Analyses of Turbulence in the Neutrally and Stably Stratified Planetary Boundary Layer

180 Pages·2017·11.107 MB·English

by  Cedrick Ansorge (auth.)

Springer Theses
Recognizing Outstanding Ph.D. Research
Cedrick Ansorge

Analyses of
Turbulence in the
Neutrally and
Stably Stratified
Planetary
Boundary Layer
Springer Theses
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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
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’
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
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