De Santi, F.

Di Savino, S.

Gallana, L.

Iovieno, M.

Richiardone, R.

English

GALLANA, LUCA

DE SANTI, FRANCESCA

DI SAVINO, SILVIO

IOVIENO, MICHELE

PORTO@iris (Publications Open Repository TOrino - Politecnico di Torino)

04 August 2020POLITECNICO DI TORINORepository ISTITUZIONALEEntrainment temporal evolution across stably and unstably stratified vapor/clear air interfaces / Gallana, L.; De Santi, F.;Di Savino, S.; Richiardone, R.; Iovieno, M.. - STAMPA. - (2015). ((Intervento presentato al convegno 15th EuropeanTurbulence Conference tenutosi a Delft nel 25 - 28 agosto 2015.OriginalEntrainment temporal evolution across stably and unstably stratified vapor/clear air interfacesPublisher:PublishedDOI:Terms of use:openAccessPublisher copyright(Article begins on next page)This article is made available under terms and conditions as specified in the  corresponding bibliographic description inthe repositoryAvailability:This version is available at: 11583/2630421 since: 2016-02-09T10:41:15Z15TH EUROPEAN TURBULENCE CONFERENCE, 25-28 AUGUST, 2015, DELFT, THE NETHERLANDSENTRAINMENT TEMPORAL EVOLUTION ACROSS STABLY AND UNSTABLY STRATIFIEDVAPOR/CLEAR AIR INTERFACES.Luca Gallana1, Francesca De Santi1, Silvio Di Savino1, Renzo Richiardone2, Michele Iovieno1 & DanielaTordella11Dipartimento di Ingegneria Meccanica ed Aerospaziale, Politecnico di Torino, Torino, Italy2Dipartimento di Fisica, Università di Torino, Torino, ItalyAbstract Warm clouds as stratocumuli swathe a significant part of earth’s surface and play a major role in the global dynamics ofatmosphere by strongly reflecting incoming solar radiation so that an accurate representation of their dynamics is important in large-scale analyses of atmoshperic flows [9].The mixing and entrainment processes at the cloud top have been identified as fundamentalto determine the internal structure of warm clouds, so that a clear and complete understanding of their physics is required [1]. Theaim of this work is to study some of the basic phenomena which occur at a stratified interface focusing on the smallest scales of theflow which influence. These scales are important to understand the global dynamic of clouds, as pointed out by Malinowsky et al.[3]. To achieve the results, a campaign of high-resolution simulation of the local transport through a dry/moist air were performedby the means of Direct Numerical Simulations (DNS) using our home produced computational code that implements a de-aliasedpseudospectral Fourier-Galerkin spatial discretization and an explicit low storage fourth order Runge-Kutta time integration scheme[2].We consider the interface between clear air and moist air in a 6m × 6m × 12m parallelepipedic domain coupling two homogeneousand isotropic turbulent regions with different kinetic energy that interact through a mixing layer. The energy ratio is of the same orderof the ones measured in warm clouds (see, e.g., [3]) and, furthermore, it allows us to compare our results with experiments on shearlessmixing (see [8, 7]) in absence of any stratification. For each simulation two interfaces have been obtained, one in highly stably stratifiedcondition, and one in unstable condition (see figure 1 for the flow configuration). The dynamics of interfaces is analyzed through anHigh kinetic energyLow kineticenergyClear airMoist airClear airTemperatureprofilezVaporprofileKineticenergyprofileLow kineticenergyStableinterfaceUnstableinterfaceFigure 1. Scheme of the initial distribution along the vertical direction x3 for the mean kinetic energy (black line), vapor concentration(blue line) and temperature profile (red line).initial temperature perturbation located across one of the vapor/clear air interfaces thus generating a local stable layer, see red line infigure 1; the water vapor is treated as a passive scalar. The level of stratification is quantified with the Froude number, Fr2 = u2rmsL2αg dTdz.For the stable cases, the Froude numbers considered ranges from 12.7 (weak stratification) to 0.6 (intense stratification), while for theunstable cases Fr2 ranges from -250 to -16. In both stable and unstable cases the evolution of the system can be split in two differentphases. In the first one, the buoyancy terms are negligible, and there are no significant differences with respect to a non-stratified case.As the system evolves, the effect of stratification becomes relevant (as soon as the stratification is intense).About the unstable case layer we observe a high intermittency and an intense growth rate of the layer, which becomes overdiffusive inthe case Fr2 = −16. In particular, the entrainment, after an initial decay, asimptotically always shows a positive growth rate.Here, for reason of space, we give details about the stably stratified layer which presents a more complex dynamics associated to theonset of a pocket very low turbulent kinetic energy. In figure 2, a visualization of the vertical velocity fluctuations in a portion of avertical surface containing the stably stratified layer is shown. It can be observed the onset of a sub-layer characterized by the presenceof low values of kinetic turbulent energy. At about 8 time scales, we observe the 8% of the energy in the wapor cloud and the 50% of thekinetic energy in the clear-air region. A similar trend was also observed in the LES cloud topped boundary layer simulations carried outby using Deardoff TKE model (NCAR group) and by using the ARAP TKE model (WVU group), [6]. The presence of such sublayerinduces the formation of two local interfaces. Both of these interfaces present an intermittent behavior, and the entrainment (flux of dryair into the moist one) is blocked, as shown in figure 3, where the velocity of the moist air front we can be considered a characteristicparameter, since the entrainment of clear air is responsible of the growth of the cloud [4, 5]. As a consequence, the entrainment of clearair is confined to a thin interfacial layer. Also the dissipative terms inside the pit becomes relatively more important compared to thekinetic energy, making the pit deeper and deeper with respect to the external regions.0.0 1.0-1.00.0-1.01.00.100.05x 1[m]x3[m]u3 [m/s]Figure 2. Elevation plot of the vertical component of the velocity in a vertical plane. The elevation is proportional to the square ofvertical velocity fluctuations and the colors respect the velocity direction verse (blue for downward, red for upward). Fr = 1.8, 8 eddyturnover times. The formation of the pit of kinetic energy can be observed.-0.02 0 0.02 0.04 0.06 0.08 0.1 0  2  4  6  8  10  12we =dz(θ=0.25)dtt/τweFr=12.7Fr=4.4Fr=1.8Fr=0.6Figure 3. Evolution of the water vapor front vertical velocity we over time in case of stable stratification (different Fr are hererepresented). we is the time derivative of the horizontal plane where the mean water vapor concentation θ is equal to 0.25 and is ameasure of the entrainment of dry air into the moist one.References[1] H. Gerber, G. Frick, Szymon P. Malinowski, H. Jonsson, D. Khelif, and Steven K. Krueger. Entrainment rates and microphysics in POSTstratocumulus. J. Geohys. Res. D, 118(21):12094–12109, NOV 16 2013.[2] M. Iovieno, C. Cavazzoni, and D. Tordella. A new technique for a parallel dealiased pseudospectral Navier-Stokes code. Comp. Phys. Comm.,141:365–374, 2001.[3] S. P. Malinowski, H. Gerber, I. Jen-La Plante, M. K. Kopec, W. Kumala, K. Nurowska, P. Y. Chuang, D. Khelif, and K. E. Haman. Physics ofStratocumulus Top (POST): turbulent mixing across capping inversion. Atmos. Chem. Phys., 13(24):12171–12186, 2013.[4] Juan Pedro Mellado. The evaporatively driven cloud-top mixing layer. J. Fluid Mech., 660:5–36, OCT 10 2010.[5] CH Moeng. Entrainment rate, cloud fraction, and liquid water path of PBL stratocumulus clouds. J. Atmos. Sci., 57(21):3627–3643, NOV 1 2000.[6] CH Moeng, WR Cotton, C Bretherton, A Chlond, M Khairoutdinov, S Krueger, WS Lewellen, MK MacVean, JRM Pasquier, HA Rand,AP Siebesma, B Stevens, and RI Sykes. Simulation of a stratocumulus-topped planetary boundary layer: Intercomparison among differentnumerical codes. Bull. Am. Meteorol. Soc., 77(2):261–278, FEB 1996.[7] D. Tordella and M. Iovieno. Small scale anisotropy in the turbulent shearless mixings. Phys. Rev. Lett., 107:194501, 2011.[8] S. Veeravalli and Z. Warhaft. The shearless turbulence mixing layer. J. Fluid Mech., 207:191–229, 1989.[9] Robert Wood. Stratocumulus Clouds. Mon. Weather Rev., 140(8):2373–2423, AUG 2012.

Entrainment temporal evolution across stably and unstably stratified vapor/clear air interfaces

Gallana, Luca

De Santi, Francesca

Di Savino, Silvio

Iovieno, Michele

PORTO Publications Open Repository TOrino

Politecnico di TorinoPorto Institutional Repository[Proceeding] Entrainment temporal evolution across stably and unstablystratified vapor/clear air interfacesOriginal Citation:Gallana, L.; De Santi, F.; Di Savino, S.; Richiardone, R.; Iovieno, M. (2015). Entrainmenttemporal evolution across stably and unstably stratified vapor/clear air interfaces. In: 15th EuropeanTurbulence Conference, Delft, 25 - 28 agosto 2015.Availability:This version is available at : http://porto.polito.it/2630421/ since: February 2016Terms of use:This article is made available under terms and conditions applicable to Open Access Policy Article("Public - All rights reserved") , as described at http://porto.polito.it/terms_and_conditions.htmlPorto, the institutional repository of the Politecnico di Torino, is provided by the University Libraryand the IT-Services. The aim is to enable open access to all the world. Please share with us howthis access benefits you. Your story matters.(Article begins on next page)15TH EUROPEAN TURBULENCE CONFERENCE, 25-28 AUGUST, 2015, DELFT, THE NETHERLANDSENTRAINMENT TEMPORAL EVOLUTION ACROSS STABLY AND UNSTABLY STRATIFIEDVAPOR/CLEAR AIR INTERFACES.Luca Gallana1, Francesca De Santi1, Silvio Di Savino1, Renzo Richiardone2, Michele Iovieno1 & DanielaTordella11Dipartimento di Ingegneria Meccanica ed Aerospaziale, Politecnico di Torino, Torino, Italy2Dipartimento di Fisica, Università di Torino, Torino, ItalyAbstract Warm clouds as stratocumuli swathe a significant part of earth’s surface and play a major role in the global dynamics ofatmosphere by strongly reflecting incoming solar radiation so that an accurate representation of their dynamics is important in large-scale analyses of atmoshperic flows [9].The mixing and entrainment processes at the cloud top have been identified as fundamentalto determine the internal structure of warm clouds, so that a clear and complete understanding of their physics is required [1]. Theaim of this work is to study some of the basic phenomena which occur at a stratified interface focusing on the smallest scales of theflow which influence. These scales are important to understand the global dynamic of clouds, as pointed out by Malinowsky et al.[3]. To achieve the results, a campaign of high-resolution simulation of the local transport through a dry/moist air were performedby the means of Direct Numerical Simulations (DNS) using our home produced computational code that implements a de-aliasedpseudospectral Fourier-Galerkin spatial discretization and an explicit low storage fourth order Runge-Kutta time integration scheme[2].We consider the interface between clear air and moist air in a 6m × 6m × 12m parallelepipedic domain coupling two homogeneousand isotropic turbulent regions with different kinetic energy that interact through a mixing layer. The energy ratio is of the same orderof the ones measured in warm clouds (see, e.g., [3]) and, furthermore, it allows us to compare our results with experiments on shearlessmixing (see [8, 7]) in absence of any stratification. For each simulation two interfaces have been obtained, one in highly stably stratifiedcondition, and one in unstable condition (see figure 1 for the flow configuration). The dynamics of interfaces is analyzed through anHigh kinetic energyLow kineticenergyClear airMoist airClear airTemperatureprofilezVaporprofileKineticenergyprofileLow kineticenergyStableinterfaceUnstableinterfaceFigure 1. Scheme of the initial distribution along the vertical direction x3 for the mean kinetic energy (black line), vapor concentration(blue line) and temperature profile (red line).initial temperature perturbation located across one of the vapor/clear air interfaces thus generating a local stable layer, see red line infigure 1; the water vapor is treated as a passive scalar. The level of stratification is quantified with the Froude number, Fr2 = u2rmsL2αg dTdz.For the stable cases, the Froude numbers considered ranges from 12.7 (weak stratification) to 0.6 (intense stratification), while for theunstable cases Fr2 ranges from -250 to -16. In both stable and unstable cases the evolution of the system can be split in two differentphases. In the first one, the buoyancy terms are negligible, and there are no significant differences with respect to a non-stratified case.As the system evolves, the effect of stratification becomes relevant (as soon as the stratification is intense).About the unstable case layer we observe a high intermittency and an intense growth rate of the layer, which becomes overdiffusive inthe case Fr2 = −16. In particular, the entrainment, after an initial decay, asimptotically always shows a positive growth rate.Here, for reason of space, we give details about the stably stratified layer which presents a more complex dynamics associated to theonset of a pocket very low turbulent kinetic energy. In figure 2, a visualization of the vertical velocity fluctuations in a portion of avertical surface containing the stably stratified layer is shown. It can be observed the onset of a sub-layer characterized by the presenceof low values of kinetic turbulent energy. At about 8 time scales, we observe the 8% of the energy in the wapor cloud and the 50% of thekinetic energy in the clear-air region. A similar trend was also observed in the LES cloud topped boundary layer simulations carried outby using Deardoff TKE model (NCAR group) and by using the ARAP TKE model (WVU group), [6]. The presence of such sublayerinduces the formation of two local interfaces. Both of these interfaces present an intermittent behavior, and the entrainment (flux of dryair into the moist one) is blocked, as shown in figure 3, where the velocity of the moist air front we can be considered a characteristicparameter, since the entrainment of clear air is responsible of the growth of the cloud [4, 5]. As a consequence, the entrainment of clearair is confined to a thin interfacial layer. Also the dissipative terms inside the pit becomes relatively more important compared to thekinetic energy, making the pit deeper and deeper with respect to the external regions.0.0 1.0-1.00.0-1.01.00.100.05x 1[m]x3[m]u3 [m/s]Figure 2. Elevation plot of the vertical component of the velocity in a vertical plane. The elevation is proportional to the square ofvertical velocity fluctuations and the colors respect the velocity direction verse (blue for downward, red for upward). Fr = 1.8, 8 eddyturnover times. The formation of the pit of kinetic energy can be observed.-0.02 0 0.02 0.04 0.06 0.08 0.1 0  2  4  6  8  10  12we =dz(θ=0.25)dtt/τweFr=12.7Fr=4.4Fr=1.8Fr=0.6Figure 3. Evolution of the water vapor front vertical velocity we over time in case of stable stratification (different Fr are hererepresented). we is the time derivative of the horizontal plane where the mean water vapor concentation θ is equal to 0.25 and is ameasure of the entrainment of dry air into the moist one.References[1] H. Gerber, G. Frick, Szymon P. Malinowski, H. Jonsson, D. Khelif, and Steven K. Krueger. Entrainment rates and microphysics in POSTstratocumulus. J. Geohys. Res. D, 118(21):12094–12109, NOV 16 2013.[2] M. Iovieno, C. Cavazzoni, and D. Tordella. A new technique for a parallel dealiased pseudospectral Navier-Stokes code. Comp. Phys. Comm.,141:365–374, 2001.[3] S. P. Malinowski, H. Gerber, I. Jen-La Plante, M. K. Kopec, W. Kumala, K. Nurowska, P. Y. Chuang, D. Khelif, and K. E. Haman. Physics ofStratocumulus Top (POST): turbulent mixing across capping inversion. Atmos. Chem. Phys., 13(24):12171–12186, 2013.[4] Juan Pedro Mellado. The evaporatively driven cloud-top mixing layer. J. Fluid Mech., 660:5–36, OCT 10 2010.[5] CH Moeng. Entrainment rate, cloud fraction, and liquid water path of PBL stratocumulus clouds. J. Atmos. Sci., 57(21):3627–3643, NOV 1 2000.[6] CH Moeng, WR Cotton, C Bretherton, A Chlond, M Khairoutdinov, S Krueger, WS Lewellen, MK MacVean, JRM Pasquier, HA Rand,AP Siebesma, B Stevens, and RI Sykes. Simulation of a stratocumulus-topped planetary boundary layer: Intercomparison among differentnumerical codes. Bull. Am. Meteorol. Soc., 77(2):261–278, FEB 1996.[7] D. Tordella and M. Iovieno. Small scale anisotropy in the turbulent shearless mixings. Phys. Rev. Lett., 107:194501, 2011.[8] S. Veeravalli and Z. Warhaft. The shearless turbulence mixing layer. J. Fluid Mech., 207:191–229, 1989.[9] Robert Wood. Stratocumulus Clouds. Mon. Weather Rev., 140(8):2373–2423, AUG 2012.

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Entrainment temporal evolution across stably and unstably stratified vapor/clear air interfaces

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