Vertical Mean Flow Research Articles

Vertical flow structures on a vegetated immobile bed under wave-current conditions: Laboratory experiments

Natural revegetation alters local hydrodynamic conditions in coastal lagoons. To investigate vertical flow structures in revegetated lagoons, a series of flume experiments are implemented on an immobile bed with Phragmites australis by a certain staggered configuration. Six incident wave heights and five inflow discharges are considered. The experimental results demonstrate that wave dominates turbulent kinetic energy (TKE) distributions under wave-current conditions. Vegetation morphology plays an important role in wave-current-vegetation interactions, which regulates TKE distributions by diminishing wave effects within 70% of water depth especially (0.3 < z/h < 1). The increasing inflow discharge has positive effects on diminishment of wave effects, while the reduction of mean streamwise flow velocity is stable under the present vegetation configuration. Moreover, the practical values of vertical mean flow velocity can be obtained from the empirical equation, which includes wave effects by a quadratic polynomial relationship between the ratio of experimental values to theorical values (U/Up) and the relative wave height H0/h. Furthermore, two relationships are established between the reduction of mean streamwise flow velocity r and z/h, involving a logarithmical relationship in the lower layer (0 < z/h < 0.3), and a cubic polynomial relationship in the upper layer (0.3 < z/h < 0.7).

The Simulation of Vortex Structures Induced by Different Local Vibrations at the Wall in a Flat-Plate Laminar Boundary Layer

The compact finite difference scheme on non-uniform meshes and the Fourier spectral hybrid method are used to directly simulate the evolution of vortex structures in a laminar boundary layer over a flat plate. To this end, two initial local vibration disturbances, namely, the positive–negative and the negative–positive models, at the wall were adopted. The numerical results show that the maximum amplitudes of vortex structures experience a process of linear growth and nonlinear rapid growth. The vertical disturbance velocity and mean flow shear and the derivative term of the stream-wise disturbance velocity and the span-wise disturbance velocity, are important factors for vortex structure development; the high- and low-speed stripe and the stream-wise vortex are consistent with structures seen in full turbulence. The maximum amplitude of the negative–positive model grows more quickly than that of the negative–positive model, and the detailed vortex structures are different for the two models. The mean flow profiles both become plump, which leads to the instability of the laminar boundary layer. The way in which the disturbance is generated with different local vibrations influences the dynamics of vortex structures in a laminar boundary layer.

Formulation of Three-Dimensional Quasi-Residual Mean Flow Balanced with Diabatic Heating Rate and Potential Vorticity Flux

Abstract Three-dimensional (3D) quasi-residual mean flow is derived to diagnose 3D dynamical material transport associated with stationary planetary waves. The 3D quasi-residual mean vertical flow does not include the vertical flow due to tilting of the potential temperature caused by stationary waves, which is apparent but not seen in the mass-weighted isentropic mean state. Thus, the quasi-residual mean vertical flow is balanced with the term of diabatic heating rate. The 3D quasi-residual mean horizontal flow is balanced with the sum of the forcing due to transient wave activity flux divergence and the forcing associated with fluctuation of the potential vorticity due to stationary waves (defined as the effective Coriolis forcing). The zonal mean of the effective Coriolis forcing corresponds to the divergence of stationary wave activity flux. Thus, the zonal mean of derived 3D quasi-residual mean flow is exactly equal to the traditional residual mean flow. To demonstrate the usefulness of this quasi-residual mean flow, we analyze material transport of atmospheric sulfur hexafluoride (SF6) by using an atmospheric chemistry transport model. Comparison between the derived 3D quasi-residual mean flow and traditional residual mean flow shows that the zonal mean of advection of SF6 associated with the 3D quasi-residual mean flow derived is almost equal to that of the traditional residual mean flow. Next, it is confirmed that the horizontal structure of advection of SF6 associated with the 3D quasi-residual mean flow is balanced with the transport because of the nonlinear, nonconservative effects of disturbances. This relation is similar to the results for traditional residual mean flow in the zonal-mean state.

Wave-driven flow induced by suspended and submerged canopies

Coastal canopies deliver a wide range of ecosystem services through the flow and transport processes within and around the canopies. This study presents a numerical investigation on the effect of suspended/floating canopies on wave-driven current around canopy using a non-hydrostatic model SWASH. The model results by SWASH for a submerged canopy are first validated with experiment measurements and compared with predictions from two Volume-of-Fluid (VOF) based free surface flow models. Then the effects of suspended/floating canopies on wave attenuation and vertical mean flow structures are examined using SWASH. The model results show that a strong shoreward wave-driven current is generated at the top of a suspended canopy in the same direction as the wave, same as that at the top of a benthic canopy. In contrast, a seaward mean current is generated at the bottom of a suspended canopy in the opposite direction to the wave. The predicted particle trajectories indicate that due to flow attenuation within canopy, at the bottom of the canopy, the fluid particles travel faster at the bottom half of their orbits outside the canopy in the opposite direction of wave propagation than at the top half of their orbits within the canopy in the direction of wave propagation. This leads to open particle orbits and a time‐averaged mean current in the opposite direction of wave propagation. The present study is the first attempt that reveals and examines this physical phenomena that would play an important role in particulate transport and exchange across the suspended canopies. The maximum magnitudes of wave induced currents at the top and bottom of canopy are consistent with a recent empirical formula extracted from the observations for submerged canopy. The predicted wave decay agrees well with a three-layer analytical solution for suspended and submerged canopy and indicates that the canopy vertical location plays an important role in wave attenuation and canopy induced currents. The spatial distribution patterns of the wave-driven current clearly support the notion that the current strength generated at the canopy interface is a function of horizontal oscillatory velocity, vertical orbital excursion and canopy density. The spanwise extent of the mean current is examined by a 3-D simulation where the canopy occupies only half the flume width. Numerical results show that the wave-driven current is mainly confined to the part of flume occupied by the canopy and that the current strength is soon attenuated to zero towards the other part of flume through a mixing-layer-like transition region at the canopy side interface.

An analytical study of the flame dynamics of a transversely forced asymmetric two-dimensional Bunsen flame

Combustion instabilities in annular combustors are of great interest because of their industrial relevance. Azimuthal acoustic modes, which involve transverse acoustic forcing to flames, have become a key process related to annular combustor instabilities. Transverse mean flow may be a factor that affects azimuthal oscillations. This paper provides an analytical model for a transversely forced two-dimensional Bunsen flame under transverse mean flow. The model is established using a low-amplitude perturbation assumption applied to a G-equation formulation. Forced flame displacement and flame transfer functions (FTFs) are calculated. The results are verified based on numerical solutions of the G-equation. Effects of frequency, transverse mean flow velocity and vertical mean flow velocity on the FTFs are discussed. The symmetric flame without transverse mean flow has a vanishing response to transverse acoustic forcing, while asymmetric flames, which are formed with transverse mean flow, have a bandpass response to transverse forcing. The response at very low and high forcing frequencies is small, with higher transfer function gains only in a certain frequency range. This bandpass response, which is inherently linked to the asymmetry of the flame, is an important factor to account for when considering the flame dynamics related to transverse acoustic effects.

A Kinematic Description of the Key Flow Characteristics in an Array of Finite-Height Rotating Cylinders

Experimental data are presented for large arrays of rotating, finite-height cylinders to study the dependence of the three-dimensional (3D) mean flows on the geometric and rotational configurations of the array. Two geometric configurations, each with two rotational configurations, were examined at a nominal Reynolds number of 600 and nominal tip-speed ratios of 0, 2, and 4. It was found that the rotation of the cylinders drives the formation of streamwise and transverse flow patterns between cylinders and that net time–space averaged transverse and vertical flows exist within the developed flow region of the array. This net vertical mean flow provides an additional mechanism for the exchange of momentum between the flow within the array and the flow above it, independent from the turbulent exchange mechanisms which are also observed to increase by almost a factor of three in a rotating array. As an array of rotating cylinders may provide insight into the flow kinematics of an array of vertical axis wind turbines (VAWTs), this planform momentum flux (both mean and turbulent) is of particular interest, as it has the potential to increase the energy resource available to turbines far downstream of the leading edge of the array. In the present study, the streamwise momentum flux into the array could be increased for the rotating-element arrays by up to a factor of 5.7 compared to the stationary-element arrays, while the streamwise flow frontally averaged over the elements could be increased by up to a factor of four in the rotating-element arrays compared to stationary-element arrays.

Mean Wind Flow Field around Idealized Block Arrays with Various Aspect Ratios

This study investigates the characteristic of spatially averaged mean velocity profile and the flow pattern within urban canopy layer especially in pedestrian level using CFD technique. Large eddies simulation (LES) was used to perform a series of simulation of the flow around block arrays with staggered arrangement under various conditions of aspect ratio, αp (roof-to-frontal area ratio) from 0.33 to 3.0. The spatially-average profiles of both mean wind speed and streamwise velocity over various block arrays were compared with each other. The analysis clarified the following two facts. 1) The vertical mean flow structure inside the canyon change due to change a plan area ratio and block aspect ratio. 2) The horizontal mean flow structure around the block change if pedestrian level change form z = 0.05h to z = 0.25h. This can be translated to the effect of high-rise building to the flow around the building.

Recharge assessment by means of vertical temperature profiles: analysis of possible influences

Temperature profiles (temperature as function of depth) can be used to derive vertical flow velocities or recharge rates. In many cases, solutions to the one-dimensional (1-D) heat transport equation are used, considering steady-state boundary conditions. Factors which can influence the derivation of the mean vertical flow velocity are studied here. Therefore, an explicit finite-difference approximation to the 1-D heat transport equation coupled with an inverse scheme was used to interpret temperature profiles. Measurement error (larger than 0.05°C) can result in important deviation of the derived mean flow velocity. Variation of vertical flow velocity as a function of time leads to asymmetric temperature envelopes. Yearly variation in vertical flow velocities, or temperature variations of the recharge water, also results in asymmetric temperature envelopes. Interpretation of these asymmetric envelopes leads to important differences between derived and actual mean vertical flow velocities. CitationVandenbohede, A. & Lebbe, L. (2010) Recharge assessment by means of vertical temperature profiles: analysis of possible influences. Hydrol. Sci. J. 55(5), 792–804.

Ventilation strategy and air change rates in idealized high-rise compact urban areas

We regarded high-rise compact urban areas as obstacles and pathways to the approaching wind. Flow rates across street openings, open street roofs and along street networks contribute to air exchange between urban airspaces and their external surroundings. We numerically studied the ventilation and air change rates in some aligned square building arrays (the building width B = 30 mm, building heights H = 2 B or 2.67 B) with building area densities of λ p = 0.25 or 0.4 (i.e. the ratio between the plan area of buildings viewed from above and the total underlying surface area). The main and secondary streets are parallel and perpendicular to the approaching wind respectively. Urban parameters are found important to the ventilation. The taller buildings ( H = 2.67 B) may capture larger inflow rates across windward street openings than the lower ( H = 2 B). Wider streets and smaller building area density provide more wind pathways and obtain larger flow rates along street networks. Meanwhile, the flow rates along the street may quickly decrease due to strong resistances produced by high-rise buildings, so the total street length should be limited, otherwise the ventilation in downstream regions is not good. The secondary streets always experience worse ventilation than the main streets. A building height variation benefits ventilation in the secondary streets by enhancing vertical mean flow rates across street roofs in contrast to those with uniform heights. If the base of all buildings is open from z = 0 to 0.33 B, the ventilation in both the main and secondary streets becomes better.

Analysis on the interaction between turbulence and secondary circulation of the surface layer at Jinta oasis in summer

The kinetic energy variations of mean flow and turbulence at three levels in the surface layer were calculated by using eddy covariance data from observations at Jinta oasis in 2005 summer. It is found that when the mean horizontal flow was stronger, the turbulent kinetic energy was increased at all levels, as well as the downward mean wind at the middle level. Since the mean vertical flow on the top and bottom were both negligible at that time, there was a secondary circulation with convergence in the upper half and divergence in the lower half of the column. After consideration of energy conversion, it was found that the interaction between turbulence and the secondary circulation caused the intensification of each other. The interaction reflected positive feedback between turbulence and the vertical shear of the mean flow. Turbulent sensible and latent heat flux anomaly were also analyzed. The results show that in both daytime and at night, when the surface layer turbulence was intensified as a result of strengthened mean flow, the sensible heat flux was decreased while the latent heat flux was increased. Both anomalous fluxes contributed to the cold island effect and the moisture island effect of the oasis.

The dynamics of two interacting compositional plumes

The dynamics of two compositionally buoyant columns of fluid rising in an infinite less buoyant fluid is studied. The fluid within and outside the columns is thermally stably stratified and has a kinematic viscosity, ν, and a thermal diffusivity, κ. The mean vertical flow and the associated temperature profiles depending on the horizontal coordinate normal to the surfaces of the columns are obtained and the associated buoyancy, heat and material fluxes are discussed. The stability of the mean state to infinitesimal disturbances is governed by the five dimensionless parameters: the number R (=UL/ν, where U and L are characteristic velocity and length, respectively) which measures the strength of the compositional buoyancy, the dimensionless measures of the thickness of the two plumes and the distance between them, respectively, and Γ representing the ratio of the strengths of the two plumes. The stability is examined for small values of R. The preferred mode of instability is studied in the space (, Γ). When a single plume is present (and x 1, d, Γ = 0), it is already known that the perturbations are neutral at O(R 0) and linearly unstable at O(R 1) for all values of x 0 and Prandtl number, σ(=ν/κ). It is shown here that at , the presence of a second interacting plume has the significant effect that the system of two plumes becomes unstable for a certain range of the parameters while it remains neutrally stable for the others. In contrast with the instability of the single plume, the instability of the two interacting plumes does not depend, at the level, on the Prandtl number of the fluid. However, the neutrally stable two plumes might suffer instability at and that instability may depend on the Prandtl number. The instability is found to be driven by the gradients of all of the concentration of light material, the flow and temperature of the basic state. The presence of the second plume destroys the definite parity of the perturbations' solution and this can lead to non-zero total helicity.

Air-sea CO2 flux by eddy covariance technique in the equatorial Indian Ocean

Direct measurements of the air-sea CO2 flux by the eddy covariance technique were carried out in the equatorial Indian Ocean. The turbulent flux observation system was installed at the top of the foremast of the R/V MIRAI, thus minimizing dynamical and thermal effects of the ship body. During the turbulent flux runs around the two stations, the vessel was steered into the wind at constant speed. The power spectra of the temperature or water vapor density fluctuations followed the Kolmogorov −5/3 power law, although that of the CO2 density fluctuation showed white noise in the high frequency range. However, the cospectrum of the vertical wind velocity and CO2 density was well matched with those of the vertical velocity and temperature or water vapor density in this frequency range, and the CO2 white noise did not influence the CO2 flux. The raw CO2 fluxes due to the turbulent transport showed a sink from the air to the ocean, and had almost the same value as the source CO2 fluxes due to the mean vertical flow, corrected by the sensible and latent heat fluxes (called the Webb correction). The total CO2 fluxes including the Webb correction terms showed a source from the ocean to the air, and were larger than the bulk CO2 fluxes estimated using the gas transfer velocity by mass balance techniques.

The influence of fuel injection and heat release on bulk flow structures in a direct-injection, swirl-supported diesel engine

Particle image velocimetry is applied to measure the vertical (r–z) plane flow structures in a light-duty direct-injection diesel engine with a realistic piston geometry. The measurements are corrected for optical distortions due to the curved piston bowl walls and the cylindrical liner. Mean flow fields are presented and contrasted for operation both with and without fuel injection and combustion. For operation with combustion, the two-dimensional divergence of the measured mean velocity fields is employed as a qualitative indicator of the locations of mean heat release. In agreement with numerical simulations, dual-vortex, vertical plane mean flow structures that may enhance mixing rates are formed approximately mid-way through the combustion event. Late in the cycle a toroidal vortex forms outside the bowl mouth. Imaging studies suggest that soot and partially oxidized fuel trapped within this vortex are slow to mix with surrounding fluid; moreover, the vortex impedes mixing of fluid exiting the bowl with air within the squish volume.

Associations between the Global Energy Cycle and Regional Rainfall in South Africa and Southwest Australia

Abstract Large-scale atmospheric processes in the Southern Hemisphere are examined on both seasonal and daily time scales in order to seek associations between these and regional rainfall variability in the summer rainfall areas of South Africa and the winter rainfall regions of South Africa and Western Australia. The basis of the analysis is atmospheric energetics of the vertical mean and shear flow. Self-organizing maps (SOMs) are then used to find archetypical states of the daily flow and to assess how the frequency characteristics of these states change between wet and dry years. The results show clear associations between the frequency of circulation archetypes on a hemispheric scale and regional rainfall for both summer and winter rainfall areas. Substantial changes in archetype frequencies between wet and dry years are found with as much as a doubling or halving of the number of days in which certain archetypes occur within a season. The physical reasons for observed teleconnections are shown by way of the atmospheric energy cycle, providing a deeper understanding of climate variability that may benefit extended-range prediction.

Properties of turbulent air avalanches in a vertical pit

Temperature and humidity measurements have been performed since 2000 in the atmosphere of the 20-m deep vertical access pit of an underground quarry. Air avalanches take place in the pit when the outside air density is larger than the equilibrium air density of the quarry. These avalanches are associated with a mean linear vertical temperature profile, and with broad-band, spatially organized and coherent temperature fluctuations. Temperature distributions are nearly Gaussian, with a skewness smoothly varying with position. The power spectra of the fluctuations show, in the frequency range from 3 ×10-4 Hz to 4 ×10-3 Hz, an exponent varying from -0.15 at the bottom of the pit, to -0.6 at the top. Heat exchange with the walls accounts for the mean temperature profile, and contributes to the power spectra for periods smaller than about 20 minutes. Vertical cross-correlations provide estimates of velocities and indicate quasi-stable polarization of the direction of the vertical mean flow. A horizontal vorticity index, constructed from a horizontal cross-correlation and the sign of the temperature gradient, exhibits properties of a scale-invariant process, similar to the structure of wind reversals observed in Rayleigh-Benard laboratory convection experiments or to the reversals of the geomagnetic fields. This experiment may offer a genuine realization of bulk turbulence forced by a linear temperature gradient. More generally, it provides a description of turbulent fluid dynamics in a medium-scale natural system in the presence of non-adiabatic boundaries.

Offshore propagation of eddy kinetic energy in the California Current

Low‐pass‐filtered velocities obtained from surface drifters and surface geostrophic velocities estimated from TOPEX/Poseidon altimeter data have recently revealed a clear and robust seasonal cycle in the surface eddy kinetic energy (EKE) in the California Current (CC) [Kelly et al., 1998; Strub and James, 2000]. The seasonal cycle begins in spring when a surface‐intensified baroclinic equatorward jet develops next to the coast in response to strong upwelling favorable winds. This jet, and a developing eddy field, then moves offshore during summer and fall. The EKE maximum associated with the jet progresses only as far as 127°W, beyond which it decreases rapidly. This is a robust characteristic of the seasonal cycle that has been previously attributed only to an unspecified dissipation process. To investigate this aspect of the surface EKE, a multiyear simulation of the CC is carried out using the Dietrich/Center for Air‐Sea Technology primitive equation regional ocean model [Dietrich, 1997]. The simulation accurately reproduces many aspects of the observed annual cycle, including the offshore propagation of the EKE at the surface. The model results indicate that the decrease of surface EKE west of 127°W in the simulation is not due to dissipation but rather is caused by the vertical redistribution of EKE to the deep ocean. This redistribution occurs through the transformation of kinetic energy from the vertical shear flow to the vertical mean flow. The transformation is a nonlinear process inherently associated with the life cycle of baroclinically unstable waves, and in the CC, it effectively energizes the deeper ocean at the expense of the upper ocean. The process is also known to be important in the atmosphere [Wiin‐Nielsen, 1962]. Taken together, the recent California Current observations and the new model results strongly suggest that the CC regularly supplies EKE to the deep waters of the eastern North Pacific.

An ecosystem model for the North Pacific embedded in a general circulation model: Part II: Mechanisms forming seasonal variations of chlorophyll

Mechanisms forming seasonal variations of the oceanic ecosystem are examined using an ecosystem model embedded in an ocean general circulation model for the North Pacific. The North Pacific can be divided into seven areas based on seasonal variation patterns of chlorophyll. The areal division compares well with that based on observations. For example, a distinct spring bloom can be found in the Bering Sea while the standing stock of phytoplankton is somewhat constant in most of the subpolar gyre throughout the year. It is shown that physical factors determining the modeled seasonal variations are the annual mean vertical flow, vertical mixing, and, less importantly, solar radiation. The annual mean vertical flow can affect the seasonal variation patterns through modifying the relation between the ecosystem and the mixed layer depth (MLD). Various combinations of these factors result in diverse patterns. But it is possible to classify them in terms of the amplitude of the seasonal variation of MLD and the annual mean vertical flow. The results suggest that the difference in physical environments can yield much of the diversity of the observed seasonal variation patterns.

Dynamic features and maintenance mechanism of asian summer monsoon subsystem

In the context of the dissociation of vertical shear flow and tropospheric mean flow based on 1980-1996 NCEP/ NCAR re-analysis, study is undertaken of the barotropic and baroclinic development characteristics and kinetic energy maintenance mechanisms of Asian summer monsoon. Evidence suggests that the monsoon activity is marked by noticeable baroclinicity in three active regions of different dynamical characteristics, located in India, East Asian tropics and subtropics, respectively, with greatly differing maintenance mechanisms of barotropic / baroclinic kinetic energy.

On Alfvén waves in a flowing atmosphere

The present paper considers Alfvén waves in an inhomogeneous medium, under a nonuniform external magnetic field and in the presence of a nonuniform flow, to obtain wave equations for the velocity and magnetic field perturbations, in some particular cases. The case which is chosen for solution is that of propagation along a vertical uniform external magnetic field, in an atmosphere with a vertical mean flow velocity, satisfying mass conservation. The wave equation has a critical layer where the mean flow velocity equals the Alfvén speed, and in the case of an isothermal atmosphere the wave equation for the magnetic field perturbation can be reduced to a Bessel type with complex order and imaginary variable. Thus it is possible to obtain exact solutions for all frequencies and distances, discussing the cases in which there are propagating or evanescent waves far below or far above the critical layer, i.e., the latter acts as a reflecting layer. The solution in the vicinity of the critical layer allows the amplitude and phase of the wave field to be plotted as a function of distance from the critical layer (measured in scale heights) for different values of the dimensionless frequency and initial Alfvén number (ratio of flow velocity to Alfvén speed). One application is the solar atmosphere, for which the magnetohydrodynamic (MHD) equations are appropriate, and the wavelengths are large compared with the density scale height, thus excluding the ray approximation.

Permeability of the stratospheric vortex edge: On the mean mass flux due to thermally dissipating, steady, non‐breaking Rossby waves

AbstractAs part of an assessment of the flowing‐processor hypothesis of Tuck et al. (1993) and references–see also Rosenlof et al. (1997)–this paper estimates possible contributions to flow through the edge of the stratospheric polar vortex due solely to distortion of the vortex by thermally dissipating Rossby waves forced from below. To isolate such contributions in a clear‐cut way, and to eliminate questions about numerical dissipation and truncation error, an idealized model is studied analytically. It assumes steady conditions and non‐breaking waves, the waves being stationary in some rotating frame such as that of the earth. The model is studied using two approaches: first via the generalized Lagrangian‐mean formalism of Andrews and McIntyre (1978), simplified by assuming small wave amplitude a; and second via a direct consideration of the three‐dimensional, finite‐amplitude undulations of the vortex edge, as defined by isentropic contours of potential vorticity, avoiding the use of any mean‐and‐deviation formalism. It is shown, in particular, that under quasi‐geostrophic scaling the Lagrangian‐mean meridional velocity V−L is given correct to O(a2) by equation image , where θB is the basic‐state potential temperature, z the altitude, η′ the meridional particle displacement and 𝒳 the wave‐induced fluctuation in the diabatic rate of change of potential temperature θ. The formula for V−L is shown to be consistent with the independently derived finite‐amplitude result; and the implication of both results is that, for disturbances dissipated by infrared radiative relaxation in the wintertime lower stratosphere, V−L may well be directed into rather than out of the vortex, though weak outward flow is possible in some cases. There is, in addition, a vertical mean flow w−L controlled by eddy dynamics above the altitude under consideration. This is usually directed downward V−L&lt; 0), and can therefore push mass out of the vortex if the vortex edge has its usual upward equatorward slope. However, under typical parameter conditions for the winter stratosphere, the magnitudes are nowhere near large enough to be consistent, by themselves, with Tuck et al.'s statement that the vortex is ‘flushed several times’ during a single winter.