Horizontal convection dynamics: insights from transient adjustment

2013 ◽  
Vol 726 ◽  
pp. 559-595 ◽  
Author(s):  
Ross W. Griffiths ◽  
Graham O. Hughes ◽  
Bishakhdatta Gayen
Keyword(s):  
Boundary Layer ◽  
Boundary Conditions ◽  
Time Scales ◽  
Time Scale ◽  
Mechanical Energy ◽  
Buoyancy Flux ◽  
Small Scale ◽  
Vertical Diffusion ◽  
Practical Applications ◽  
Horizontal Convection

AbstractThe dynamics of horizontal convection are revealed by examining transient adjustment toward thermal equilibrium. We restrict attention to high Rayleigh numbers (of $O(1{0}^{12} )$) and a Prandtl number ${\sim }5$ that characterize many practical applications, and consider responses to small changes in the thermal boundary conditions, using laboratory experiments, three-dimensional direct numerical simulations (DNS) and simple theoretical models. The experiments and the mechanical energy budget from the DNS demonstrate that unsteady forcing can produce flow dramatically more active than horizontal convection under steady forcing. The physical mechanisms at work are indicated by the time scales of approach to the new equilibrium, and we show that these can range over two orders of magnitude depending on the imposed change in boundary conditions. Changes that lead to a net destabilizing buoyancy flux give rapid adjustments: for applied heat flux conditions the whole of the circulation is controlled by conduction through the stable portion of the boundary layer, whereas for applied temperature difference the circulation is controlled by small-scale convection within the unstable part of the boundary layer. The experiments, DNS and models are in close agreement and show that the time scale under applied temperatures is as small as 0.01 vertical diffusion time scales, a factor of four smaller than for imposed flux. Both cases give adjustments too rapid for diffusion in the interior to play a significant role, at least through 99 % of the adjustment, and we conclude that diffusion through the full depth is not significant in setting the equilibrium state. Boundary changes leading to a net stabilizing buoyancy flux give a very different response, causing the convection to quickly form a shallow circulation cell, followed eventually by a return to full-depth overturning through a combination of penetrative convection and conduction. The time scale again varies by orders of magnitude, depending on the boundary conditions and the location of the imposed boundary perturbation.

scholarly journals Stochastic modelling of star-formation histories II: star-formation variability from molecular clouds and gas inflow

2020 ◽  
Vol 497 (1) ◽  
pp. 698-725 ◽  
Author(s):  
Sandro Tacchella ◽  
John C Forbes ◽  
Neven Caplar
Keyword(s):  
Life Cycle ◽  
Star Formation ◽  
Time Scales ◽  
Time Scale ◽  
Molecular Clouds ◽  
Star Formation History ◽  
Small Scale ◽  
Inflow Rate ◽  
Wide Range ◽  
The Galaxy

ABSTRACT A key uncertainty in galaxy evolution is the physics regulating star formation, ranging from small-scale processes related to the life-cycle of molecular clouds within galaxies to large-scale processes such as gas accretion on to galaxies. We study the imprint of such processes on the time-variability of star formation with an analytical approach tracking the gas mass of galaxies (‘regulator model’). Specifically, we quantify the strength of the fluctuation in the star-formation rate (SFR) on different time-scales, i.e. the power spectral density (PSD) of the star-formation history, and connect it to gas inflow and the life-cycle of molecular clouds. We show that in the general case the PSD of the SFR has three breaks, corresponding to the correlation time of the inflow rate, the equilibrium time-scale of the gas reservoir of the galaxy, and the average lifetime of individual molecular clouds. On long and intermediate time-scales (relative to the dynamical time-scale of the galaxy), the PSD is typically set by the variability of the inflow rate and the interplay between outflows and gas depletion. On short time-scales, the PSD shows an additional component related to the life-cycle of molecular clouds, which can be described by a damped random walk with a power-law slope of β ≈ 2 at high frequencies with a break near the average cloud lifetime. We discuss star-formation ‘burstiness’ in a wide range of galaxy regimes, study the evolution of galaxies about the main sequence ridgeline, and explore the applicability of our method for understanding the star-formation process on cloud-scale from galaxy-integrated measurements.

scholarly journals Parameters for the Collapse of Turbulence in the Stratified Plane Couette Flow

2018 ◽  
Vol 75 (9) ◽  
pp. 3211-3231 ◽  
Author(s):  
Ivo G. S. van Hooijdonk ◽  
Herman J. H. Clercx ◽  
Cedrick Ansorge ◽  
Arnold F. Moene ◽  
Bas J. H. van de Wiel
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Boundary Conditions ◽  
Couette Flow ◽  
Neumann Boundary ◽  
Surface Flux ◽  
Shear Capacity ◽  
Buoyancy Flux ◽  
Dirichlet Boundary Conditions ◽  
Obukhov Length

Abstract We perform direct numerical simulation of the Couette flow as a model for the stable boundary layer. The flow evolution is investigated for combinations of the (bulk) Reynolds number and the imposed surface buoyancy flux. First, we establish what the similarities and differences are between applying a fixed buoyancy difference (Dirichlet) and a fixed buoyancy flux (Neumann) as boundary conditions. Moreover, two distinct parameters were recently proposed for the turbulent-to-laminar transition: the Reynolds number based on the Obukhov length and the “shear capacity,” a velocity-scale ratio based on the buoyancy flux maximum. We study how these parameters relate to each other and to the atmospheric boundary layer. The results show that in a weakly stratified equilibrium state, the flow statistics are virtually the same between the different types of boundary conditions. However, at stronger stratification and, more generally, in nonequilibrium conditions, the flow statistics do depend on the type of boundary condition imposed. In the case of Neumann boundary conditions, a clear sensitivity to the initial stratification strength is observed because of the existence of multiple equilibriums, while for Dirichlet boundary conditions, only one statistically steady turbulent equilibrium exists for a particular set of boundary conditions. As in previous studies, we find that when the imposed surface flux is larger than the maximum buoyancy flux, no turbulent steady state occurs. Analytical investigation and simulation data indicate that this maximum buoyancy flux converges for increasing Reynolds numbers, which suggests a possible extrapolation to the atmospheric case.

WRF4PALM v1.0: A Mesoscale Dynamic Driver for the Microscale PALM Model System 6.0

2021 ◽  
Author(s):  
Dongqi Lin ◽  
Basit Khan ◽  
Marwan Katurji ◽  
Leroy Bird ◽  
Ricardo Faria ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Boundary Conditions ◽  
Open Source ◽  
Weather Forecasting ◽  
Regional Scale ◽  
Academic Research ◽  
Model System ◽  
Small Scale ◽  
Meteorological Forcing ◽  
Large Eddy Simulation Model

<p>A set of Python-based tools, WRF4PALM, has been developed for offline-nesting of the PALM model system 6.0 into the Weather Research and Forecasting (WRF) modelling system. Time-dependent boundary conditions of the atmosphere are critical for accurate representation of microscale meteorological dynamics in high resolution real-data simulations. WRF4PALM generates initial and boundary conditions from WRF outputs to provide time-varying meteorological forcing for PALM. The WRF model has been used across the atmospheric science community for a broad range of multidisciplinary applications. The PALM model system 6.0 is a turbulence-resolving large-eddy simulation model with an additional Reynolds averaged Navier–Stokes (RANS) mode for atmospheric and oceanic boundary layer studies at microscale (Maronga et al., 2020). Currently PALM has the capability to ingest output from the regional scale Consortium for Small-scale Modelling (COSMO) atmospheric prediction model. However, COSMO is not an open source model which requires a licence agreement for operational use or academic research (). This paper describes and validates the new free and open-source WRF4PALM tools (available on ). Two case studies using WRF4PALM are presented for Christchurch, New Zealand, which demonstrate successful PALM simulations driven by meteorological forcing from WRF outputs. The WRF4PALM tools presented here can potentially be used for micro- and mesoscale studies worldwide, for example in boundary layer studies, air pollution dispersion modelling, wildfire emissions and spread, urban weather forecasting, and agricultural meteorology.</p>

scholarly journals Time Scales of the Trade Wind Boundary Layer Adjustment

2013 ◽  
Vol 70 (4) ◽  
pp. 1071-1083 ◽  
Author(s):  
Gilles Bellon ◽  
Bjorn Stevens
Keyword(s):  
Boundary Layer ◽  
Time Scales ◽  
Time Scale ◽  
Mixed Boundary ◽  
Trade Wind ◽  
Physical Processes ◽  
Layer Depth ◽  
Scale Separation ◽  
Near Surface ◽  
Surface Warming

Abstract The adjustment of the trade wind atmospheric boundary layer to an abrupt sea surface warming is investigated using a large-eddy simulation (LES) and two simple bulk models: a mixed-layer model (MLM), and a model based on the mixing-line hypothesis (XLM). The near-surface temperature adjusts in a few hours, faster than can be expected from the characteristic time scales associated with the physical processes at play. The near-surface humidity adjusts more slowly, with a time scale of about a day, and it exhibits an initial decrease before increasing to its equilibrium value. An analysis of the MLM suggests that the initial tendency of humidity and temperature results from the difference in Bowen ratios between the equilibrium and the perturbation. An analysis of the three linear modes of the XLM shows that the fastest-decaying mode adjusts the subcloud-layer buoyancy, with a constructive interaction of all of the physical processes. The second-fastest-decaying mode is an adjustment of the boundary layer thermodynamical structure and the slowest mode adjusts the boundary layer depth. Approximate analytical expressions of the time scales characterizing these linear modes are derived both for the MLM and the XLM. The MLM exhibits no scale separation between the fastest and second-fastest time scales and a scale separation between these and the slowest time scale only in the case of a shallow well-mixed boundary layer. The XLM exhibits a scale separation between the buoyancy adjustment of the subcloud layer and the overall thermodynamic adjustment, while conserving the scale separation with the slower adjustment of the boundary layer depth.

Electromechanical Bistable Behavior of a Novel Dielectric Elastomer Actuator

2013 ◽  
Vol 81 (4) ◽  
Author(s):  
Tiefeng Li ◽  
Zhanan Zou ◽  
Guoyong Mao ◽  
Shaoxing Qu
Keyword(s):  
High Voltage ◽  
Electrical Breakdown ◽  
Mechanical Energy ◽  
Electrical Energy ◽  
High Voltage Pulse ◽  
Dielectric Elastomer ◽  
Small Scale ◽  
Practical Applications ◽  
Design And Optimization ◽  
Bistable Structure

High voltage is required for the existing dielectric elastomer (DE) actuators to convert electrical energy to mechanical energy. However, maintaining high voltage on DE membranes can cause various failures, such as current leakage and electrical breakdown, which limits their practical applications, especially in small-scale devices. To overcome the above drawback of DE actuators, this paper proposes a new actuation method using DE membranes with a properly designed bistable structure. Experiment shows that the actuator only requires a high-voltage pulse to drive the structure forward and backward with electromechanical snap-through instability. The actuator can maintain its stroke when the voltage is removed. An analytical model based on continuum mechanics is developed, showing good agreement with experiment. The study may inspire the design and optimization of DE transducers.

scholarly journals A theoretical model for horizontal convection at high Rayleigh number

2007 ◽  
Vol 581 ◽  
pp. 251-276 ◽  
Author(s):  
G. O. HUGHES ◽  
R. W. GRIFFITHS ◽  
J. C. MULLARNEY ◽  
W. H. PETERSON
Keyword(s):  
Boundary Layer ◽  
Steady State ◽  
Point Source ◽  
Large Scale ◽  
Numerical Solutions ◽  
Laboratory Data ◽  
Vertical Diffusion ◽  
Horizontal Boundary ◽  
Horizontal Convection ◽  
Dimensional Boundary

We present a simple flow model and solution to describe ‘horizontal convection’ driven by a gradient of temperature or heat flux along one horizontal boundary of a rectangular box. Following laboratory observations of the steady-state convection, the model is based on a localized vertical turbulent plume from a line or point source that is located anywhere within the area of the box and that maintains a stably stratified interior. In contrast to the ‘filling box’ process, the convective circulation involves vertical diffusion in the interior and a stabilizing buoyancy flux distributed over the horizontal boundary. The stabilizing flux forces the density distribution to reach a steady state. The model predictions compare well with previous laboratory data and numerical solutions. In the case of a point source for the plume (the case which best mimics the localized sinking in the large-scale ocean overturning) the thermal boundary layer is much thicker than that given by the two-dimensional boundary layer scaling of H. T. Rossby (Tellus, vol. 50, 1965, p. 242).

scholarly journals Countergradient heat flux observations during the evening transition period

2014 ◽  
Vol 14 (6) ◽  
pp. 7711-7737 ◽  
Author(s):  
E. Blay-Carreras ◽  
E. R. Pardyjak ◽  
D. Pino ◽  
D. C. Alexander ◽  
F. Lohou ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Surface Layer ◽  
Time Scale ◽  
Transition Period ◽  
Potential Temperature ◽  
Buoyancy Flux ◽  
Horizontal Shear ◽  
Evening Transition ◽  
Virtual Potential Temperature

Abstract. Gradient-based turbulence models generally assume that the buoyancy flux ceases to introduce heat into the surface layer of the atmospheric boundary layer in temporal consonance with the gradient of the local virtual potential temperature. Here, we hypothesize that during the evening transition a delay exists between the instant when the buoyancy flux goes to zero and the time when the local gradient of the virtual potential temperature indicates a sign change. This phenomenon is studied using a range of data collected over several Intensive Observational Periods (IOPs) during the Boundary Layer Late Afternoon and Sunset Turbulence field campaign conducted in Lannemezan, France. The focus is mainly on the lower part of the surface layer using a tower instrumented with high-speed temperature and velocity sensors. The results from this work confirm and quantify a flux-gradient delay. Specifically, the observed values of the delay are ~30–80 min. The existence of the delay and its duration can be explained by considering the convective time scale and the competition of forces associated with the classical Rayleigh–Bénard problem. This combined theory predicts that the last eddy formed while the sensible heat flux changes sign during the evening transition should produce a delay. It appears that this last eddy is decelerated through the action of turbulent momentum and thermal diffusivities, and that the delay is related to the convective turn – over time – scale. Observations indicate that as horizontal shear becomes more important, the delay time apparently increases to values greater than the convective turnover time-scale.

scholarly journals An experimental investigation on Lagrangian correlations of small-scale turbulence at low Reynolds number

2007 ◽  
Vol 574 ◽  
pp. 405-427 ◽  
Author(s):  
MICHELE GUALA ◽  
ALEXANDER LIBERZON ◽  
ARKADY TSINOBER ◽  
WOLFGANG KINZELBACH
Keyword(s):  
Reynolds Number ◽  
Time Scales ◽  
Correlation Functions ◽  
Time Scale ◽  
Cross Correlation ◽  
Strain Tensor ◽  
Three Dimensional ◽  
Small Scale ◽  
Production Term ◽  
Long Time

Lagrangian auto- and cross-correlation functions of the rate of strain s2, enstrophy ω2, their respective production terms −sijsjkski and ωiωjsij, and material derivatives, Ds2/Dt and Dω2/Dt are estimated using experimental results obtained through three-dimensional particle tracking velocimetry (three-dimensional-PTV) in homogeneous turbulence at Reλ=50. The autocorrelation functions are used to estimate the Lagrangian time scales of different quantities, while the cross-correlation functions are used to clarify some aspects of the interaction mechanisms between vorticity ω and the rate of strain tensor sij, that are responsible for the statistically stationary, in the Eulerian sense, levels of enstrophy and rate of strain in homogeneous turbulent flow. Results show that at the Reynolds number of the experiment these quantities exhibit different time scales, varying from the relatively long time scale of ω2 to the relatively shorter time scales of s2, ωiωjsij and −sijsjkski. Cross-correlation functions suggest that the dynamics of enstrophy and strain, in this flow, is driven by a set of different-time-scale processes that depend on the local magnitudes of s2 and ω2. In particular, there are indications that, in a statistical sense, (i) strain production anticipates enstrophy production in low-strain–low-enstrophy regions (ii) strain production and enstrophy production display high correlation in high-strain–high-enstrophy regions, (iii) vorticity dampening in high-enstrophy regions is associated with weak correlations between −sijsjkski and s2 and between −sijsjkski and Ds2/Dt, in addition to a marked anti-correlation between ωiωjsij and Ds2/Dt. Vorticity dampening in high-enstrophy regions is thus related to the decay of s2 and its production term, −sijsjkski.

scholarly journals Direct numerical simulation of free convection over a heated plate

2012 ◽  
Vol 712 ◽  
pp. 418-450 ◽  
Author(s):  
Juan Pedro Mellado
Keyword(s):  
Boundary Layer ◽  
Free Convection ◽  
Boundary Conditions ◽  
Similarity Theory ◽  
Buoyancy Flux ◽  
Heated Plate ◽  
Molecular Diffusivity ◽  
Rayleigh Numbers ◽  
Rayleigh Benard ◽  
Overlap Region

AbstractDirect numerical simulations of free convection over a smooth, heated plate are used to investigate unbounded, unsteady turbulent convection. Four different boundary conditions are considered: free-slip or no-slip walls, and constant buoyancy or constant buoyancy flux. It is first shown that, after the initial transient, the vertical structure agrees with observations in the atmospheric boundary layer and predictions from classical similarity theory. A quasi-steady inner layer and a self-preserving outer layer are clearly distinguished, with an overlap region between them of constant turbulent buoyancy flux. The extension of the overlap region reached in our simulations is more than 100 wall units$ \mathop{ ({\kappa }^{3} / {B}_{s} )}\nolimits ^{1/ 4} $, where${B}_{s} $is the surface buoyancy flux and$\kappa $the corresponding molecular diffusivity (the Prandtl number is one). The buoyancy fluctuation inside the overlap region already exhibits the$\ensuremath{-} 1/ 3$power-law scaling with height for the four types of boundary conditions, as expected in the local, free-convection regime. However, the mean buoyancy gradient and the vertical velocity fluctuation are still evolving toward the corresponding power laws predicted by the similarity theory. The second major result is that the relation between the Nusselt and Rayleigh numbers agrees with that reported in Rayleigh–Bénard convection when the heated plate is interpreted as half a convection cell. The range of Rayleigh numbers covered in the simulations is then$5\ensuremath{\times} 1{0}^{7} \text{{\ndash}} 1{0}^{9} $. Further analogies between the two problems indicate that knowledge can be transferred between steady Rayleigh–Bénard and unsteady convection. Last, we find that the inner scaling based on$\{ {B}_{s} , \hspace{0.167em} \kappa \} $reduces the effect of the boundary conditions to, mainly, the diffusive wall layer, the first 10 wall units. There, near the plate, free-slip conditions allow stronger mixing than no-slip ones, which results in 30 % less buoyancy difference between the surface and the overlap region and 30–40 % thinner diffusive sublayers. However, this local effect also entails one global, substantial effect: with an imposed buoyancy, free-slip systems develop a surface flux 60 % higher than that obtained with no-slip walls, which implies more intense turbulent fluctuations across the whole boundary layer and a faster growth.

scholarly journals Non-linear population discrete models with two time scales: re-scaling of part of the slow process

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Luis Sanz ◽  
Rafael Bravo de la Parra ◽  
Marcos Marvá ◽  
Eva Sánchez
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
Linear Models ◽  
Discrete Models ◽  
Fast Time ◽  
Compact Sets ◽  
Practical Applications ◽  
Fast Time Scale ◽  
Non Linear ◽  
Time Systems

Abstract In this work we present a reduction result for discrete-time systems with two time scales. In order to be valid, previous results in the field require some strong hypotheses that are difficult to check in practical applications. Roughly speaking, the iterates of a map as well as their differentials must converge uniformly on compact sets. Here, we eliminate the hypothesis of uniform convergence of the differentials at no significant cost in the conclusions of the result. This new result is then used to extend to non-linear cases the reduction of some population discrete models involving processes acting at different time scales. In practical cases, some processes that occur at a fast time scale are often only measured at slow time intervals, notably mortality. For a general class of linear models that include such a kind of processes, it has been shown that a more realistic approach requires the re-scaling of those processes to be considered at the fast time scale. We develop the same type of re-scaling in some non-linear models and prove the corresponding reduction results. We also provide an application to a particular model of a structured population in a two-patch environment.

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