@misc{MelladoStevensSchmidtetal., author = {Mellado, Juan Pedro and Stevens, Bjorn and Schmidt, Heiko and Peters, Norbert}, title = {Probability density functions in the cloud-top mixing layer}, language = {en} } @misc{MelladoStevensSchmidtetal., author = {Mellado, Juan Pedro and Stevens, Bjorn and Schmidt, Heiko and Peters, Norbert}, title = {Two-fluid formulation of the cloud-top mixing layer for direct numerical simulation}, series = {Theoretical and computational fluid dynamics}, volume = {24}, journal = {Theoretical and computational fluid dynamics}, number = {6}, issn = {1432-2250}, doi = {10.1007/s00162-010-0182-x}, pages = {511 -- 536}, abstract = {A mixture fraction formulation to perform direct numerical simulations of a disperse and dilute two-phase system consisting of water liquid and vapor in air in local thermodynamic equilibrium using a twofluid model is derived and discussed. The goal is to understand the assumptions intrinsic to this simplified but commonly employed approach for the study of two-layer buoyancy reversing systems like the cloud-top mixing layer. Emphasis is placed on molecular transport phenomena. In particular, a formulation is proposed that recovers the actual nondiffusive liquid-phase continuum as a limiting case of differential diffusion. High-order numerical schemes suitable for direct numerical simulations in the compressible and Boussinesq limits are described, and simulations are presented to validate the incompressible approach. As expected, the Boussinesq approximation provides an accurate and efficient description of the flow on the scales (of the order of meters) that are considered.}, language = {en} } @misc{MelladoStevensSchmidtetal., author = {Mellado, Juan Pedro and Stevens, Bjorn and Schmidt, Heiko and Peters, Norbert}, title = {Buoyancy reversal in cloud-top mixing layers}, series = {Quarterly Journal of the Royal Meteorological Society}, volume = {135}, journal = {Quarterly Journal of the Royal Meteorological Society}, number = {641}, issn = {1477-870X}, doi = {10.1002/qj.417}, pages = {963 -- 978}, language = {en} } @inproceedings{MelladoSchmidtStevensetal., author = {Mellado, Juan Pedro and Schmidt, Heiko and Stevens, Bjorn and Peters, Norbert}, title = {Analysis of the cloud top mixing layer using DNS}, language = {en} } @misc{DietzeMelladoStevensetal., author = {Dietze, Eckhard and Mellado, Juan Pedro and Stevens, Bjorn and Schmidt, Heiko}, title = {Study of low-order numerical effects in the two-dimensional cloud-top mixing layer}, series = {Theoretical Computational Fluid Dynamic}, journal = {Theoretical Computational Fluid Dynamic}, issn = {0935-4964}, doi = {doi:10.1007/s00162-012-0263-0}, language = {en} } @inproceedings{MelladoStevensSchmidtetal., author = {Mellado, Juan Pedro and Stevens, Bjorn and Schmidt, Heiko and Peters, Norbert}, title = {The evaporatively driven cloud-top mixing layer}, series = {63rd Annual Meeting of the APS Division of Fluid Dynamics}, booktitle = {63rd Annual Meeting of the APS Division of Fluid Dynamics}, language = {en} } @inproceedings{KumarStevensSchmidtetal., author = {Kumar, Suvarchal Kumar and Stevens, Bj{\"o}rn and Schmidt, Heiko and Mellado, Juan Pedro}, title = {Sensitivity of the ECHAM6 Single Column Model to Vertical Resolution and Implementation of the Level Set Method}, series = {EGU General Assembly 2010, held in Vienna, Austria, 02 - 07 May 2010}, booktitle = {EGU General Assembly 2010, held in Vienna, Austria, 02 - 07 May 2010}, publisher = {European Geophysical Society}, address = {Katlenburg-Lindau}, language = {en} } @inproceedings{DietzeStevensMelladoetal., author = {Dietze, Eckhard and Stevens, Bjorn and Mellado, Juan Pedro and Peters, Norbert and Schmidt, Heiko}, title = {Level set methods for meteorological multi scale problems}, series = {EGU General Assembly 2010, held in Vienna, Austria, 02 - 07 May 2010}, booktitle = {EGU General Assembly 2010, held in Vienna, Austria, 02 - 07 May 2010}, language = {en} } @inproceedings{DietzeSchmidtMelladoetal., author = {Dietze, Eckhard and Schmidt, Heiko and Mellado, Juan Pedro and Stevens, Bjorn}, title = {LES vs. DNS simulation of a two-dimensional evaporatively driven cloud-top mixing layer}, series = {Conference on Multiple Scales in Fluid Dynamics and Meteorology}, booktitle = {Conference on Multiple Scales in Fluid Dynamics and Meteorology}, language = {en} } @inproceedings{MelladoStevensSchmidtetal., author = {Mellado, Juan Pedro and Stevens, Bjorn and Schmidt, Heiko and Peters, Norbert}, title = {Buoyancy reversal in the cloud-top mixing layer}, series = {4th IMS Turbulence Workshop, Workshop, 23-25 March 2009,}, booktitle = {4th IMS Turbulence Workshop, Workshop, 23-25 March 2009,}, language = {en} } @inproceedings{MelladoSchmidtStevensetal., author = {Mellado, Juan Pedro and Schmidt, Heiko and Stevens, Bjorn and Peters, Norbert}, title = {DNS of the turbulent cloud-top mixing layer}, series = {Advances in turbulence XII, proceedings of the 12th EUROMECH European Turbulence Conference, September 7 - 10, 2009, Marburg, Germany}, booktitle = {Advances in turbulence XII, proceedings of the 12th EUROMECH European Turbulence Conference, September 7 - 10, 2009, Marburg, Germany}, publisher = {Springer}, address = {Berlin [u.a.]}, isbn = {978-3-642-03084-0}, pages = {401 -- 404}, language = {en} } @inproceedings{DietzeSchmidtMelladoetal., author = {Dietze, Eckhard and Schmidt, Heiko and Mellado, Juan Pedro and Stevens, Bjorn}, title = {Comparison of LES and DNS results for a two-dimensional evaporatively driven cloud-top mixing layer}, series = {EGU General Assembly 2011, Vienna, Austria, 03 - 08 April 2011}, booktitle = {EGU General Assembly 2011, Vienna, Austria, 03 - 08 April 2011}, language = {en} } @inproceedings{MelladoStevensSchmidtetal., author = {Mellado, Juan Pedro and Stevens, Bjorn and Schmidt, Heiko and Peters, Norbert}, title = {Investigation of the Cloud-Top Interface Using Direct Numerical Simulation}, series = {Oberwolfach reports, Mathematical Theory and Modelling in Atmosphere-Ocean Science}, volume = {7}, booktitle = {Oberwolfach reports, Mathematical Theory and Modelling in Atmosphere-Ocean Science}, number = {3}, doi = {10.4171/OWR/2010/34}, pages = {2061 -- 2062}, language = {en} } @inproceedings{SchmidtMelladoPetersetal., author = {Schmidt, Heiko and Mellado, Juan Pedro and Peters, Norbert and Stevens, Bjorn}, title = {Towards a modular superparameterization for Stratocumulus clouds considering unsteady entrainment}, series = {4th PAN-GCSS Meeting on Advances in modeling and observing clouds and convection, 2-6 June 2008, Toulouse, France}, booktitle = {4th PAN-GCSS Meeting on Advances in modeling and observing clouds and convection, 2-6 June 2008, Toulouse, France}, language = {en} } @inproceedings{SchmidtMelladoPetersetal., author = {Schmidt, Heiko and Mellado, Juan Pedro and Peters, Norbert and Stevens, Bjorn}, title = {Towards modular front tracking for Stratocumulus clouds considering unsteady entrainment processes}, series = {European Geosciences Union General Assembly 2008, Vienna, Austria, 13 - 18 April 2008}, booktitle = {European Geosciences Union General Assembly 2008, Vienna, Austria, 13 - 18 April 2008}, publisher = {European Geophysical Society}, address = {Katlenburg-Lindau}, language = {en} } @inproceedings{MelladoStevensSchmidtetal., author = {Mellado, Juan Pedro and Stevens, Bjorn and Schmidt, Heiko and Peters, Norbert}, title = {New results about the cloud-top entrainment instability}, series = {Conference on Multiple Scales in Fluid Dynamics and Meteorology}, booktitle = {Conference on Multiple Scales in Fluid Dynamics and Meteorology}, pages = {31}, language = {en} } @misc{MelladoStevensSchmidt, author = {Mellado, Juan Pedro and Stevens, Bjorn and Schmidt, Heiko}, title = {Wind shear and buoyancy reversal at the stratocumulus top}, series = {Journal of the Atmospheric Sciences}, volume = {71}, journal = {Journal of the Atmospheric Sciences}, number = {3}, issn = {1520-0469}, pages = {1040 -- 1057}, abstract = {A numerical experiment is designed to study the interaction at the stratocumulus top between a mean vertical shear and the buoyancy reversal due to evaporative cooling, without radiative cooling. Direct numerical simulation is used to eliminate the uncertainty introduced by turbulence models. It is found that the enhancement by shear-induced mixing of the turbulence caused by buoyancy reversal can render buoyancy reversal comparable to other forcing mechanisms. However, it is also found that (i) the velocity jump across the capping inversion Du needs to be relatively large and values of about 1ms21 that are typically associated with the convective motions inside the boundary layer are generally too small and (ii) there is no indication of cloud-top entrainment instability. To obtain these results,parameterizations of the mean entrainment velocity and the relevant time scales are derived from the study of the cloud-top vertical structure. Two overlapping layers can be identified: a background shear layer with a thickness (1/3)(Du)2/Db, where Db is the buoyancy increment across the capping inversion and a turbulence layer dominated by free convection inside the cloud and by shear production inside the relatively thin overlap region. As turbulence intensifies, the turbulence layer encroaches into the background shear layer and defines thereby the entrainment velocity. Particularized to the first research flight of the Second Dynamics andChemistry of theMarine Stratocumulus (DYCOMS II) field campaign, the analysis predicts an entrainment velocity of about 3mms21 after 5-10 min—a velocity comparable to the measurements and thus indicative of the relevance of mean shear in that case.}, language = {en} } @inproceedings{MelladoStevensSchmidt, author = {Mellado, Juan Pedro and Stevens, Bjorn and Schmidt, Heiko}, title = {Wind shear and evaporative cooling at the stratocumulus top}, series = {21st Symposium on Boundary Layers and Turbulence, 9-13 June 2014, Leeds, United Kingdom}, booktitle = {21st Symposium on Boundary Layers and Turbulence, 9-13 June 2014, Leeds, United Kingdom}, abstract = {Turbulent entrainment at the stratocumulus top and its interaction with local processes like radiative or evaporative cooling still remains a source of uncertainty in current atmospheric models. The reason is, at least partly, that the characteristic scales at which those cloud-top processes occur are relatively small, of the order of a few tens of meters, and access to accurate data at those scales has been difficult. In this contribution, we present a simplified model designed to investigate these cloud-top processes in detail and we address some questions regarding the role of buoyancy reversal by evaporative cooling at the cloud top. As a tool, we use direct numerical simulation to remove the uncertainty associated with turbulence models. Buoyancy reversal refers to the formation of negatively buoyant parcels of fluid within an otherwise stable stratification as a consequence of the local cooling caused by the evaporation of the droplets at the cloud interface. This process leads to convective instability, as heavier parcels of fluid lie on top of lighter ones. This instability promotes turbulence, and hence entrainment and further evaporation of droplets, a feedback process that could eventually lead to a rapid dessication of the cloud -- the so-called cloud-top entrainment instability. Recent work has demonstrated that, in contrast to previous postulates, buoyancy reversal caused by evaporative cooling is not a sufficient condition to break up the cloud: turbulence is indeed enhanced, but very mildly. The reason is that buoyancy reversal alone leads to a meta-stable layer as the mixing rate, or entrainment rate, is diffusively limited, so that the eventual breakup of the cloud by buoyancy reversal alone occurs on time scales that are much too long to be relevant to the stratocumulus-top boundary layer. To become relevant, evaporative cooling requires the interaction with other local mechanisms of turbulence generation, like wind shear or radiative cooling. In this work, we study wind shear effects, without radiative cooling. There are at least two reasons to study shear effects. First, shear is ubiquitous, as local shear associated with large-scale eddies will also be evident even in the absence of a mean wind. Second, shear alone cannot sustain a continuous deepening of the layer, as shear generated turbulence will locally thicken the entrainment zone, but in the absence of other sources, the turbulence will eventually decay once a critical entrainment-zone thickness is reached. The latter makes it interesting to combine shear with the convective destabilization of the cloud-top layer through buoyancy reversal, as neither process acting alone is efficient in supporting significant mixing at the cloud top. In contrast, by generating convective eddies which locally thin the entrainment zone, buoyancy reversal might help enhance shear, which in turn locally enhances the mixing which sustains the buoyancy reversal, raising the possibility that the processes are self-reinforcing. Results show that the enhancement by local wind shear can render buoyancy reversal comparable to other forcing mechanisms. However, we also find that (i) the velocity jump across the capping inversion, Δu, needs to be relatively large and typical values of about 1 m s-1 associated with the convective motions inside the boundary layer are generally too small, and (ii) there is no indication of cloud-top entrainment instability. To obtain these results, parametrizations of the mean entrainment velocity and the relevant time scales are derived from the study of the cloud-top vertical structure. Two overlapping layers can be identified: a background shear layer with a thickness (1/3) (Δu)2/(Δb), where Δb is the buoyancy increment across the capping inversion, and a turbulence layer dominated by free convection inside the cloud and by shear production inside the relatively thin overlap region. As turbulence intensifies, the turbulence layer encroaches into the background shear layer and defines thereby the entrainment velocity. Particularized to the first research flight of the Second Dynamics and Chemistry of Marine Stratocumulus (DYCOMS-II) field campaign, the analysis predicts an entrainment velocity of about 3 mm s-1 after 5-10 minutes, a velocity comparable to the measurements and thus indicative of the relevance of mean shear in that case.}, language = {en} } @misc{DietzeSchmidtStevensetal., author = {Dietze, Eckhard and Schmidt, Heiko and Stevens, Bjorn and Mellado, Juan Pedro}, title = {Controlling entrainment in the smoke cloud using level set-based front tracking}, series = {Meteorologische Zeitschrift}, volume = {23}, journal = {Meteorologische Zeitschrift}, number = {6}, doi = {10.1127/metz/2014/0595}, pages = {661 -- 674}, abstract = {Although large-eddy simulation (LES) has been shown to produce a reasonable representation of the turbulent circulations within the stratocumulus-topped boundary layer, it has difficulties to accurately predict cloud-top entrainment rates. In this paper, we present a front-tracking algorithm for LES to untangle the numerical and physical contributions to entrainment. Instead of resolving the cloud-top inversion, we treat it as a discontinuity separating the boundary layer from the free atmosphere and use the level set method to track its location. We apply our method to the smoke cloud test case as presented by BRETHERTON et al. (1999) which is simpler than stratocumulus in that it is only driven by radiative cooling avoiding evaporative feedbacks on entrainment. We present three-dimensional LES results with and without use of the level set method varying the grid resolution and the flux limiter. With the level set method, we prescribe zero entrainment and use this case to evaluate our method's ability to maintain a non-entraining smoke-cloud layer. We use an empirically-based entrainment law to estimate numerical errors. With the level set method, the prescribed entrainment rate was maintained with errors about one order of magnitude smaller than the entrainment errors found in the standard LES. At the same time, the dependence of the entrainment errors on the choice of the limiter was reduced by more than a factor of 10.}, language = {en} } @misc{SchmidtMelladoStevens, author = {Schmidt, Heiko and Mellado, Juan Pedro and Stevens, Bjorn}, title = {Wind Shear and Buoyancy Reversal at the Top of Stratocumulus}, series = {Journal of the atmospheric sciences}, volume = {71}, journal = {Journal of the atmospheric sciences}, number = {3}, issn = {1520-0469}, pages = {1040 -- 1057}, abstract = {A numerical experiment is designed to study the interaction at the stratocumulus top between a mean vertical shear and the buoyancy reversal due to evaporative cooling, without radiative cooling. Direct numerical simulation is used to eliminate the uncertainty introduced by turbulence models. It is found that the enhancement by shear-induced mixing of the turbulence caused by buoyancy reversal can render buoyancy reversal comparable to other forcing mechanisms. However, it is also found that (i) the velocity jump across the capping inversion Du needs to be relatively large and values of about 1ms21 that are typically associated with the convective motions inside the boundary layer are generally too small and (ii) there is no indication of cloud-top entrainment instability. To obtain these results, parameterizations of the mean entrainment velocity and the relevant time scales are derived from the study of the cloud-top vertical structure. Two overlapping layers can be identified: a background shear layer with a thickness (1/3)(Du)2/Db, where Db is the buoyancy increment across the capping inversion and a turbulence layer dominated by free convection inside the cloud and by shear production inside the relatively thin overlap region. As turbulence intensifies, the turbulence layer encroaches into the background shear layer and defines thereby the entrainment velocity. Particularized to the first research flight of the Second Dynamics andChemistry of theMarine Stratocumulus (DYCOMS II) field campaign, the analysis predicts an entrainment velocity of about 3mms21 after 5-10 min—a velocity comparable to the measurements and thus indicative of the relevance of mean shear in that case.}, language = {en} }