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Turbulence modelling applied to the atmospheric boundary layer
KTH, School of Engineering Sciences (SCI), Mechanics, Turbulence. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
2015 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Turbulent flows affected by buoyancy lie at the basis of many applications, both within engineering and the atmospheric sciences. A prominent example of such an application is the atmospheric boundary layer, the lowest layer of the atmosphere, in which many physical processes are heavily influenced by both stably stratified and convective turbulent transport. Modelling these turbulent flows correctly, especially in the presence of stable stratification, has proven to be a great challenge and forms an important problem in the context of climate models. In this thesis, we address this issue considering an advanced class of turbulence models, the so-called explicit algebraic models.In the presence of buoyancy forces, a mutual coupling between the Reynolds stresses and the turbulent heat flux exists, which makes it difficult to derive a fully explicit turbulence model. A method to overcome this problem is presented based on earlier studies for cases without buoyancy. Fully explicit and robust models are derived for turbulence in two-dimensional mean flows with buoyancy and shown to give good predictions compared with various data from direct numerical simulations (DNS), most notably in the case of stably stratified turbulent channel flow. Special attention is given to the problem of determining the production-to-dissipation ratio of turbulent kinetic energy, for which the exact equation cannot be solved analytically. A robust approximative method is presented to calculate this quantity, which is important for obtaining a consistent formulation of the model.The turbulence model derived in this way is applied to the atmospheric boundary layer in the form of two idealized test cases. First, we consider a purely stably stratified boundary layer in the context of the well-known GABLS1 study. The model is shown to give good predictions in this case compared to data from large-eddy simulation (LES). The second test case represents a full diurnal cycle containing both stable stratification and convective motions. In this case, the current model yields interesting dynamical features that cannot be captured by simpler models. These results are meant as a first step towards a more thorough investigation of the pros and cons of explicit algebraic models in the context of the atmospheric boundary layer, for which additional LES data are required. 

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2015. , xvi, 64 p.
Series
TRITA-MEK, ISSN 0348-467X ; 2015.05
Keyword [en]
turbulence; RANS models; explicit algebraic Reynolds-stress models; buoyancy; stable stratification; thermal convection; atmospheric boundary layer
National Category
Fluid Mechanics and Acoustics Meteorology and Atmospheric Sciences
Identifiers
URN: urn:nbn:se:kth:diva-166806ISBN: 978-91-7595-603-9 (print)OAI: oai:DiVA.org:kth-166806DiVA: diva2:812382
Public defence
2015-06-12, Kollegiesalen, Brinellvägen 8, KTH, Stockholm, 10:15 (English)
Opponent
Supervisors
Note

QC 20150522

Available from: 2015-05-22 Created: 2015-05-18 Last updated: 2015-05-22Bibliographically approved
List of papers
1. An explicit algebraic Reynolds-stress and scalar-flux model for stably stratified flows
Open this publication in new window or tab >>An explicit algebraic Reynolds-stress and scalar-flux model for stably stratified flows
2013 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 723, 91-125 p.Article in journal (Refereed) Published
Abstract [en]

This work describes the derivation of an algebraic model for the Reynolds stresses and turbulent heat flux in stably stratified turbulent flows, which are mutually coupled for this type of flow. For general two-dimensional mean flows, we present a correct way of expressing the Reynolds-stress anisotropy and the (normalized) turbulent heat flux as tensorial combinations of the mean strain rate, the mean rotation rate, the mean temperature gradient and gravity. A system of linear equations is derived for the coefficients in these expansions, which can easily be solved with computer algebra software for a specific choice of the model constants. The general model is simplified in the case of parallel mean shear flows where the temperature gradient is aligned with gravity. For this case, fully explicit and coupled expressions for the Reynolds-stress tensor and heat-flux vector are given. A self-consistent derivation of this model would, however, require finding a root of a polynomial equation of sixth-order, for which no simple analytical expression exists. Therefore, the nonlinear part of the algebraic equations is modelled through an approximation that is close to the consistent formulation. By using the framework of a K-omega model (where K is turbulent kinetic energy and omega an inverse time scale) and, where needed, near-wall corrections, the model is applied to homogeneous shear flow and turbulent channel flow, both with stable stratification. For the case of homogeneous shear flow, the model predicts a critical Richardson number of 0.25 above which the turbulent kinetic energy decays to zero. The channel-flow results agree well with DNS data. Furthermore, the model is shown to be robust and approximately self-consistent. It also fulfils the requirements of realizability.

Place, publisher, year, edition, pages
Cambridge University Press, 2013
Keyword
stratified turbulence, turbulence modelling, turbulent flows
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-122471 (URN)10.1017/jfm.2013.116 (DOI)000317659400005 ()2-s2.0-84876206588 (Scopus ID)
Funder
Swedish Research Council, 621-2010-4147Formas
Note

QC 20130523

Available from: 2013-05-22 Created: 2013-05-22 Last updated: 2017-12-06Bibliographically approved
2. Explicit algebraic models for turbulent flows with buoyancy effects
Open this publication in new window or tab >>Explicit algebraic models for turbulent flows with buoyancy effects
2013 (English)Report (Other academic)
Abstract [en]

An explicit algebraic model for the Reynolds stresses and turbulent heat fluxis presented for turbulent parallel shear flows in which buoyancy forces arepresent. The derivation is based on a model framework for two-dimensionalmean flows that was already presented in a previous work (Lazeroms et al.2013), and new test cases are investigated here. The model is formulated interms of the Reynolds-stress anisotropy and a normalized heat flux, which areexpanded as a linear combination of appropriate basis tensors. The coefficientsin this expansion can be found from a system of 18 linear equations. Thisformulation is complemented with a nonlinear equation for a quantity relatedto the total production-to-dissipation ratio, the solution of which is modelledwith an appropriate expression. Fully explicit model expressions are found fortwo fundamentally different flow geometries: a horizontal channel for whichthe temperature gradient is aligned with gravity, and a vertical channel wherethe temperature gradient and gravity are perpendicular. In the first case, weconsider both stable and unstable stratification, while in the second case, bothmixed and natural convection flows are investigated. Comparison with DNSdata shows that the model gives predictions that are substantially better thanstandard eddy-viscosity/eddy-diffusivity models.

National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-122473 (URN)
Note

QC 20150701

Available from: 2013-05-22 Created: 2013-05-22 Last updated: 2015-07-01Bibliographically approved
3. Efficient treatment of the nonlinear features in algebraic Reynolds-stress and heat-flux models for stratified and convective flows
Open this publication in new window or tab >>Efficient treatment of the nonlinear features in algebraic Reynolds-stress and heat-flux models for stratified and convective flows
2015 (English)In: International Journal of Heat and Fluid Flow, ISSN 0142-727X, E-ISSN 1879-2278, Vol. 53, 15-28 p.Article in journal (Refereed) Published
Abstract [en]

This work discusses a new and efficient method for treating the nonlinearity of algebraic turbulence models in the case of stratified and convective flows, for which the equations for the Reynolds stresses and turbulent heat flux are strongly coupled. In such cases, one finds a quasi-linear set of equations, which can be solved through an appropriate linear expansion in basis tensors and vectors, as discussed in earlier work. However, finding a consistent and truly explicit algebraic turbulence model requires solving an additional equation for the production-to-dissipation ratio (P+G)/ε of turbulent kinetic energy. Due to the nonlinear nature of the problem, the equation for (P+G)/ε is a higher-order polynomial equation for which no analytical solution can be found. Here we provide a new method to approximate the solution of this polynomial equation through an analysis of two special limits (shear-dominated and buoyancy-dominated), in which exact solutions are obtainable. The final result is a model that appropriately combines the two limits in more general cases. The method is tested for turbulent channel flow, both with stable and unstable stratification, and the atmospheric boundary layer with periodic and rapid changes between stable and unstable stratification. In all cases, the model is shown to give consistent results, close to the exact solution of (P+G)/ε. This new method greatly increases the range of applicability of explicit algebraic models, which otherwise would rely on the numerical solution of the polynomial equation.

National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-166800 (URN)10.1016/j.ijheatfluidflow.2015.01.005 (DOI)000355367500002 ()2-s2.0-84923270425 (Scopus ID)
Funder
Swedish Research Council, 621-2013-5784
Note

QC 20150521

Available from: 2015-05-18 Created: 2015-05-18 Last updated: 2017-12-04Bibliographically approved
4. Study of transitions in the atmospheric boundary layer using explicit algebraic turbulence models.
Open this publication in new window or tab >>Study of transitions in the atmospheric boundary layer using explicit algebraic turbulence models.
Show others...
(English)Manuscript (preprint) (Other academic)
National Category
Fluid Mechanics and Acoustics Meteorology and Atmospheric Sciences
Identifiers
urn:nbn:se:kth:diva-166803 (URN)
Note

QS 2015

Available from: 2015-05-18 Created: 2015-05-18 Last updated: 2015-05-22Bibliographically approved
5. A generalized method for deriving explicit algebraic turbulence models.
Open this publication in new window or tab >>A generalized method for deriving explicit algebraic turbulence models.
(English)Manuscript (preprint) (Other academic)
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-166804 (URN)
Note

QS 2015

Available from: 2015-05-18 Created: 2015-05-18 Last updated: 2015-05-22Bibliographically approved

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