A scale analysis of the turbulent mixing rate for various Prandtl number flow fields in rod bundles

A parameterization of the Prandtl number as a function of the gradient Richardson number is proposed in order to correctly take into account stratification when calculating the thermohydrodynamic regime of inland water bodies. This parameterization allows the existence of turbulence at any values &#8203;&#8203;of the Richardson number.The proposed function is used to calculate the turbulent thermal conductivity coefficient in a k-epsilon mixing scheme. Modification is implemented in the three-dimensional hydrostatic model developed at the Research Computing Center of Moscow State University.It is demonstrated that the proposed modification (in contrast to the standard scheme with a constant Prandtl number) leads to smoothing all sharp changes in vertical distributions of turbulent mixing parameters (turbulent kinetic energy, temperature and thickness of the shock layer) and imposes a Richardson number-dependent relation on the empirical constants of k-epsilon turbulent mixing scheme.The work was supported by grants of the RF President&#8217;s Grant for Young Scientists (MK-1867.2020.5) and by the RFBR (19-05-00249, 20-05-00776).&#160;

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Stellar Convection as a Low Prandtl Number Flow

International Astronomical Union Colloquium ◽

10.1017/s0252921100079380 ◽

1991 ◽

Vol 130 ◽

pp. 57-61

Author(s):

Josep M. Massaguer

Keyword(s):

Nusselt Number ◽

Prandtl Number ◽

Heat Transport ◽

Large Scale ◽

Shear Layers ◽

Turbulent Convection ◽

The Sun ◽

Stellar Convection ◽

Cool Stars ◽

Number Flow

AbstractThermal convection in the Sun and cool stars is often modeled with the assumption of an effective Prandtl number σ ≃ 1. Such a parameterization results in masking of the presence of internal shear layers which, for small σ, might control the large scale dynamics. In this paper we discuss the relevance of such layers in turbulent convection. Implications for heat transport – i.e. for the Nusselt number power law – are also discussed.

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Scale Analysis of Thermocapillary Weld Pool Shape With High Prandtl Number

Volume 10: Heat and Mass Transport Processes, Parts A and B ◽

10.1115/imece2011-62464 ◽

2011 ◽

Author(s):

P. S. Wei ◽

C. L. Lin ◽

H. J. Liu

Keyword(s):

Prandtl Number ◽

Boundary Layers ◽

Molten Pool ◽

Surface Flow ◽

Transport Processes ◽

Surface Boundary ◽

Scale Analysis ◽

Melting Front ◽

Pool Shape ◽

High Prandtl Number

The molten pool shape and thermocapillary convection during melting or welding of metals or alloys are self-consistently predicted from parametric scale analysis for the first time. Determination of the molten pool shape is crucial due to its close relationship with the strength and properties of the fusion zone. In this work, surface tension coefficient is considered to be negative values, indicating an outward surface flow, whereas high Prandtl number represents the thermal boundary layer thickness to be less than that of momentum. Since Marangoni number is usually very high, the scaling of transport processes is divided into the hot, intermediate and cold corner regions on the flat free surface, boundary layers on the solid-liquid interface and ahead of the melting front. Coupling among distinct regions and thermal and momentum boundary layers, the results find that the width and depth of the pool can be determined as functions of Marangoni, Prandtl, Peclet, Stefan, and beam power numbers. The predictions agree with numerical computations and available experimental data.

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Turbulent mixing at the top of stratocumulus clouds

Journal of Fluid Mechanics ◽

10.1017/s0022112063001257 ◽

1963 ◽

Vol 17 (2) ◽

pp. 212-224 ◽

Cited By ~ 12

Author(s):

J. S. Turner ◽

I. K. Yang

Keyword(s):

Liquid Water ◽

Turbulent Mixing ◽

Model Experiment ◽

Small Decrease ◽

Mixing Rate ◽

Turbulent Region ◽

Laboratory Results ◽

Non Linear ◽

Stratocumulus Clouds ◽

New Feature

The process of mixing at the top of a turbulent cloud layer contains a new feature which has not been considered in previous studies of mixing; evaporation of liquid water can cause density changes which may affect the dynamics. A model experiment has been devised to study this problem, using liquids whose density behaviour is non-linear to simulate evaporation.The existence of a moist, stable, turbulent region above cloudtop can be explained using the laboratory results, which suggest that this region can be regarded dynamically as part of the cloud. Comparison of the rates of mixing in the model experiments with and without ‘evaporation’ suggests that evaporation could cause a small decrease in the mixing rate for a given density difference, but the change would be negligible in practice. This result also sheds some light on the mechanism of mixing, in both the linear and non-linear cases.

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Multiscale Models for Cumulus Cloud Dynamics

Journal of the Atmospheric Sciences ◽

10.1175/2010jas3380.1 ◽

2010 ◽

Vol 67 (10) ◽

pp. 3269-3285 ◽

Cited By ~ 7

Author(s):

Samuel N. Stechmann ◽

Bjorn Stevens

Keyword(s):

Turbulent Mixing ◽

Apparent Magnitude ◽

Scale Analysis ◽

Cumulus Cloud ◽

Multiscale Models ◽

Cloud Droplets ◽

Shallow Cumulus ◽

Cloud Dynamics ◽

The Difference ◽

Balanced Dynamics

Abstract Cumulus clouds involve processes on a vast range of scales—including cloud droplets, turbulent mixing, and updrafts and downdrafts—and it is often difficult to determine how processes on different scales interact with each other. In this article, several multiscale asymptotic models are derived for cumulus cloud dynamics in order to (i) provide a systematic scale analysis on each scale and (ii) clarify the nature of interactions between different scales. In terms of scale analysis, it is shown that shallow cumulus updrafts can be described by balanced dynamics with a balance between source terms and ascent/descent; this is a cloud-scale version of so-called weak-temperature-gradient models. In terms of multiscale interactions, a model is derived that connects these balanced updrafts to the fluctuations within the balanced updraft envelope. These fluctuations describe parcels and updraft pulses, and this model encompasses some of the multiscale aspects of entrainment. In addition to this shallow cumulus model, to provide a broad picture of general cumulus dynamics, multiscale models are also derived for other scales; these include models for parcels and subparcel turbulent mixing and models for deep cumulus. Broadly speaking, the differences between the shallow and deep cases convey the notion that shallow cumulus dynamics are parcel dominated, whereas deep cumulus dynamics are updraft dominated; this is largely due to the difference in the apparent magnitude of the background temperature stratification. In addition to their use in guiding theory, the multiscale models also provide a framework for multiscale numerical simulations.

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