Time-dependent response of a zonally averaged ocean–atmosphere–sea ice model to Milankovitch forcing

Author Posting. © The Author(s), 2010. This is the author's version of the work. It is posted here by permission of Springer-Verlag for personal use, not for redistribution. The definitive version was published in Climate Dynamics 6 (2010): 763-779, doi:10.1007/s00382-010-0790-6.An ocean-atmosphere-sea ice model is developed to explore the time-dependent response of climate to Milankovitch forcing for the time interval 5-3 Myr BP. The ocean component is a zonally averaged model of the circulation in five basins (Arctic, Atlantic, Indian, Pacific, and Southern Oceans). The atmospheric component is a one-dimensional (latitudinal) energy balance model, and the sea-ice component is a thermodynamic model. Two numerical experiments are conducted. The first experiment does not include sea ice and the Arctic Ocean; the second experiment does. Results from the two experiments are used to investigate (i) the response of annual mean surface air and ocean temperatures to Milankovitch forcing, and (ii) the role of sea ice in this response. In both experiments, the response of air temperature is dominated by obliquity cycles at most latitudes. On the other hand, the response of ocean temperature varies with latitude and depth. Deep water formed between 45°N-65°N in the Atlantic Ocean mainly responds to precession. In contrast, deep water formed south of 60°S responds to obliquity when sea ice is not included. Sea ice acts as a time-integrator of summer insolation changes such that annual mean sea-ice conditions mainly respond to obliquity. Thus, in the presence of sea ice, air temperature changes over the sea ice are amplified, and temperature changes in deep water of southern origin are suppressed since water below sea ice is kept near the freezing point.This work was supported by an NSERC Discovery Grant awarded to L.A.M. We also thank GEC3 for a Network Grant

Measurements and computations of flow in an urban street system

We present results from laboratory and computational experiments on the turbulent flow over an array of rectangular blocks modelling a typical, asymmetric urban canopy at various orientations to the approach flow. The work forms part of a larger study on dispersion within such arrays (project DIPLOS) and concentrates on the nature of the mean flow and turbulence fields within the canopy region, recognising that unless the flow field is adequately represented in computationalmodels there is no reason to expect realistic simulations of the nature of the dispersion of pollutants emitted within the canopy. Comparisons between the experimental data and those obtained from both large-eddy simulation (LES) and direct numerical simulation (DNS) are shown and it is concluded that careful use of LES can produce generally excellent agreement with laboratory and DNS results, lending further confidence in the use of LES for such situations. Various crucial issues are discussed and advice offered to both experimentalists and those seeking to compute canopy flows with turbulence resolving models

Numerical simulation of cloud-clear air interfacial mixing: Effects on cloud microphysics

This paper extends the previously published numerical study of Andrejczuk et al. on microscale cloud-clear air mixing. Herein, the primary interest is on microphysical transformations. First, a convergence study is performed - with well-resolved direct numerical simulation of the interfacial mixing in the limit - to optimize the design of a large series of simulations with varying physical parameters. The principal result is that all conclusions drawn from earlier low-resolution (Δx = 10-2 m) simulations are corroborated by the high-resolution (Δx = 0.25 × 10-2 m) calculations, including the development of turbulent kinetic energy (TKE) and the evolution of microphysical properties. This justifies the use of low resolution in a large set of sensitivity simulations, where microphysical transformations are investigated in response to variations of the initial volume fraction of cloudy air, TKE input, liquid water mixing ratio in cloudy filaments, relative humidity (RH) of clear air, and size of cloud droplets. The simulations demonstrate that regardless of the initial conditions the evolutions of the number of cloud droplets and the mean volume radius follow a universal path dictated by the TKE input, RH of clear air filaments, and the mean size of cloud droplets. The resulting evolution path only weakly depends on the progress of the homogenization. This is an important conclusion because it implies that a relatively simple rule can be developed for representing the droplet-spectrum evolution in cloud models that apply parameterized microphysics. For the low-TKE input, when most of the TKE is generated by droplet evaporation during mixing and homogenization, an inhomogencous scenario is observed with approximately equal changes in the dimensionless droplet number and mean volume radius cubed. Consistent with elementary scale analysis, higher-TKE inputs, higher RH of cloud-free filaments, and larger cloud droplets enhance the homogeneity of mixing. These results are discussed in the context of observations of entrainment and mixing in natural clouds. © 2006 American Meteorological Society

Numerical simulation of cloud-clear air interfacial mixing: Homogeneous versus inhomogeneous mixing

This note presents an analysis of several dozens of direct numerical simulations of the cloud - clear air mixing in a setup of decaying moist turbulence with bin microphysics. The goal is to assess the instantaneous relationship between the homogeneity of mixing and the ratio of the time scales of droplet evaporation and turbulent homogenization. Such a relationship is important for developing improved microphysical parameterizations for large-eddy simulation of clouds. The analysis suggests a robust relationship for the range of time scale ratios between 0.5 and 10. Outside this range, the scatter of numerical data is significant, with smaller and larger time scale ratios corresponding to mixing scenarios that approach the extremely inhomogeneous and homogeneous limits, respectively. This is consistent with the heuristic argument relating the homogeneity of mixing to the time scale ratio. © 2009 American Meteorological Society

Cloud-clear air interfacial mixing: Anisotropy of turbulence generated by evaporation of liquid water. Laboratory observations and numerical modelling

Small scale mixing of cloud with unsaturated environment is investigated in numerical simulations (spatial resolution of 2.5mm) and in laboratory cloud chamber experiments by means of Particle Image Velocimetry (PIV) with spatial resolution of 0.07mm. Despite substantial differences in physical conditions and various spatial resolutions (resolving well the dissipation scale in the laboratory and applying grid length larger than the Kolmogorov scale in the simulation), results of both investigations indicate that small-scale turbulence in such conditions is highly anisotropic with the preferred direction in the vertical. Buoyancy forces resulting from evaporation of cloud droplets substantially influence smallest scales of turbulence. The vertical direction, in which buoyancy force acts, is preferred. Typically, <(u′) 2> is about two times smaller than <(w′)2>. The probability distribution functions of w′ are wider than those of u′. It is still uncertain to what extent these results apply to real clouds. In situ measurements of turbulent velocity fluctuations from various types of clouds are necessary to validate common assumptions of small-scale cloud isotropy

Laboratory and modeling studies of cloud-clear air interfacial mixing: Anisotropy of small-scale turbulence due to evaporative cooling

Small-scale mixing between cloudy air and unsaturated clear air is investigated in numerical simulations and in a laboratory cloud chamber. Despite substantial differences in physical conditions and some differences in resolved scales of motion, results of both studies indicate that small-scale turbulence generated through cloud-clear air interfacial mixing is highly anisotropic. For velocity fluctuations, numerical simulations and cloud chamber observations demonstrate that the vertical velocity variance is up to a factor of two larger than the horizontal velocity variance. The Taylor microscales calculated separately for the horizontal and vertical directions also indicate anisotropy of turbulent eddies. This anisotropy is attributed to production of turbulent kinetic energy (TKE) by buoyancy forces due to evaporative cooling of cloud droplets at the cloud-clear air interface. Numerical simulations quantify the effects of buoyancy oscillations relative to the values expected from adiabatic and isobaric mixing, standardly assumed in cloud physics. The buoyancy oscillations result from microscale transport of liquid water due to the gravitational sedimentation of cloud droplets. In the particular modeling setup considered here, these oscillations contribute to about a fifth of the total TKE production. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft

Direct numerical simulation of fully saturated flow in natural porous media at the pore scale: a comparison of three computational systems

Direct numerical simulations of flow through two millimeter-scale rock samples of limestone and sandstone are performed using three diverse fluid dynamic simulators. The resulting steady-state velocity fields are compared in terms of the associated empirical probability density functions (PDFs) and key statistics of the velocity fields. The pore space geometry of each sample is imaged at 5.06−μm voxel size resolution using X-ray microtomography. The samples offer contrasting characteristics in terms of total connected porosity (about 0.31 for the limestone and 0.07 for the sandstone) and are typical of several applications in hydrogeology and petroleum engineering. The three-dimensional fluid velocity fields within the explicit pore spaces are simulated using ANSYS® FLUENT® ANSYS Inc. (2009), EULAG Prusa et al. (Comput. Fluids 37, 1193–1207 2008), and SSTOKES Sarkar et al. (2002). These computational approaches are highly disperse in terms of algorithmic complexity, differ in terms of their governing equations, the adopted numerical methodologies, the enforcement of internal no-slip boundary conditions at the fluid-solid interface, and the computational mesh structure. As metrics of comparison to probe in a statistical sense the internal similarities/differences across sample populations of velocities obtained through the computational systems, we consider (i) integral quantities, such as the Darcy flux and (ii) main statistical moments of local velocity distributions including local correlations between velocity fields. Comparison of simulation results indicates that mutually consistent estimates of the state of flow are obtained in the analyzed samples of natural pore spaces despite the considerable differences associated with the three computational approaches. We note that in the higher porosity limestone sample, the structures of the velocity fields obtained using ANSYS FLUENT and EULAG are more alike than either compared against the results obtained using SSTOKES. In the low-porosity sample, the structures of the velocity fields obtained by EULAG and SSTOKES are more similar than either is to the fields obtained using ANSYS FLUENT. With respect to macroscopic quantities, ANSYS FLUENT and SSTOKES provide similar results in terms of the average vertical velocity for both of the complex microscale geometries considered, while EULAG tends to render the largest velocity values. The influence of the pore space structure on fluid velocity field characteristics is also discussed