Analyses of Turbulence in the Neutrally and Stably Stratified Planetary Boundary Layer PDF
Preview Analyses of Turbulence in the Neutrally and Stably Stratified Planetary Boundary Layer
Springer Theses Recognizing Outstanding Ph.D. Research Cedrick Ansorge Analyses of Turbulence in the Neutrally and Stably Stratified Planetary Boundary Layer Springer Theses Recognizing Outstanding Ph.D. Research Aims and Scope The series “Springer Theses” brings together a selection of the very best Ph.D. theses from around the world and across the physical sciences. Nominated and endorsed by two recognized specialists, each published volume has been selected foritsscientificexcellenceandthehighimpactofitscontentsforthepertinentfield of research. For greater accessibility to non-specialists, the published versions includeanextendedintroduction,aswellasaforewordbythestudent’ssupervisor explainingthespecialrelevanceoftheworkforthefield.Asawhole,theserieswill provide a valuable resource both for newcomers to the research fields described, and for other scientists seeking detailed background information on special questions. Finally, it provides an accredited documentation of the valuable contributions made by today’s younger generation of scientists. Theses are accepted into the series by invited nomination only and must fulfill all of the following criteria (cid:129) They must be written in good English. (cid:129) ThetopicshouldfallwithintheconfinesofChemistry,Physics,EarthSciences, Engineeringandrelatedinterdisciplinary fields such asMaterials,Nanoscience, Chemical Engineering, Complex Systems and Biophysics. (cid:129) The work reported in the thesis must represent a significant scientific advance. (cid:129) Ifthethesisincludespreviouslypublishedmaterial,permissiontoreproducethis must be gained from the respective copyright holder. (cid:129) They must have been examined and passed during the 12 months prior to nomination. (cid:129) Each thesis should include a foreword by the supervisor outlining the signifi- cance of its content. (cid:129) The theses should have a clearly defined structure including an introduction accessible to scientists not expert in that particular field. More information about this series at http://www.springer.com/series/8790 Cedrick Ansorge Analyses of Turbulence in the Neutrally and Stably fi Strati ed Planetary Boundary Layer Doctoral Thesis accepted by University of Hamburg, Hamburg, Germany 123 Author Supervisor Cedrick Ansorge JuanPedroMellado Atmosphere inthe EarthSystem Atmosphere inthe EarthSystem MaxPlanckInstitute for Meteorology MaxPlanckInstitute for Meteorology Hamburg Hamburg Germany Germany ISSN 2190-5053 ISSN 2190-5061 (electronic) SpringerTheses ISBN978-3-319-45043-8 ISBN978-3-319-45044-5 (eBook) DOI 10.1007/978-3-319-45044-5 LibraryofCongressControlNumber:2016948802 ©SpringerInternationalPublishingAG2017 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission orinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfrom therelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authorsortheeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinor foranyerrorsoromissionsthatmayhavebeenmade. Printedonacid-freepaper ThisSpringerimprintispublishedbySpringerNature TheregisteredcompanyisSpringerInternationalPublishingAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland ’ Supervisor s Foreword Atmospheric models rely on turbulence parametrizations to represent the effect of unresolved motions on resolved properties of the planetary boundary layer. According to observations, common parametrizations fail to reproduce the correct effect in conditions of strongly stable stratification, when turbulence collapses and becomesintermittentinspaceandtime.Thisproblemhashamperedtheadvanceof our understanding of the planetary boundary layer for decades. In this book, Cedrick Ansorge demonstrates that we can eliminate this problem by simulating turbulence directly, without turbulence parametrizations, which allows him to investigate systematically, for the first time, key properties in conditions ranging from weak to strong stratification. Directnumericalsimulationoftheplanetaryboundarylayerhasbecomefeasible only recently with the advent of massively parallel supercomputers. Besides the well-established measurement-driven and conceptual approaches, direct numerical simulation opens a new avenue to study the planetary boundary layer. Direct numerical simulation removes the uncertainty of turbulence parametrizations; it does not use any turbulence parametrization, which turns out to be of critical importance in conditions of strongly stable stratification. But direct numerical simulation alone is no guarantee to advance physical understanding—direct numerical simulation serves this purpose only in combination with well-defined, physically sounded physical models that allow experiments in controlled condi- tions.CedrickAnsorgeemploysastablystratifiedEkmanlayerasaphysicalmodel of the stable boundary layer, which he demonstrates to successfully reproduce the threestratificationregimesobservedinnature:weakly,intermediatelyandstrongly stratified. Bymeansofthisnoveltechnique,theworkpresentedinthisbookprovidesnew answers to long-standing questions. For example, it shows that both turbulence collapseandthedecouplingbetweenthesurfaceandtheouterlayer,neednotbean on–offprocessintimebutcanratheroccurintermittentlyinspacewithouttheneed of external triggers, such as surface heterogeneity. It suffices that wave-like, large-scale structures (with a size of several boundary-layer depths) have enough spaceandtimetodevelop.Thisresulthelpstoexplainthedifficultytoobtainspatial v vi Supervisor’sForeword intermittency in simulations, because we need to retain these large scales and, simultaneously, resolve the small-scale turbulence inside the turbulence regions. Anotherimportantquestionaddressedinthisbookishowthisintermittencyaffects conventionalstatisticsandturbulenceparametrizations.Anewconditioningmethod is developed to partition the flow into turbulent and non-turbulent regions in the vicinityof thewall. Systematic applicationof thisconditioning method shows that turbulence properties inside the turbulent regions in the weakly and intermediately stratified cases are similar to turbulence properties in the neutrally stratified case. The order-of-one changes observed in the conventional statistics as stratification increases are mainly caused by the change of the volume fraction occupied by the turbulent regions. To conclude, this work exemplifies how process-level studies that combine physicalset-upsofreducedcomplexitywithdirectnumericalsimulationscanyield new insight into relevant atmospheric phenomena. The numerical methods and physicalset-upofstratifiedEkmanflowsarepresentedingreatdetail,butthiswork also translates results from this simplified set-up into new physical understanding of the planetary boundary layer. Hence, the research presented in this book is an excellent example of how new computational capabilities are opening new very promising avenues in atmospheric research. As Cedrick’s advisor, I enjoyed learning with him about the intricacies of stably stratified turbulence in the plan- etary boundary layer, and I congratulate him for an outstanding work. I hope this bookinspiresotherscientiststoalsoexploitthesenewcomputationalcapabilitiesin the study of geophysical turbulence. Hamburg, Germany Juan Pedro Mellado July 2016 Parts of this thesis have been published in the following journal articles: (cid:129) J.P. Mellado and C. Ansorge (2012): Factorization of the Fourier transform of the pressure-Poisson equation using finite differences in colocated grids. Zeitschrift für Angewandte Mathematik und Mechanik/Journal of Applied Mathematics and Mechanics, 92(5) pp 380–392 (cid:129) C. Ansorge and J.P. Mellado (2014): Global intermittency and collapsing turbulence in the stratified planetary boundary layer. Boundary-Layer Meteorology, 153(1) pp 89–116 (cid:129) C. Ansorge and J.P. Mellado (2016): Analyses of external and global inter- mittencyinthelogarithmiclayerofEkmanflow.Acceptedforpublicationinthe Journal of Fluid Mechanics vii Acknowledgments ComputingtimeforthisprojectwasprovidedbytheJülichSupercomputingCentre undertheprojectgrantHHH07.Testsanddevelopmentofthealgorithmhavepartly been undertaken on the Max Planck Institute for Meteorology’s cluster thunder provided by CIS whose kind support is also acknowledged here. Financial support through the Research Group Programme of the Max Planck Societyisgratefullyacknowledged;thisthesiswaswrittenintheresearchgroupon TurbulentmixingprocessesintheearthsystemleadbyJuanPedroMellado,Ph.D. and located at the Max Planck Institute for Meteorology in Hamburg. ix Contents Part I Preliminaries 1 Introduction... .... .... ..... .... .... .... .... .... ..... .... 3 1.1 Turbulence Regimes. ..... .... .... .... .... .... ..... .... 4 1.2 Global Intermittency. ..... .... .... .... .... .... ..... .... 5 1.3 Approaches to Studying the Stable Boundary Layer.. ..... .... 7 1.4 Research Proposition ..... .... .... .... .... .... ..... .... 8 References. .... .... .... ..... .... .... .... .... .... ..... .... 9 2 Problem Formulation and Tools.... .... .... .... .... ..... .... 13 2.1 The Governing Equations.. .... .... .... .... .... ..... .... 13 2.2 Non-dimensionalization and Parameter Space... .... ..... .... 17 2.2.1 The Neutrally Stratified Regime ... .... .... ..... .... 17 2.2.2 Uniqueness of the Solution... .... .... .... ..... .... 17 2.2.3 Imposing Stratification: Initial and Boundary Conditions... ..... .... .... .... .... .... ..... .... 18 2.2.4 Parameter Space of the Non-dimensionalized Problem ... 20 2.3 Analysis Tools . .... ..... .... .... .... .... .... ..... .... 21 2.3.1 Conditional Sampling ... .... .... .... .... ..... .... 22 2.3.2 Temporally Resolved Probes.. .... .... .... ..... .... 22 2.4 Summary . .... .... ..... .... .... .... .... .... ..... .... 23 References. .... .... .... ..... .... .... .... .... .... ..... .... 23 Part II Numerics 3 Discretization.. .... .... ..... .... .... .... .... .... ..... .... 29 3.1 The Pressure Problem..... .... .... .... .... .... ..... .... 29 3.2 Spatial Discretization ..... .... .... .... .... .... ..... .... 30 3.3 Time Stepping Schemes... .... .... .... .... .... ..... .... 31 3.3.1 Explicit Runge–Kutta Schemes.... .... .... ..... .... 32 3.3.2 Semi-implicit Runge–Kutta Schemes.... .... ..... .... 33 xi
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