Exposé des Dissertationsvorhabens
Wave-Induced Boundary Layer Separation
Eingereicht von: Mag. Johannes Sachsperger
Betreut durch: Univ.-Prof. Dr. Vanda Grubišić
Institut für Meteorologie und Geophysik
Fakultät für Geowissenschaften, Geographie und Astronomie
Universität Wien
Althanstraße 14 / UZA II, A-1090 Wien
November 2013
Abstract
Due to its potentially hazardous impact on human activities (e.g., general aviation, road
traffic, wind parks in mountainous areas, etc.), boundary layer separation (BLS) has
increasingly gained attention over the last 30 years in atmospheric studies and has become extensively investigated with theoretical, experimental and numerical approaches.
However, most of the previous research remained focused on wave-induced BLS in conjunction with resonant lee-wave trains. In this PhD study, wave-induced BLS in flow
over isolated topography will be examined in flows with uniform upstream stratification
and wind profiles giving rise to a range of wave responses downwind. Fundamental open
questions of the interaction of a larger-scale flow with BLS, the unsteadiness of the separation point and BLS behind 3D topography will be addressed in this numerical study
whose results are expected to bare relevance to many applied research studies in complex
terrain.
Kurzfassung
Wellen-induzierte Grenzschichtablösung
Durch die teils verheerenden Auswirkungen auf den Menschen (z.B. Luftfahrt, Straßenverkehr und Windkraftanlagen in Gebirgsregionen) hat das Phänomen der Grenzschichtablösung zunehmend an Aufmerksamkeit gewonnen und wurde in den letzten 30 Jahren
ausgiebig in theoretischen, experimentellen und numerischen Studien erforscht. Allerdings wurde in diesen Arbeiten hauptsächlich welleninduzierte Grenzschichtablösung in
Verbindung mit resonanten Leewellen untersucht. In dieser Doktoratsarbeit über welleninduzierte Grenzschichtablösung wird diese auch in gleichförmig geschichteter Strömung
über Topographie untersucht. Fundamentale offene Fragen wie die Interaktion zwischen größerskaliger Strömung und Grenzschichtablösung, sowie die Nichtstationarität
des Ablösungspunktes und auch das Auftreten von Grenzschichtablösung hinter isolierter
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3D-Topographie werden in dieser numerischen Studie behandelt werden, um eine umfassendere Kenntnis über dieses Phänomen zu erlangen.
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1.1
Introduction to the Research Topic
Atmospheric Boundary Layer
The Atmospheric Boundary Layer (ABL) is the part of the atmosphere that is
in direct contact with the earth’s surface and is characterized by turbulent exchange processes of momentum, heat and moisture on a time scale of less than
one hour. The vertical extent of the ABL can range from a few tens of meters,
under very stable night time conditions, up to 3 km under strongly convective conditions. The ABL is typically topped by a temperature inversion which separates
the laminar flow in the free atmosphere above the inversion from the turbulent
ABL below. A typical daytime boundary layer is characterized by strong vertical shear of the horizontal wind due to friction at the earth surface and neutral
stratification throughout the ABL resulting from adiabatic mixing due to surface
heating. The typical ABL at night is more complex, with a very stable layer close
to the surface owing its origin to surface cooling and a neutral residual layer above
it. The lowest part of the ABL, characterized by strong vertical wind shear and
the logarithmic vertical wind profile, is called the atmospheric surface layer. The
surface layer typically occupies the bottom 10% of the ABL. For simplicity, the
focus of this work will be on boundary layers without heat exchange at the earth
surface.
1.2
Boundary Layer Separation
A sufficiently strong deceleration of flow within a fluid layer adjoining a solid
boundary, driven by an externally imposed pressure gradient, can lead to detachment of that fluid from the solid boundary. That process is termed boundary layer
separation (BLS) and is a common occurrence in fluid flows. BLS is a common
phenomenon in stratified flows over topography as well and has been both observed directly at the top of very steep mountains (e.g., Zugspitze in Germany;
Wirth et al., 2012) or further down on the lee slope induced by mountain waves
(e.g., Sierra Nevada; Grubišić et al., 2008). The former is termed bluff body separation and the latter wave-induced BLS. Wave-induced BLS can be induced by
hydrostatic or non-hydrostatic mountain waves in a uniformly stratified upstream
flow, or in a layered flow with strong stratification in a lower layer (wave duct) and
weaker stratification above, where wave trapping is supported in the lower layer
and BLS is triggered below the crests of the resonant lee-wave train.
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Hydraulic transition
Blocked Fluid upstream
10.0
hm/A d
5.0
2.0
1.0
NA d
U
= 0.1
Lee-side bluff body
boundary-layer
separation
�
1.0
0.5
10
0.2
0.1
No separation
0.05 on obstacle
Post-wave
separation
0.02
0.01
0.1 0.2
0.5
1.0 2.0
N h/U
5.0 10.0
Figure 1: Vertical cross section through
Figure 2: This regime diagram shows tran-
an atmospheric rotor. The shear layer at
the surface which enters the cross section
from the left detaches from the surface at
the separation point at 166 km. Downstream of the separation point, a very
turbulent atmospheric rotor forms underneath a wave crest.
sitions of BLS regimes in dependence of the
flow governing parameters NH/U and H/L.
Solid lines indicate transition lines between BLS
regimes. (From Baines, 1995)
Downstream of the location where the boundary layer detaches from the surface
(separation point), atmospheric rotors may form (see Figure 1). Rotors are zones
within the boundary layer that are characterized by strong turbulence, surface
wind directions opposing the mean flow, large values of spanwise vorticity and
neutral stability. Due to the high level of turbulence, atmospheric rotors pose a
hazard for general aviation (Kahn et al., 1997), road traffic and can significantly
impact energy yield of wind parks in mountainous terrain. Thus, it is important
to understand the physical mechanisms behind BLS in order to improve the ability
of NWP models to provide more accurate forecasts of severe weather.
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State of Research
One of the early systematic studies of BLS is that of Baines and Hoinka (1985)
who conducted water tank experiments to explore BLS under different flow conditions, from hydrostatic to non-hydrostatic and from linear to non-linear flows
using uniform upstream stratification and wind speed. The results of these experiments are summarized in a BLS regime diagram (Baines, 1995) shown in Figure 2.
The diagram shows three main regimes: no separation, bluff body separation and
wave-induced BLS. Ambaum and Marshall (2005) confirmed these results using
linear theory.
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A recent seminal study of rotor formation is that of Doyle and Durran (2007) who
attributed the turbulence within a rotor to smaller scale vortices within the rotor interior - termed as subrotors - which appear to result from Kelvin-Helmholtz
(KH) instability of the lifted vorticity sheet.
Only a few numerical studies of BLS have explored the parameter space of Baines
and Hoinka (1985) experiments using constant stratification. So far, BLS was
studied mostly in mountain flows with variable vertical stratification, with either
a wave duct that promotes wave trapping (e.g., Doyle and Durran, 2007, 2002;
Jiang et al., 2007) or a strong elevated inversion (e.g., Vosper, 2004; Hertenstein
and Kuettner, 2005; Jiang et al., 2007).
The exception is a study by Zängl (2003) who performed simulations of nonhydrostatic flow over mountains and found rotor formation triggered by nonhydrostatic modes of a mountain wave. Another study with uniform upstream
stratification is that of Smith and Skyllingstad (2009) who studied wave breaking
induced boundary layer separation, which is part of the wave-induced BLS regime
of Baines (1995). However, fundamental questions regarding the dependence of
BLS on the large-scale flow have not been addressed yet.
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3.1
Research Questions
RQ1: Dependence of BLS on the large scale flow
BLS occurring in conjunction with trapped lee waves and elevated inversions is a
well studied problem. However, studies examining the onset of wave-induces BLS
in flows with uniform wind and stability are rare. Therefore, sets of 2D and 3D
numerical simulations of a uniformly stratified flow over a single mountain will
be carried out to partially map the parameter regime diagram of Baines (1995)
and the linear-theory based equivalent diagram by Ambaum and Marshall (2005).
The parameter space is spanned by the non-dimensional mountain height, NH/U, a
measure of non-linearity, and the vertical aspect ratio H/L of the mountain. In this
study, this parameter space will be expanded by adding the second mountain width
for 3D obstacles and the surface exchange coefficient for momentum which controls
friction. Together with NH/U, H/L controls the degree of the hydrostatic effect of
the flow. In the above N, H, L and U are, respectively the Brunt Väisälä frequency
(stability), mountain height, mountain width and flow speed. The dependence
of the separation point location, as well as the size and shape of rotors on the
large scale flow (degree of hydrostatic effect, non-linearity and friction) will be
investigated. Preliminary results confirm the location of the transition line between
the no separation regime and the wave induced BLS regime in Figure 2.
In addition to the impact of the large-scale flow on BLS, we will investigate the
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effect of BLS on the large-scale flow. Our preliminary results indicate that rotors
can act as “virtual topography” in a sense that internal gravity waves, similar to
mountain waves, are triggered in a stratified flow over a train of rotors. This is
strongly supported by simulations and will be further investigated.
3.2
RQ2: Non-stationarity of BLS
In observations of downslope wind storms (e.g., Scinocca and Peltier, 1989), pulsations in the downslope winds are often evident. These variations (time-scale of
minutes) may have an impact on the location of BLS. Scinocca and Peltier (1989)
found wind speed pulsations in their numerical simulation of the Boulder wind
storm of 1972 as well. Smith (1991) and Peltier and Scinocca (1991) showed that
these pulsations are likely related to Kelvin-Helmholtz instability at the interface
between the shooting flow and a stagnant wave-breaking region aloft.
Unsteadiness on a longer time-scale (hours) was investigated by Nance and Durran
(1997, 1998). They hypothesized that temporal transitions of the upstream flow
profile and non-linear wave interactions can modify the phase and group velocity, as well as the wavelength, of resonant lee-wave trains and, ultimately, lead to
unsteadiness. However, these experiments were carried out under free-slip lower
boundary conditions.
Systematic studies of BLS under temporally changing upstream flow will be conducted in addition to investigations of the interior structure of a rotor, both using
3D simulations. A deeper insight into the processes that lead to pulsations in
wind speed is expected to help with understanding its effect on the location of the
separation point.
3.3
RQ3: BLS behind 3D isolated topography
Detailed numerical studies of BLS have been previously carried out mostly in 2D
domains with periodic boundary conditions in the spanwise direction, representing
the flow over an infinitely long ridge. LES studies of BLS downwind of isolated
3D topography became possible only recently due to significant computational
costs (e.g. Doyle and Durran, 2007; Knigge, 2012). However, the implemented
mountains are still quite elongated and the dynamics are comparable to that of
an infinitely long ridge.
3D simulations of flow impacted by isolated topography with a horizontal aspect
ratio of the order of unity are planned in order to explore the impact of the
mountain width on the behavior of the separation of the boundary layer.
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4
Methods
Simulations
• Numerical experiments will be performed with the fully compressible, nonlinear and non-hydrostatic Large Eddy Simulation (LES) model CM1 Release
16 developed by George Bryan, at the National Center for Atmospheric
Research (NCAR). Initial simulation tests of cases from literature (Doyle
and Durran, 2002, 2007) showed very good agreement. LES is a technique in
which the most energetic eddies of turbulent flow (e.g. boundary layer) are
explicitly resolved on the numeric grid. The horizontal and vertical resolution
in such simulations is comparable with grid increments of typically a few tens
of meters.
• In order to achieve a turbulent ABL at the inflow boundary of the domain,
a turbulence recycling method is being used. In this method, initial random
perturbations get recycled and are not damped out in time. Using this
technique, the domain size can be reduced dramatically and the BL has
more realistic characteristics.
Analysis
• The analysis of the simulation results will be based on linear wave theory
(which can be extended quite far into the non-linear regime) as well as on
hydraulic theory. Both are standard and extensively and successfully applied
in atmospheric sciences.
• Using trajectory analysis for dynamical studies is becoming increasingly popular. The power of this technique is that flow properties can be stored along
parcel trajectories allowing one to diagnose various processes affecting a parcel throughout its travel through the fluid. This analysis can be particularly
helpful for RQ1.
• During the model integration process, a module which calculates the resolved
eddy covariances u0i u0j is used. In combination with the output of the subgridscale eddy covariances from the turbulence parametrization, the turbulent
fluxes of heat and momentum can be computed and analyzed.
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5
Funding and Work Plan
Year
Tasks
• Learn the model and reproduce previous literature results
• Prepare analysis- and plot scripts
1
• Study literature
• Perform and analyze 2D simulations in dependence of NH/U
and H/L (RQ1)
• Compute and analyze 2D simulations with variable friction
(RQ1)
• Re-perform and analyze selected 2D simulations in 3D (RQ1)
2
• Carry out and analyze simulations with time variable inflow conditions (RQ2)
• Investigate the interior of the rotor (RQ2)
3
• Compute and analyze 3D simulations of narrow isolated topography (RQ3)
• Write up results for publication
This thesis project is funded on a 30 h basis for 3 years by a research grant
from the Austrian Science Fund (FWF) (grant P24726).
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Mentoring and Scientific Interactions
• Theoretical Meteorology Working Group (TM): There is an intense scientific
exchange in the TM working group in form of weekly meetings and discussions. These include include the mentor and the head of the TM working
group Prof. Vanda Grubišić (remotely connected), the local supervisor Dr.
Stefano Serafin and other members of the TM group.
• National Center for Atmospheric Research (NCAR): Prof. Grubišić is currently at the National Center for Atmospheric Research (NCAR) in Boulder,
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Colorado, US, where she is the Director of the Earth Observing Laboratory
(EOL). Research stays at NCAR are planned during the course of this study
in order to foster scientific exchange with scientists at NCAR.
• Conferences: Additional scientific input and interactions are expected to
be gained from oral and/or poster presentations at suitable conferences
(e.g., International Conference on Alpine Meteorology (ICAM), American
Geosciences Union (AGU) meetings, European Geosciences Union (EGU)
meetings, American Meteorological Society Mountain Meteorology conference), symposia related to boundary layers and mountain weather or summer
schools.
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Computing Resources
• Felix Linux Cluster of the department: This TM working group cluster with
60 cores will be mainly used for model code development and computationally
cheap simulations.
• Vienna Scientific Custer (VSC): This super-computer is operated by the University of Vienna, the Technical University of Vienna (TU), the University
of Natural Resources and Applied Life Sciences Vienna (BOKU), the Graz
University of Technology (TU Graz), and the University of Innsbruck. Computationally intense numerical simulations will be computed and analyzed
on this machine.
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References
Ambaum, M. H. P. and D. P. Marshall, 2005: The effects of stratification on flow
separation. Journal of the Atmospheric Sciences, 62, 2618–2625.
Baines, P. G., 1995: Topographic effects in stratified fluids. Cambridge University
Press.
Baines, P. G. and K. P. Hoinka, 1985: Stratified flow over two-dimensional topography in fluid of infinite depth: A laboratory simulation. Journal of the
Atmospheric Sciences, 42, 1614–1630.
Doyle, J. D. and D. R. Durran, 2002: The dynamics of mountains-wave-induced
rotors. Journal of the Atmospheric Sciences, 59, 186–201.
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Doyle, J. D. and D. R. Durran, 2007: Rotor and subrotor dynamics in the lee of
three-dimensional terrain. Journal of the Atmospheric Sciences, 64, 4202–4221.
Grubišić, V., et al., 2008: The Terrain-Induced Rotor Experiment: A field campaign overview including observational highlights. Bulletin of the American Meteorological Society, 89, 1513–1533.
Hertenstein, R. F. and J. Kuettner, 2005: Rotor types associated with steep lee
topography: Influence of the wind profile. Tellus A, 57, 117–135.
Jiang, Q., J. D. Doyle, S. Wang, and R. B. Smith, 2007: On boundary layer separation in the lee of mesoscale topography. Journal of the Atmospheric Sciences,
63, 401–419.
Kahn, B. H., W. Chan, and P. F. Lester, 1997: An investigation of rotor flow using
dfdr data. Proceedings of the 7th Conference on Aviation, Range, and Aerospace
Meteorology, 206–210.
Knigge, C., 2012: Untersuchungen von atmosphärischen gebirgsrotoren mit hilfe
von laborexperimenten und grobstruktursimulationen. Ph.D. thesis, Gottfried
Wilhelm Leibniz University of Hannover.
Nance, L. B. and D. R. Durran, 1997: A modeling study of nonstationary trapped
mountain lee waves. part i: Mean-flow variability. Journal of the Atmospheric
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Nance, L. B. and D. R. Durran, 1998: A modeling study of nonstationary trapped
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Peltier, W. R. and J. F. Scinocca, 1991: The origin of severe downslope windstorm
pulsations. Journal of the Atmospheric Sciences, 47, 2853–2870.
Scinocca, J. F. and W. R. Peltier, 1989: Pulsating downslope windstorms. Journal
of the Atmospheric Sciences, 46, 2885–2914.
Smith, C. M. and E. D. Skyllingstad, 2009: Investigation of upstream boundary
layer influence on mountain wave breaking and lee wave rotors using a large-eddy
simulation. Journal of the Atmospheric Sciences, 66, 3147–3164.
Smith, R. B., 1991: Kelvin-Helmholtz instability in severe downslope wind flow.
Journal of the Atmospheric Sciences, 48, 1319–1324.
Vosper, S. B., 2004: Inversion effects on mountain lee waves. Quarterly Journal of
the Royal Meteorological Society, 130, 1723–1748.
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Wirth, V. et al., 2012: Banner clouds observed at Mount Zugspitze. Atmospheric
Chemistry and Physics, 12, 3611–3625.
Zängl, G., 2003: Orographic gravity waves close to the nonhydrostatic limit of
vertical propagation. Journal of the Atmospheric Sciences, 60, 2045–2063.
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