Mean Flow Generation Research Articles

Noise induced effects in the axisymmetric spherical Couette flow.

We study the axisymmetric, wide gap, spherical Couette flow in the presence of noise in numerical simulations and experiments. Such studies are important because most of the flows in nature are subjected to random fluctuations. Noise is introduced into the flow by adding fluctuations to the inner sphere rotation which are random in time with zero mean. Flows of a viscous incompressible fluid are induced either by rotation of the inner sphere only or by the co-rotation of the spheres. Mean flow generation was found to occur under the action of additive noise. A higher relative amplification of meridional kinetic energy compared to the azimuthal component was also observed under certain conditions. Calculated flow velocities were validated by laser Doppler anemometer measurements. A model is proposed to elucidate the rapid growth of meridional kinetic energy for flows induced by varying the co-rotation of the spheres. Our linear stability analysis for flows induced by the rotation of the inner sphere revealed a decrease in the critical Reynolds number, corresponding to the onset of the first instability. Also, in this case, a local minimum of the mean flow generation on approaching the critical Reynolds number was observed, which is consistent with the available theoretical predictions. This article is part of the theme issue 'Taylor-Couette and related flows on the centennial of Taylor's seminal Philosophical Transactions paper (Part 2)'.

The influence of noises with different spectra on viscous incompressible fluid flows

The results of an experimental study of the effects of noises on flows in a rotating spherical layer are presented. Noise is introduced into the flow in the form of random fluctuations of the inner sphere rotational rate relative to a time constant mean value. The flow velocity was measured with a laser Doppler anemometer. It was found that the noises of the equal amplitude, but with different spectra cause the generation of mean flows of different intensity. It is shown that the increase in the average velocities under the action of the noise is larger for the stable flows compared to unstable ones Keywords: noise, flows with rotation, spherical Couette flow.

Влияние шумов с различными спектрами на течения вязкой несжимаемой жидкости

The results of an experimental study of the effects of noises on flows in a rotating spherical layer are presented. Noise is introduced into the flow in the form of random fluctuations of the inner sphere rotational rate relative to a time constant mean value. The flow velocity was measured with a laser Doppler anemometer. It was found that the noises of the equal amplitude, but with different spectra cause the generation of mean flows of different intensity. It is shown that the increase in the average velocities under the action of the noise is larger for the stable flows compared to unstable ones.

An entropy analysis in a slip condition flow over a linear stretching sheet

In this study, we present the slip conditions along with entropy generation of 2-D flow induced by a linear stretching surface with thermo-physical characteristics. We used the viscous model for shear flow conduct and calculate the steady flow field with the slip effect near the stretching surface. The concentration and energy equations are analyzed under the effect of thermo-physical properties. In this study, the thermo-physical properties are presumed to be variable. The system of equations occurs with boundary layer technique are transformed into ODEs by new similarity approach. The study is analyzed completely on base flow and entropy profiles. The radial slip coefficient shows reduction in the radial velocity and normal velocity profile creates incrementing in roughness of surface. The entropy function increases due to upper values of Brinkman number and diffusivity parameter. The mass diffusion coefficient and concentration ratio variable creates enhancement in entropy generation. The physical aspects are given through figures. The correlation of mean flow and entropy generation are presented by making the graphical plots. The comparison analysis with already published articles is also reported here.

Spectral Analysis of Gravity Waves in the Martian Thermosphere during Low Solar Activity Based on MAVEN/NGIMS Observations

Gravity waves (GWs) are important for vertical coupling between the lower and upper atmosphere on Mars. Saturated GWs will promote the acceleration of mean flow and turbulence generation, causing diffuse transport of energy and momentum. We analyze the spectral characteristics of GWs in the thermosphere on Mars during the low solar activity of Martian Year (MY) 35, based on CO2 density measured by the Neutral Gas and Ion Mass Spectrometer (NGIMS) on board Mars Atmosphere and Volatile EvolutioN (MAVEN). The results are compared with those of MY33 at the higher solar activity. The vertical wavenumber spectral density obtained in the Martian thermosphere is similar to the semi-empirically predicted saturation spectrum in the Earth’s atmosphere, with a logarithmic spectral slope around −3. The average spectral density of GWs shows saturation between 160 and 200 km and decreases with increasing altitude. Compared to MY33, GW activity is larger and less attenuated in MY35 as it propagates upward, implying that waves experience more favorable propagation conditions during low solar activity. Also, the dependence of GW activity on local time during this period is found to be different from previous studies, with the strongest GWs in the spring of MY35 occurring within 6–12 hr on the dayside, suggesting that the amplitude of the GWs in the Martian thermosphere during low solar activity is less controlled by the background temperature and is subject to dissipative effects of other factors, such as molecular viscosity and thermal conduction.

Generation of mean flows in rotating anisotropic turbulence: The case of solar near-surface shear layer

Context.Results from helioseismology indicate that the radial gradient of the rotation rate in the near-surface shear layer (NSSL) of the Sun is independent of latitude and radius. Theoretical models using the mean-field approach have been successful in explaining this property of the NSSL, while global direct or large-eddy magnetoconvection models have so far been unable to reproduce this.Aims.We investigate the reason for this discrepancy by measuring the mean flows, Reynolds stress, and turbulent transport coefficients under conditions mimicking those in the solar NSSL.Methods.Simulations with as few ingredients as possible to generate mean flows were studied. These ingredients are inhomogeneity due to boundaries, anisotropic turbulence, and rotation. The parameters of the simulations were chosen such that they matched the weakly rotationally constrained NSSL. The simulations probe locally Cartesian patches of the star at a given depth and latitude. The depth of the patch was varied by changing the rotation rate such that the resulting Coriolis numbers covered the same range as in the NSSL. We measured the turbulent transport coefficient relevant for the nondiffusive (Λ-effect) and diffusive (turbulent viscosity) parts of the Reynolds stress and compared them with predictions of current mean-field theories.Results.A negative radial gradient of the mean flow is generated only at the equator where meridional flows are absent. At other latitudes, the meridional flow is comparable to the mean flow corresponding to differential rotation. We also find that the meridional components of the Reynolds stress cannot be ignored. Additionally, we find that the turbulent viscosity is quenched by rotation by about 50% from the surface to the bottom of the NSSL.Conclusions.Our local simulations do not validate the explanation for the generation of the NSSL from mean-field theory where meridional flows and stresses are neglected. However, the rotational dependence of the turbulent viscosity in our simulations agrees well with theoretical predictions. Moreover, our results agree qualitatively with global convection simulations in that an NSSL can only be obtained near the equator.

Mean zonal flows induced by weak mechanical forcings in rotating spheroids

Abstract

Weakly nonlinear analysis of mean flow generation for tidally locked exoplanets

We study a model developed by Showman and Polvani [Equatorial superrotation on tidally locked exoplanets. Astrophys. J. 2011, 738, 71–94] to study the behaviour of a thin, upper atmospheric layer of a tidally locked exoplanet; in particular, the behaviour of the atmospheres of “hot Jupiters”, gas giants orbiting close to their stars and tidally locked to them, having a dayside and a nightside. We are interested in trying to elucidate the mechanism found by Showman and Polvani for the generation on such planets of an equatorial superrotation, ie. a rapid easterly current in the region about the equator. We extend their analysis of the two simple linear cases studied in the appendices of their paper by including the (small) nonlinear terms which then interact to generate mean flows. In the first of these cases, we expand about the small radiative time scale and find that the mean flow at the equator is eastward, This case may be particularly relevant for the hottest of tidally locked exoplanets. In the other case, we use a multiple parameter asymptotic expansion where the drag time scale is very large but much less than the reciprocal of the small amplitude scale of the expansion. In this case, we again find that the nonlinear terms generate a mean flow that is eastward at the equator. These results may help to provide a possible explanation for the equatorial superrotation.

Multimodal Excitation to Model the Quasibiennial Oscillation.

The quasibiennial oscillation (QBO) of stratospheric winds is the most striking example of mean-flow generation and reversal by the nonlinear interactions of internal waves. Previous studies have used an idealized monochromatic forcing to investigate the QBO. Here we instead force a more realistic continuous wave spectrum. Unexpectedly, spreading the wave energy across a wide frequency range leads to more regular oscillations. We also find that different forcing spectra can yield the same QBO. Multimodal wave forcing is thus essential for understanding wave-mean-flow interactions in nature.

Long-time dynamics of internal wave streaming

Abstract

Mean flow generation due to longitudinal librations of sidewalls of a rotating annulus

Laboratory experiments with a rotating cylindrical annulus are reported that reveal a prograde jet, which is adjacent to a (longitudinally) librating inner straight cylindrical wall. Here, wall libration is realised as a time-harmonic modulation of the inner cylinder's rotation rate. The outer cylindrical wall and bottom and top lids rotate with constant angular velocity. The main purpose of our study is to contribute to a qualitative and quantitative understanding of non-linearities that are present in oscillating, but centrifugally stable, vertical boundary layers frequently encountered in rotating wall-bounded flows. We consider a problem that is in a sense complementary to that of previous works that focused on oscillating Ekman layers but neglected the vertical Stokes−Stewartson layers. A simple analytical model is proposed that is able to predict the magnitude and spatial structure of the emerging prograde near-wall jet in terms of nonlinearity inherent in the inner cylinder's boundary layer dynamics.

Anomalous winter moisture transport associated with the recent surface warming over the Barents–Kara seas region since the mid‐2000s

AbstractObservational evidences have shown that the increased water vapour and accompanying enhancement of downward infrared radiation (IR) can explain the abrupt warming of surface air temperature (SAT) over the Barents–Kara Seas during boreal winter. This study investigates anomalous moisture transport associated with the abrupt change of SAT since the mid‐2000s over the Barents–Kara Seas, since moisture transport contributes to the anomalous water vapour and downward IR. Results show that anomalous stationary moisture flux induces anomalous moisture convergence over the Barents–Kara Seas region, whereas the anomalous transient flux opposes the anomalous moisture convergence there. Hence, the anomalous stationary moisture transport is suggested to be responsible to the increased water vapour over the Barents–Kara Seas region. Further decomposition of the stationary moisture flux indicates that the anomalous moisture convergence associated with the change in atmospheric mean flow plays an important role in the increased water vapour on both interannual and decadal time scales. In addition, decrease in the synoptic‐scale eddy activity observed over northern Siberia may contribute to generation of the anomalous atmospheric mean flow via eddy feedback processes.

On mean flow generation due to oblique reflection of internal waves at a slope

AbstractSmall‐amplitude expansions are utilized to discuss the mean flow induced by the reflection of a weakly nonlinear internal gravity wave beam at a uniform rigid slope, in the case where the beam planes of constant phase meet the slope at an arbitrary direction, not necessarily parallel to the isobaths, and the flow cannot be taken as two dimensional. Along the vertical, the Eulerian mean flow, due to such an oblique reflection, is equal and opposite to the Stokes drift so the Lagrangian mean flow vanishes, similar to a two‐dimensional reflection. The horizontal Eulerian mean flow, however, is controlled by the mean potential vorticity (PV) and the corresponding Lagrangian mean flow is generally nonzero, in contrast to two‐dimensional flow where PV identically vanishes. For an oblique reflection, furthermore, viscous dissipation can trigger generation of horizontal mean flow via irreversible production of mean PV, a phenomenon akin to streaming.

Mean flow generation by three-dimensional nonlinear internal wave beams

We study the generation of resonantly growing mean flow by weakly nonlinear internal wave beams. With a perturbational expansion, we construct analytic solutions for three-dimensional internal wave beams, exact up to first-order accuracy in the viscosity parameter. We specifically focus on the subtleties of wave beam generation by oscillating boundaries, such as wave makers in laboratory set-ups. The exact solutions to the linearized equations allow us to derive an analytic expression for the mean vertical vorticity production term, which induces a horizontal mean flow. Whereas mean flow generation associated with viscous beam attenuation – known as streaming – has been described before, we are the first to also include a peculiar inviscid mean flow generation in the vicinity of the oscillating wall, resulting from line vortices at the lateral edges of the oscillating boundary. Our theoretical expression for the mean vertical vorticity production is in good agreement with earlier laboratory experiments, for which the previously unrecognized inviscid mean flow generation mechanism turns out to be significant.

Wake vortex regimes of a pitching cantilever plate in quiescent air and their correlation with mean flow generation

Jet flows induced by oscillating cantilever plates enable power-efficient cooling enhancement and fluid acceleration. We report a combined experimental and numerical study of the vortex regimes present in the wake of a harmonically oscillating thin cantilever plate in a quiescent fluid and analyze their effect on the flow generation downstream. We use Particle Image Velocimetry (PIV) in conjunction with two-dimensional numerical simulations to investigate the vortex evolution around the trailing edge of the plates with different geometries and vibrational properties. Our observations suggest the existence of three distinct regimes in the wake: non-propagating, intermediate and propagating. Comparing the temporal decay of the vortex circulation in different regimes shows that different mechanisms are involved in the formation of these vortical patterns. A regime map is proposed next, denoting the incident of each vortex regime as a function of relevant dimensionless parameters. Our analysis of the mean jet on the normal mid-plane, as quantified by the momentum-averaged Reynolds number Rejet, shows that the induced jet downstream the trailing edge is tightly correlated with the identified vortex regimes. The present study improves our understanding of vortex generation and propagation in oscillating cantilevers and facilitates optimized design and operation of piezoelectric fans and similar devices.

Mean flow generation by an intermittently unstable boundary layer over a sloping wall

Direct numerical simulations (DNS) of the flow in various rotating annular confinements have been conducted to investigate the effects of wall inclination on secondary fluid motions due to an unstable boundary layer. The inner wall resembles a truncated cone (frustum) whose apex half-angle is varied from$18^{\circ }$to$0^{\circ }$(straight cylinder). The large inner radius$r_{1}$, the mean rotation rate$\unicode[STIX]{x1D6FA}_{0}$and the kinematic viscosity$\unicode[STIX]{x1D708}$were kept constant resulting in the constant Ekman number$E=\unicode[STIX]{x1D708}/(\unicode[STIX]{x1D6FA}_{0}r_{1}^{2})=4\times 10^{-5}$. Flows were excited by time-harmonic modulation of the inner wall’s rotation rate (so-called longitudinal libration) by prescribing the amplitude$\unicode[STIX]{x1D700}\unicode[STIX]{x1D6FA}_{0}$and the forcing frequency$\unicode[STIX]{x1D714}=\unicode[STIX]{x1D6FA}_{0}$. By steepening the inner wall and hence reducing the effect of the local Coriolis force in the boundary layer three different flow regimes can be realized: a rotation-dominated, a libration-dominated and an intermediate regime. In the present study we focus on the libration-dominated regime. For small libration amplitudes (here$\unicode[STIX]{x1D700}=0.2$), a laminar Ekman–Stokes boundary layer (ESBL) is realized at the librating wall. With the aid of laminar boundary layer theory and DNS we show that the ESBL exhibits an oscillatory mass flux along the librating wall (Ekman property) and an oscillatory azimuthal velocity, which resembles a radially damped wave (Stokes property). For large libration amplitudes (here$\unicode[STIX]{x1D700}=0.8$), the DNS results exhibit an intermittently unstable ESBL, which turns centrifugally unstable during the prograde (faster) part of a libration period. This instability is due to the Stokes property and gives rise to Görtler vortices, which are found to be tilted with respect to the azimuth when the librating wall is at a finite angle relative to the axis of rotation. We show that this tilt is related to the Ekman property of the ESBL. This suggests that linear and nonlinear dynamics are equally important for this intermittent instability. Our DNS results indicate further that the Görtler vortices propagate into the fluid bulk where they generate an azimuthal mean flow. This mean flow is notably different from the mean flow driven in the case of the stable ESBL. A diagnostic analysis of the Reynolds-averaged Navier–Stokes (RANS) equations in the unstable flow regime hints at a competition between the radial and axial turbulent transport terms which act as generating and destructing agents for the azimuthal mean flow, respectively. We show that the balance of both terms depends on the wall inclination, that is, on the wall-tangential component of the Coriolis force.

Phase dynamics of edge transport bifurcation induced by external biasing

Edge transport bifurcation induced by external biasing is explored with self-consistent turbulence simulations in a flux-driven system with both closed and open magnetic field lines. Without bias, the nonlinear evolution of interchange turbulence produces large-scale turbulent eddies, leading to the high levels of radial transport in the edge region. With sufficiently strong biasing, a strong suppression of turbulence is found. The plasma potential structures are strongly modified with the generation of sheared mean flows at the plasma edge. Consequently, the turbulence-driven flux is decreased to a much lower level, indicating a transition to a state of reduced transport. The simulations show that the dynamics of the phase and amplitude of fluctuations play a crucial role in the mechanism of transport suppression driven by biasing.

Mechanism of mean flow generation in rotating turbulence through inhomogeneous helicity

Numerical simulations have revealed that mean flow directed to the rotation axis is generated against the turbulent diffusion only in the case of both inhomogeneous helical forcing and system rotation. The origin of the phenomenon is examined in terms of the Reynolds-stress transport equation.

Linear stability assessment of a cryogenic rocket engine

The linear high frequency stability of DLR’s cryogenic H2/O2 BKD test chamber is assessed using a hybrid computational fluid dynamic/computational aeroacoustic methodology, which is based on single flame simulations for the generation of an adequate mean flow and for the calibration of feedback models as well as on frequency space transformed linearized Euler equations. The application of a realistic mean flow field including combustion explains the spatial separation of transverse modes into a near face plate mode, which is found linearly unstable under certain operation conditions for the first transverse and a rear part mode. The axial mode shape length as well as eigenfrequencies is affected by propellant injection specifications and, in consequence, decisively influence pressure and transverse velocity sensitive dynamic flame response. The stability assessment procedure is finally applied to four operation conditions and the linear stability is predicted for the first transverse mode.

Mean flow generation by Görtler vortices in a rotating annulus with librating side walls

Time periodic variation of the rotation rate of an annulus induces in supercritical regime an unstable Stokes boundary layer over the cylinder side walls, generating Görtler vortices in a portion of a libration cycle as a discrete event. Numerical results show that these vortices propagate into the fluid bulk and generate an azimuthal mean flow. Direct numerical simulations of the fluid flow in an annular container with librating outer (inner) cylinder side wall and Reynolds-averaged Navier–Stokes (RANS) equations as diagnostic equations are used to investigate generation mechanism of the retrograde (prograde) azimuthal mean flow in the bulk. First, we explain, phenomenologically, how absolute angular momentum of the bulk flow is mixed and changed due to the propagation of the Görtler vortices, causing a new vortex of basin size. Then we investigate the RANS equations for intermediate time scale of the development of the Görtler vortices and for long time scale of the order of several libration periods. The former exhibits sign selection of the azimuthal mean flow. Investigating the latter, we predict that the azimuthal mean flow is proportional to the libration amplitude squared and to the inverse square root of the Ekman number and libration frequency and then confirms this using the numerical data. Additionally, presence of an upscale cascade of energy is shown, using the kinetic energy budget of fluctuating flow.