Direct numerical simulations of turbulent Ekman layers with increasing static stability: modifications to the bulk structure and second-order statistics

2014 ◽  
Vol 760 ◽  
pp. 494-539 ◽  
Author(s):  
Stimit K. Shah ◽  
Elie Bou-Zeid
Keyword(s):  
Reynolds Number ◽  
Vertical Velocity ◽  
Richardson Number ◽  
Momentum Flux ◽  
Static Stability ◽  
Direct Numerical Simulations ◽  
Temperature Variance ◽  
Ekman Layers ◽  
Velocity Variance ◽  
Shear Production

AbstractDirect numerical simulations of stably stratified Ekman layers are conducted to study the effect of increasing static stability on turbulence dynamics and modelling in wall-bounded flows at three moderate Reynolds numbers. The flow field is analysed by examining the mean profiles of wind speed, potential temperature and momentum flux, as well as streamwise velocity and temperature spectra. The maximum stabilizing buoyancy flux that a flow can sustain while remaining fully turbulent is found to depend on the Reynolds number. The flows with the highest Reynolds number display a relatively well-developed inertial range and logarithmic layer, and are found to bear similarities to much higher-Reynolds-number flows like the ones encountered in the atmospheric boundary layer. In particular, the near-wall mean profiles follow the Monin–Obukhov similarity theory. However, several flow features, such as the critical Richardson number and the stress–strain alignment, are found to maintain significant dependence on the Reynolds number. The budgets of turbulence kinetic energy (TKE), vertical velocity variance, momentum and buoyancy fluxes, and temperature variance are analysed. The results indicate that the effect of stability on turbulence is first directly manifested in the vertical velocity variance budget, and results in damping of vertical motions. This then leads to a reduction in the downward transport of horizontal momentum components towards the surface, and consequently to a decrease in the shear production term in the TKE budget: changes in the vertical profile of TKE shear production with increasing Richardson number are significant and have a larger impact on TKE than direct buoyancy destruction. The reduction in vertical velocity variance also results in significant drops in the production terms in the momentum flux, buoyancy flux and temperature variance budgets. Various assumptions and parameters related to low-order turbulence closures are investigated. The results suggest that the vertical velocity variance is a more appropriate parameter than the full TKE on which to base eddy-diffusivity and viscosity models.

Direct numerical simulations of the turbulence evolution in a uniformly sheared and stably stratified flow

1997 ◽  
Vol 342 ◽  
pp. 231-261 ◽  
Author(s):  
FRANK G. JACOBITZ ◽  
SUTANU SARKAR ◽  
CHARLES W. VAN ATTA
Keyword(s):  
Growth Rate ◽  
Reynolds Number ◽  
Kinetic Energy ◽  
Numerical Simulations ◽  
Turbulent Kinetic Energy ◽  
Richardson Number ◽  
Direct Numerical Simulations ◽  
Initial Value ◽  
Critical Richardson Number ◽  
Stably Stratified Flow

Direct numerical simulations (DNS) are performed to investigate the evolution of turbulence in a uniformly sheared and stably stratified flow. The spatial discretization is accomplished by a spectral collocation method, and the solution is advanced in time with a third-order Runge–Kutta scheme. The turbulence evolution is found to depend strongly on at least three parameters: the gradient Richardson number Ri, the initial value of the Taylor microscale Reynolds number Reλ, and the initial value of the shear number SK/<ε. The effect of each parameter is individually studied while the remaining parameters are kept constant. The evolution of the turbulent kinetic energy K is found to follow approximately an exponential law. The shear number SK/<ε, whose effect has not been investigated in previous studies, was found to have a strong non-monotone influence on the turbulence evolution. Larger values of the shear number do not necessarily lead to a larger value of the eventual growth rate of the turbulent kinetic energy. Variation of the Reynolds number Reλ indicated that the turbulence growth rate tends to become insensitive to Reλ at the higher end of the Reλ range studied here. The dependence of the critical Richardson number Ricr, which separates asymptotic growth of the turbulent kinetic energy K from asymptotic decay, on the initial values of the Reynolds number Reλ and the shear number SK/<ε was also obtained. It was found that the critical Richardson number varied over the range 0.04<Ricr<0.17 in our DNS due to its strong dependence on Reynolds and shear numbers.

scholarly journals Closure Schemes for Stably Stratified Atmospheric Flows without Turbulence Cutoff

2016 ◽  
Vol 73 (12) ◽  
pp. 4817-4832 ◽  
Author(s):  
Dan Li ◽  
Gabriel G. Katul ◽  
Sergej S. Zilitinkevich
Keyword(s):  
Vertical Velocity ◽  
Richardson Number ◽  
Sensible Heat Flux ◽  
Physical Space ◽  
Heat Fluxes ◽  
Atmospheric Flows ◽  
Gradient Richardson Number ◽  
Velocity Variance ◽  
Momentum And Heat Fluxes ◽  
Flow Variables

Abstract Two recently proposed turbulence closure schemes are compared against the conventional Mellor–Yamada (MY) model for stably stratified atmospheric flows. The Energy- and Flux-Budget (EFB) approach solves the budgets of turbulent momentum and heat fluxes and turbulent kinetic and potential energies. The Cospectral Budget (CSB) approach is formulated in wavenumber space and integrated across all turbulent scales to obtain flow variables in physical space. Unlike the MY model, which is subject to a “critical gradient Richardson number,” both EFB and CSB models allow turbulence to exist at any gradient Richardson number and predict a saturation of flux Richardson number () at sufficiently large . The CSB approach further predicts the value of and reveals a unique expression linking the Rotta and von Kármán constants. Hence, all constants in the CSB model are nontunable and stability independent. All models agree that the dimensionless sensible heat flux decays with increasing . However, the decay rate and subsequent cutoff in the MY model appear abrupt. The MY model further exhibits an abrupt cutoff in the turbulent stress normalized by vertical velocity variance, while the CSB and EFB models display increasing trends. The EFB model produces a rapid increase in the ratio of turbulent potential energy and vertical velocity variance as is approached, suggesting a strong self-preservation mechanism. Vertical anisotropy in the turbulent kinetic energy is parameterized in different ways in MY and EFB, but this consideration is not required in CSB. Differences between EFB and CSB model predictions originate from how the vertical anisotropy is specified in the EFB model.

The flow of liquid in a stream from the standard turbine impeller

1979 ◽  
Vol 44 (3) ◽  
pp. 700-710 ◽  
Author(s):  
Ivan Fořt ◽  
Hans-Otto Möckel ◽  
Jan Drbohlav ◽  
Miroslav Hrach
Keyword(s):  
Reynolds Number ◽  
Kinematic Viscosity ◽  
Momentum Flux ◽  
Relative Size ◽  
Mean Velocity ◽  
Axial Profile ◽  
The Mean ◽  
Hot Film ◽  
Turbine Impeller

Profiles of the mean velocity have been analyzed in the stream streaking from the region of rotating standard six-blade disc turbine impeller. The profiles were obtained experimentally using a hot film thermoanemometer probe. The results of the analysis is the determination of the effect of relative size of the impeller and vessel and the kinematic viscosity of the charge on three parameters of the axial profile of the mean velocity in the examined stream. No significant change of the parameter of width of the examined stream and the momentum flux in the stream has been found in the range of parameters d/D ##m <0.25; 0.50> and the Reynolds number for mixing ReM ##m <2.90 . 101; 1 . 105>. However, a significant influence has been found of ReM (at negligible effect of d/D) on the size of the hypothetical source of motion - the radius of the tangential cylindrical jet - a. The proposed phenomenological model of the turbulent stream in region of turbine impeller has been found adequate for values of ReM exceeding 1.0 . 103.

scholarly journals Effects of atmospheric dynamics and aerosols on the fraction of supercooled water clouds

2017 ◽  
Vol 17 (3) ◽  
pp. 1847-1863 ◽  
Author(s):  
Jiming Li ◽  
Qiaoyi Lv ◽  
Min Zhang ◽  
Tianhe Wang ◽  
Kazuaki Kawamoto ◽  
...  
Keyword(s):  
Relative Humidity ◽  
Vertical Velocity ◽  
Meteorological Parameters ◽  
Temporal Correlation ◽  
Supercooled Liquid ◽  
Satellite Observation ◽  
Static Stability ◽  
Global Scale ◽  
Atmospheric Dynamics ◽  
Horizontal Wind

Abstract. Based on 8 years of (January 2008–December 2015) cloud phase information from the GCM-Oriented Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) Cloud Product (GOCCP), aerosol products from CALIPSO and meteorological parameters from the ERA-Interim products, the present study investigates the effects of atmospheric dynamics on the supercooled liquid cloud fraction (SCF) during nighttime under different aerosol loadings at global scale to better understand the conditions of supercooled liquid water gradually transforming to ice phase. Statistical results indicate that aerosols' effect on nucleation cannot fully explain all SCF changes, especially in those regions where aerosols' effect on nucleation is not a first-order influence (e.g., due to low ice nuclei aerosol frequency). By performing the temporal and spatial correlations between SCFs and different meteorological factors, this study presents specifically the relationship between SCF and different meteorological parameters under different aerosol loadings on a global scale. We find that the SCFs almost decrease with increasing of aerosol loading, and the SCF variation is closely related to the meteorological parameters but their temporal relationship is not stable and varies with the different regions, seasons and isotherm levels. Obviously negative temporal correlations between SCFs versus vertical velocity and relative humidity indicate that the higher vertical velocity and relative humidity the smaller SCFs. However, the patterns of temporal correlation for lower-tropospheric static stability, skin temperature and horizontal wind are relatively more complex than those of vertical velocity and humidity. For example, their close correlations are predominantly located in middle and high latitudes and vary with latitude or surface type. Although these statistical correlations have not been used to establish a certain causal relationship, our results may provide a unique point of view on the phase change of mixed-phase cloud and have potential implications for further improving the parameterization of the cloud phase and determining the climate feedbacks.

scholarly journals Waves and vortices in the inverse cascade regime of stratified turbulence with or without rotation

2016 ◽  
Vol 806 ◽  
pp. 165-204 ◽  
Author(s):  
Corentin Herbert ◽  
Raffaele Marino ◽  
Duane Rosenberg ◽  
Annick Pouquet
Keyword(s):  
Reynolds Number ◽  
Numerical Simulations ◽  
Direct Numerical Simulations ◽  
Vertical Shear ◽  
Energy Spectra ◽  
Stratified Turbulence ◽  
Viscous Effects ◽  
Inverse Cascade ◽  
Main Effects ◽  
The Waves

We study the partition of energy between waves and vortices in stratified turbulence, with or without rotation, for a variety of parameters, focusing on the behaviour of the waves and vortices in the inverse cascade of energy towards the large scales. To this end, we use direct numerical simulations in a cubic box at a Reynolds number $Re\approx 1000$, with the ratio between the Brunt–Väisälä frequency $N$ and the inertial frequency $f$ varying from $1/4$ to 20, together with a purely stratified run. The Froude number, measuring the strength of the stratification, varies within the range $0.02\leqslant Fr\leqslant 0.32$. We find that the inverse cascade is dominated by the slow quasi-geostrophic modes. Their energy spectra and fluxes exhibit characteristics of an inverse cascade, even though their energy is not conserved. Surprisingly, the slow vortices still dominate when the ratio $N/f$ increases, also in the stratified case, although less and less so. However, when $N/f$ increases, the inverse cascade of the slow modes becomes weaker and weaker, and it vanishes in the purely stratified case. We discuss how the disappearance of the inverse cascade of energy with increasing $N/f$ can be interpreted in terms of the waves and vortices, and identify the main effects that can explain this transition based on both inviscid invariants arguments and viscous effects due to vertical shear.

scholarly journals Analysis of transient mixed convection in a horizontal channel partially heated from below

2021 ◽  
Vol 4 (8(112)) ◽  
pp. 16-22
Author(s):  
Mahmoud A. Mashkour
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Heat Source ◽  
Local Nusselt Number ◽  
Richardson Number ◽  
Stokes Equations ◽  
Heat Convection ◽  
Horizontal Channel ◽  
Outlet Temperature

The heat convection phenomenon has been investigated numerically (mathematically) for a channel located horizontally and partially heated at a uniform heat flux with forced and free heat convection. The investigated horizontal channel with a fluid inlet and the enclosure was exposed to the heat source from the bottom while the channel upper side was kept with a constant temperature equal to fluid outlet temperature. Transient, laminar, incompressible and mixed convective flow is assumed within the channel. Therefore, the flow field is estimated using Navier Stokes equations, which involves the Boussinesq approximation. While the temperature field is calculated using the standard energy model, where, Re, Pr, Ri are Reynolds number, Prandtl number, and Richardson number, respectively. Reynolds number (Re) was changed during the test from 1 to 50 (1, 10, 25, and 50) for each case study, Richardson (Ri) number was changed during the test from 1 to 25 (1, 5, 10, 15, 20, and, 25). The average Nusselt number (Nuav) increases exponentially with the Reynold number for each Richardson number and the local Nusselt number (NuI) rises in the heating point. Then gradually stabilized until reaching the endpoint of the channel while the local Nusselt number increases with a decrease in the Reynolds number over there. In addition, the streamlines and isotherms patterns in case of the very low value of the Reynolds number indicate very low convective heat transfer with all values of Richardson number. Furthermore, near the heat source, the fluid flow rate rise increases the convection heat transfer that clarified the Nusselt number behavior with Reynolds number indicating that maximum Nu No. are 6, 12, 27 and 31 for Re No. 1, 10, 25 and 50, respectively

scholarly journals Numerical Analysis of Mixed Convective Heat Transfer from a Square Cylinder Utilizing Nanofluids with Multi-Phase Modelling Approach

Energies ◽  
2021 ◽  
Vol 14 (17) ◽  
pp. 5485
Author(s):  
Rajendra S. Rajpoot ◽  
Shanmugam. Dhinakaran ◽  
Md. Mahbub Alam
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Convective Heat Transfer ◽  
Richardson Number ◽  
Base Fluid ◽  
Square Cylinder ◽  
Heat Transfer Characteristics ◽  
Flow And Heat Transfer ◽  
Multi Phase ◽  
Modelling Approach

The present study deals with the numerical simulation of mixed convective heat transfer from an unconfined heated square cylinder using nanofluids (Al2O3-water) for Reynolds number (Re) 10–150, Richardson number (Ri) 0–1, and nanoparticles volume fractions (φ) 0–5%. Two-phase modelling approach (i.e., Eulerian-mixture model) is adopted to analyze the flow and heat transfer characteristics of nanofluids. A square cylinder with a constant temperature higher than that of the ambient is exposed to a uniform flow. The governing equations are discretized and solved by using a finite volume method employing the SIMPLE algorithm for pressure–velocity coupling. The thermo-physical properties of nanofluids are calculated from the theoretical models using a single-phase approach. The flow and heat transfer characteristics of nanofluids are studied for considered parameters and compared with those of the base fluid. The temperature field and flow structure around the square cylinder are visualized and compared for single and multi-phase approaches. The thermal performance under thermal buoyancy conditions for both steady and unsteady flow regimes is presented. Minor variations in flow and thermal characteristics are observed between the two approaches for the range of nanoparticle volume fractions considered. Variation in φ affects CD when Reynolds number is varied from 10 to 50. Beyond Reynolds number 50, no significant change in CD is observed with change in φ. The local and mean Nusselt numbers increase with Reynolds number, Richardson number, and nanoparticle volume fraction. For instance, the mean Nusselt number of nanofluids at Re = 100, φ = 5%, and Ri = 1 is approximately 12.4% higher than that of the base fluid. Overall, the thermal enhancement ratio increases with φ and decreases with Re regardless of Ri variation.

Stratified Ekman layers evolving under a finite-time stabilizing buoyancy flux

2018 ◽  
Vol 840 ◽  
pp. 266-290 ◽  
Author(s):  
S. M. Iman Gohari ◽  
Sutanu Sarkar
Keyword(s):  
Finite Time ◽  
Richardson Number ◽  
Ekman Layer ◽  
Buoyancy Flux ◽  
Late Time ◽  
Near Surface ◽  
Obukhov Length ◽  
Low Level ◽  
Ekman Layers ◽  
Low Level Jet

Stratified flow in nocturnal boundary layers is studied using direct numerical simulation (DNS) of the Ekman layer, a model problem that is useful to understand atmospheric boundary-layer (ABL) turbulence. A stabilizing buoyancy flux is applied for a finite time to a neutral Ekman layer. Based on previous studies and the simulations conducted here, the choice of $L_{\mathit{cri}}^{+}=Lu_{\ast }/\unicode[STIX]{x1D708}\approx 700$ ($L$ is the Obukhov length scale and $u_{\ast }$ is the friction velocity) provides a cooling flux that is sufficiently strong to cause the initial collapse of turbulence. The turbulent kinetic energy decays over a time scale of $4.06L/u_{\ast }$ during the collapse. The simulations suggest that imposing $L_{\mathit{cri}}^{+}\approx 700$ on the neutral Ekman layer results in turbulence collapse during the initial transient, independent of Reynolds number, $Re_{\ast }$. However, the long-time state of the flow, i.e. turbulent with spatial intermittency or non-turbulent, is found to depend on the initial value of $Re_{\ast }$ since the cooling flux and resultant stratification increase with $Re_{\ast }$ for a given $L^{+}$. The lower-$Re_{\ast }$ cases have sustained turbulence with shear and stratification profiles that evolve in a manner such that the gradient Richardson number, $Ri_{g}$, in the near-surface layer, including the low-level jet, remains subcritical. The highest $Re_{\ast }$ case has supercritical $Ri_{g}$ in the low-level jet and turbulence does not recover. A theoretical discussion is performed to infer that the bulk Richardson number, $Ri_{b}$, is more suitable than $L^{+}$ to determine the fate of stratified Ekman layers at late time. DNS results support the implications of $Ri_{b}$ for the effect of initial $Re_{\ast }$ and $L^{+}$ on the flow.

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