer can be formed.

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&gt;&gt;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.

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