Fractal reconstruction of the subgrid scales in turbulence models in applications to cloud microphysics

Mapping Intimacies ◽

10.5194/egusphere-egu2020-18503 ◽

2020 ◽

Author(s):

Emmanuel Akinlabi ◽

Marta Waclawczyk ◽

Szymon Malinowski

Keyword(s):

Climate Models ◽

A Priori ◽

Turbulence Models ◽

Random Variable ◽

Fractal Model ◽

Cloud Microphysics ◽

Small Scale ◽

Mixing Processes ◽

Subgrid Scales ◽

Scale Turbulence

Modelling of small-scale turbulence in the atmosphere play a significant role in improving our understanding of cloud processes, thereby contributing to the development of better parameterization of climate models. One of the important problems is related to the transport of cloud particles, their activation and growth, which are influenced by small-scale turbulence motions. The idea presented in this work is to use fractal interpolation to reconstruct structures which are typically not resolved in the Large Eddy Simulations (LES) of clouds. Known filtered values of velocities on LES are basis of the reconstruction. The reconstructed small scales depend on the stretching parameter d, which is related to the fractal dimension of the signal. In many previous studies, the stretching parameter values were assumed to be constant in space and time. We modify this approach by treating the stretching parameter as a random variable with a prescribed probability density function (pdf). This function can be determined from a priori analysis of numerical or experimental data and within a certain range of wavenumbers it has a universal form, independent of the Reynolds number. We show, such modification leads to improvement in terms of reconstruction of two-point statistics of turbulent velocities. Preliminary results of simulations with Lagrangian particles (superdroplets) in the reconstructed field show the fractal model properly mimics the turbulent mixing processes at subgrid scales.

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Field study of the dynamics and modelling of subgrid-scale turbulence in a stable atmospheric surface layer over a glacier

Journal of Fluid Mechanics ◽

10.1017/s0022112010004015 ◽

2010 ◽

Vol 665 ◽

pp. 480-515 ◽

Cited By ~ 47

Author(s):

ELIE BOU-ZEID ◽

CHAD HIGGINS ◽

HENDRIK HUWALD ◽

CHARLES MENEVEAU ◽

MARC B. PARLANGE

Keyword(s):

Surface Layer ◽

Atmospheric Surface Layer ◽

Dynamic Models ◽

A Priori ◽

Small Scale ◽

Stability Parameters ◽

Stable Conditions ◽

Stable Surface Layer ◽

Subgrid Scales ◽

Scale Turbulence

A field experiment – the Snow Horizontal Array Turbulence Study (SnoHATS) – has been performed over an extensive glacier in Switzerland in order to study small-scale turbulence in the stable atmospheric surface layer, and to investigate the role, dynamics and modelling of the subgrid scales (SGSs) in the context of large-eddy simulations. Thea prioridata analysis aims at comparing the role and behaviour of the SGSs under stable conditions with previous studies under neutral or unstable conditions. It is found that the SGSs in a stable surface layer remain an important sink of temperature variance and turbulent kinetic energy from the resolved scales and carry a significant portion of the fluxes when the filter scale is larger than the distance to the wall. The fraction of SGS fluxes (out of the total fluxes) is found to be independent of stability. In addition, the stress–strain alignment is similar to the alignment under neutral and unstable conditions. The model coefficients vary considerably with stability but in a manner consistent with previous findings, which also showed that scale-dependent dynamic models can capture this variation. Furthermore, the variation of the coefficients for both momentum and heat SGS fluxes can be shown to be better explained by stability parameters based on vertical gradients, rather than vertical fluxes. These findings suggest that small-scale turbulence dynamics and SGS modelling under stable conditions share many important properties with neutral and convective conditions, and that a unified approach is thus possible. This paper concludes with a discussion of some other challenges for stable boundary-layer simulations that are not encountered in the neutral or unstable cases.

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Some statistical properties of small scale turbulence in an atmospheric boundary layer

Journal of Fluid Mechanics ◽

10.1017/s002211207000054x ◽

1970 ◽

Vol 41 (1) ◽

pp. 141-152 ◽

Cited By ~ 48

Author(s):

R. W. Stewart ◽

J. R. Wilson ◽

R. W. Burling

Keyword(s):

Boundary Layer ◽

Lognormal Distribution ◽

A Priori ◽

Inertial Subrange ◽

Small Scale ◽

Order Structure ◽

Third Order ◽

The Difference ◽

Scale Turbulence ◽

Derivatives Of

Derivatives of velocity signals obtained in a turbulent boundary layer are examined for correspondence to the lognormal distribution. It is found that there is rough agreement but that unlikely events at high values are much less common in the observed fields than would be inferred from the lognormal distribution. The actual distributions correspond more to those obtained from a random walk with a limited number of steps, so the difference between these distributions and the lognormal may be related to the fact that the Reynolds number is finite.The third-order structure function is examined, and found to be roughly consistent with the existence of an inertial subrange of a Kolmogoroff equilibrium reacute;gime over a range of scale which is a priori reasonable but which is far less extensive than the $-\frac{5}{3}$ region of the spectrum.

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Small-scale mixing processes enhancing troposphere-to-stratosphere transport by pyro-cumulonimbus storms

Atmospheric Chemistry and Physics Discussions ◽

10.5194/acpd-7-10371-2007 ◽

2007 ◽

Vol 7 (4) ◽

pp. 10371-10403

Author(s):

G. Luderer ◽

J. Trentmann ◽

K. Hungershöfer ◽

M. Herzog ◽

M. Fromm ◽

...

Keyword(s):

Forest Fires ◽

Lower Stratosphere ◽

Deep Convection ◽

Cloud Microphysics ◽

Small Scale ◽

Temperature Pattern ◽

Mixing Processes ◽

Close Link ◽

Brightness Temperatures ◽

Cloud Resolving Model

Abstract. Deep convection induced by large forest fires is an efficient mechanism for transport of aerosol particles and trace gases into the upper troposphere and lower stratosphere (UT/LS). For many pyro-cumulonimbus clouds (pyroCbs) as well as other cases of severe convection without fire forcing, radiometric observations of cloud tops in the thermal infrared (IR) reveal characteristic structures, featuring a region of relatively high brightness temperatures (warm center) surrounded by a U-shaped region of low brightness temperatures. We performed a numerical simulation of a specific case study of pyroCb using a non-hydrostatic cloud resolving model with a two-moment cloud microphysics parameterization and a prognostic turbulence scheme. The model is able to reproduce the thermal IR structure as observed from satellite radiometry. Our findings establish a close link between the observed temperature pattern and small-scale mixing processes atop and downwind of the overshooting dome of the pyroCb. Such small-scale mixing processes are strongly enhanced by the formation and breaking of a stationary gravity wave induced by the overshoot. They are found to enhance the stratospheric penetration of the smoke by up to 30 K and thus are of major significance for irreversible transport of forest fire smoke into the lower stratosphere.

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Statistical Properties of Subgrid-Scale Turbulence Models

Annual Review of Fluid Mechanics ◽

10.1146/annurev-fluid-060420-023735 ◽

2021 ◽

Vol 53 (1) ◽

pp. 255-286

Author(s):

Robert D. Moser ◽

Sigfried W. Haering ◽

Gopal R. Yalla

Keyword(s):

Turbulent Flows ◽

A Priori ◽

Turbulence Models ◽

Statistical Characteristics ◽

Scale Model ◽

Subgrid Scale ◽

Dissipation Energy ◽

Eddy Simulation ◽

Scale Turbulence ◽

Subgrid Stress

This review examines large eddy simulation (LES) models from the perspective of their a priori statistical characteristics. The most well-known statistical characteristic of an LES subgrid-scale model is its dissipation (energy transfer to unresolved scales), and many models are directly or indirectly formulated and tuned for consistency of this characteristic. However, in complex turbulent flows, many other subgrid statistical characteristics are important. These include such quantities as mean subgrid stress, subgrid transport of resolved Reynolds stress, and dissipation anisotropy. Also important are the statistical characteristics of models that account for filters that do not commute with differentiation and of the discrete numerical operators in the LES equations. We review the known statistical characteristics of subgrid models to assess these characteristics and the importance of their a priori consistency. We hope that this analysis will be helpful in continued development of LES models.

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Small-scale mixing processes enhancing troposphere-to-stratosphere transport by pyro-cumulonimbus storms

Atmospheric Chemistry and Physics ◽

10.5194/acp-7-5945-2007 ◽

2007 ◽

Vol 7 (23) ◽

pp. 5945-5957 ◽

Cited By ~ 11

Author(s):

G. Luderer ◽

J. Trentmann ◽

K. Hungershöfer ◽

M. Herzog ◽

M. Fromm ◽

...

Keyword(s):

Forest Fires ◽

Lower Stratosphere ◽

Deep Convection ◽

Cloud Microphysics ◽

Small Scale ◽

Temperature Pattern ◽

Mixing Processes ◽

Close Link ◽

Brightness Temperatures ◽

Cloud Resolving Model

Abstract. Deep convection induced by large forest fires is an efficient mechanism for transport of aerosol particles and trace gases into the upper troposphere and lower stratosphere (UT/LS). For many pyro-cumulonimbus clouds (pyroCbs) as well as other cases of severe convection without fire forcing, radiometric observations of cloud tops in the thermal infrared (IR) reveal characteristic structures, featuring a region of relatively high brightness temperatures (warm center) surrounded by a U-shaped region of low brightness temperatures. We performed a numerical simulation of a specific case study of pyroCb using a non-hydrostatic cloud resolving model with a two-moment cloud microphysics parameterization and a prognostic turbulence scheme. The model is able to reproduce the thermal IR structure as observed from satellite radiometry. Our findings establish a close link between the observed temperature pattern and small-scale mixing processes atop and downwind of the overshooting dome of the pyroCb. Such small-scale mixing processes are strongly enhanced by the formation and breaking of a stationary gravity wave induced by the overshoot. They are found to increase the stratospheric penetration of the smoke by up to almost 30 K and thus are of major significance for irreversible transport of forest fire smoke into the lower stratosphere.

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Detailed dual-Doppler structure of Kelvin-Helmholtz waves from an airborne profiling radar over complex terrain. Part II: Evidence for precipitation enhancement from observations and modeling

Journal of the Atmospheric Sciences ◽

10.1175/jas-d-20-0392.1 ◽

2021 ◽

Author(s):

Coltin Grasmick ◽

Bart Geerts ◽

Xia Chu ◽

Jeffrey R. French ◽

Robert M. Rauber

Keyword(s):

Cloud Microphysics ◽

Mixed Phase ◽

Small Scale ◽

Eddy Simulation ◽

Stratiform Clouds ◽

Ice Water Content ◽

Microphysical Processes ◽

Scale Turbulence ◽

Ice Water ◽

Quantitative Impact

AbstractKelvin-Helmholtz (KH) waves are a frequent source of turbulence in stratiform precipitation systems over mountainous terrain. KH waves introduce large eddies into otherwise laminar flow, with updrafts and downdrafts generating small-scale turbulence. When they occur in-cloud, such dynamics influence microphysical processes that impact precipitation growth and fallout. Part I of this paper used dual-Doppler, 2D wind and reflectivity measurements from an airborne cloud radar to demonstrate the occurrence of KH waves in stratiform orographic precipitation systems and identified four mechanisms for triggering KH waves. In Part II, we use similar observations to explore the effects of KH wave updrafts and turbulence on cloud microphysics. Measurements within KH wave updrafts reveal the production of liquid water in otherwise ice-dominated clouds, which can contribute to snow generation or enhancement via depositional and accretional growth. Fallstreaks beneath KH waves contain higher ice water content, composed of larger and more numerous ice particles, suggesting that KH waves and associated turbulence may also increase ice nucleation.A Large-Eddy Simulation (LES), designed to model the microphysical response to the KH wave eddies in mixed phase cloud, shows that depositional and accretional growth can be enhanced in KH waves, resulting in more precipitation when compared to a baseline simulation. While sublimation and evaporation occur in KH downdrafts, persistent supersaturation with respect to ice allows for net increase in ice mass. These modeling results and observations suggest that KH waves embedded in mixed-phase stratiform clouds may increase precipitation, although the quantitative impact remains uncertain.

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