land-surface
interactions (top)
International H2O Project (IH2OP-2002) surface characteristics
Peggy LeMone, Diane Strassberg (MMM
student visitor), and Joe Alfieri (RAP student assistant)
compared the
normalized differential vegetation index (NDVI) from
hand-held sensors at the ten IH2OP surface flux stations
to corresponding values from the University of Wyoming
King Air Aircraft. They used aircraft videos to verify
that the aircraft was over the correct land cover for
comparison. This procedure proved robust, with early-season
difficulties in distinguishing winter wheat from grasses
resolved through use of post-harvest videos. In addition,
landmark identification confirmed that corrected aircraft
location was accurate to within the researchers’ ability
to relate video images to aircraft location.
Atmospheric response of spatial variations of soil
moisture
Jielun Sun, in collaboration
with Larry Mahrt and Dean Vickers (both of Oregon State
University), Thomas
Jackson (USDA/ARS Hydrology), Ian MacPherson (National
Research Council, Canada), Paul Houser (NASA Goddard
Space Flight
Center),
and Eleanor Burke (University of Arizona), investigated
the response of atmospheric moisture flux to temporal
and spatial variations in soil moisture and spatial
vegetation heterogeneity (http://www.mmm.ucar.edu/science/abl/sgp/sgp.html).
Sun generalized the
commonly used parameterization for estimating evapotranspiration
with consideration
of soil moisture and surface type. Using the Southern
Great Plains (SGP) dataset, Sun found that evapotranspiration
depends not only on soil moisture and surface type,
but also on atmospheric conditions for ventilation.
Response of the PBL to land-surface heterogeneity
Edward Patton (MMM
visitor, Pennsylvania State University), Peter
Sullivan, and Chin-Hoh
Moeng used
their coupled PBL/land-surface large-eddy simulation
code to study the planetary boundary layer (PBL) response
to large-scale soil moisture heterogeneity (with scales
ranging from 1-18 times the PBL height). In the presence
of heterogeneity, the atmospheric transport of moisture
varies with the initial atmospheric state, wet versus
dry. In both situations, land-surface heterogeneity
induces organized motions that scale with the heterogeneity.
Surface fluxes respond asymmetrically in that they
are minimum near the center of the heterogeneity and
maximum at about one-fifth the way into the dry soil
region. Phase-averaged statistics also reveal this
skewed distribution; intense vertical motion is found
in a narrow band centered over the dry soil, while
the descending leg of the circulation is weaker and
extends over a area greater than the wet soil region
(see Figure 34).
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| Figure
34: Normalized phase-averaged horizontal
velocity (up/w*, top) and
vertical velocity (wp/w*,
bottom) as a function of x/l and
z/zi for the case with l/zi
= 4. The dashed-line is the phase-averaged boundary
layer depth, zip;
dotted contours represent negative phase-correlated
values; and the hatches demarcate the x/l
extent
of the wet soil. |
The horizontal motions (associated with
the circulations) also show an asymmetric response.
Depending on the moisture state of the overlying atmosphere,
time-averaged measurements at a point can incorrectly
estimate the total vertical moisture flux by up to
60%. The error varies with the height and location
of the measurement station in the region of heterogeneity
(see Figure 35).
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| Figure
35: Vertical profiles of normalized
vertical water
vapor mixingratio flux for a case with a dry
PBL over top of heterogeneitythat is about four
times the height of the PBL. The greenprofile
represents the the total flux. The blue line
representscontribution to the total flux by the
background turbulence (or the non-organized component
of the turbulence), and the hatchmarks demarcate
plus and minus one standard deviation of thisbackground
component from the y-average. The red line
isthe time-average at each x/l and
z/zi location at y =Ly/2. The (top-left, top-right,
lower-left, lower-right) panels represent locations x/\lambda = (0 or 1, 0.25,
0.5, 0.75). |
Investigation of impacts of cold land transition for
global climate change
Sun participated in the Fluxes over Snow Surfaces
(FLOSS) experiment that focused on energy transfer
over snow-covered cold land (http://www.mmm.ucar.edu/science/abl/floss/).
This effort was organized by Larry Mahrt (Oregon State
University) and was sponsored by the NASA Hydrology
program. Sun designed an observation plan for measuring
radiative flux divergence close to the ground in the
presence of a snow layer. She contributed thermocouples
to the observational study and measured temperature
distributions around sage shrubs, in collaboration
with Steve Oncley, Tony Delany, and Steve Semmer (all
of ATD) and Larry Mahrt, Dean Vickers, and Richard
Cuenca (all of Oregon State University). These results
will shed light on the role of sage shrubs in energy
transfer during snow-covered freezing periods and also
lead to better understanding of scenarios related to
the global warming associated with snow and frozen-land
melting. This research effort is an interdisciplinary
study relating ecology, micrometeorology, and hydrology.
CO2 transport over complex terrain
Jeilun Sun and Sean
Burns, in
collaboration with Steve Oncley, Tony Delany, Britt
Stephens, and
Teresa Campos (all of ATD),
and Alex Guenther and Andrew Turnipseed (both of ACD),
Russell Monson (University of Colorado), and Dean Anderson
(USGS) led an investigation of CO2 transport over complex
terrain at Niwot Ridge, Colorado in September 2002
(http://www.mmm.ucar.edu/science/abl/forest/).
The research was sponsored by the NCAR Director's Opportunity
Fund and is now a research focus of the NCAR Biogeoscience
Initiative. In addition, this research concept has
led to a successful NSF proposal for a full-scale study
of CO2 transport over complex terrain. Using data from
the 2002 field campaign, Sun and
Burns found that
the spatial distribution of CO2 is sensitive to
major steep slopes,
and also to small gullies embedded in steep slopes
(Figure 36).
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| Figure
36: Investigation of CO2 transport over complex
terrain at Niwot Ridge showed that spatial distribution
of CO2 depends on radiative energy transfer and
atmospheric wind gusts. The results
provide critical information on the many ongoing long-term
observational programs, which currently ignore horizontal
transport of CO2 in their CO2 budgets. |
The spatial distribution of CO2 depends on radiative
energy transfer and atmospheric wind gusts. The results
provide critical information on the many ongoing long-term
observational programs, which currently ignore horizontal
transport of CO2 in their CO2 budgets.
LES of stable boundary layers
Sullivan and Moeng participated
in the first intercomparison of LES solutions of stable
planetary boundary layers
organized by the GEWEX atmospheric boundary layer study
(GABLS). The long-term goal of this international working
group is to improve the parameterization of stable
(nocturnal) PBLS in large-scale numerical weather prediction
codes (see the May issue of GEWEX news posted on http://www.gewex.org/gewex_nwsltr.html).
This first intercomparison case focused on the idealized
Arctic boundary layer described by Kosovic and Curry
(JAS 2000). Nine-hour simulations with resolutions
varying from 643 to 2003 were generated using the two-part
subgrid scale model described in Sullivan et al. (1994).
Sullivan and Moeng's results,
along with those from the nine groups that participated
in the intercomparison,
are described at http://metresearch.net/gabls/index.shtml.
The findings show that LES is capable of simulating
stratified surface layers, but the results from the
different groups are highly variable depending on the
grid resolution and subgrid-scale model. High resolution
LES, run with two-m spacing (2003 grid points see figure
36) tend to converge, but still exhibit surprising
differences because of varying subgrid scale parameterizations
used in the surface layer. Sullivan and Moeng plan
to utilize results from HATS to develop an improved
subgrid parameterization and thus enhance the fidelity
of LES predictions for stable surface layers.
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Figure
37: Snapshot
of the instantaneous vertical velocity (w) field
in x-z, y-z and
x-y planes from an LES of a stable PBL with 2m
resolution illustrating
how w is dominated by small scale, intermittent
motions. In this
simulation a persistent low-level jet develops
at approximately z =
200m above the surface. Color contours are in
m/s and the size of the computational domain
is 400x400x400m.
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Energy transfer under nocturnal stable conditions
Sun, in collaboration with Sean
Burns, Donald Lenschow, Tom Horst (ATD), Tony Delany (ATD), and Steve
Oncley (ATD) continued analyzing data collected from
the Cooperative Atmosphere-Surface Exchange Study-1999
(CASES-99, http://www.mmm.ucar.edu/science/abl/cases/cases.html).
Sun focused on the nocturnal heat balance. This effort
is the first attempt to measure precisely radiative
flux divergence over a relatively deep stable layer
with consideration of surface heterogeneity. She found
that the radiative flux divergence decreases with height
and is large during the early evening when the ground
is still warm. The research is fundamental since it
sheds light on the applicability of Monin-Obukhov similarity
theory, which is used in all numerical models to relate
surface fluxes and mean flowfields. This research is
currently being supported by the Army Research Office,
and additional funding has been awarded to support
further data analysis.
Numerical simulation of sand dune evolution in severe
winds
Predicting sediment transport and bed evolution in
severe wind conditions depends on accurate prediction
of flow past a complex boundary evolving with the flow
itself. The geometrical complexity of the evolving
interfaces, which either accommodate dynamically to
the external/internal boundaries of the domain or convolute
in response to internal flows, is per se a challenge
to numerical modeling. Pablo Ortiz (University of Granada,
Spain) and Piotr Smolarkiewicz developed
a variant of the nonhydrostatic model EULAG that couples
the
internal flow with a lower boundary evolving in response
to the sand saltation and/or dust storms (Fig.
38).
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| Figure
38: Two numerical simulations of a sand dune evolution.
First three
frames show potential-flow initial condition (including
perspective view of the initial
sand pile placed on a hard bed and isolines of vertical velocity in the vertical
center plane and following the surface). Next three frames show the developed
solution, whereas the subsequent three frames show a similar solution, but for
the initial sand pile placed on a layer of sand. |
The key prerequisite facilitating this development
is the use of a time-dependent curvilinear coordinate
transformation that accommodates rapid changes in the
boundary shape. The nonoscillatory forward-in-time
numerical technology of EULAG enables novel numerical
designs that improve the accuracy, stability, and robustness
of the traditional saltation models that govern the
evolution of dunes.
Improvements in subgrid-scale modeling of plant canopy
environments
Roger Shaw (University of California, Davis) and Patton (visitor,
Pennsylvania State University) developed a subgrid-scale
(SGS) model for large-eddy
simulations of canopy flows that incorporates the clumpiness
of leaf matter on the breakdown of resolved- and subgrid-scale
motions into wake-scale (WS) motions in the lee of
plants.
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| Figure
39: Schematic of the processes that convert resolved-scale
kineticenergy to subgrid scale, wake scale, and
ultimately to internalenergy. The numbers identify
the various physical processesof energy exchange. |
Figure 39 is a schematic of the processes responsible
for energy transfer from the mean flow to internal
energy and depicts the processes included in the new
SGS model. In this study, it was found that inclusion
of the breakdown from SGS motions into WS motions (Process
6 in the figure) is vital to the proper simulation
of canopy flows as WS motions act to enhance dissipation
of SGS energy. Ongoing collaborations with Monique
Leclerc (University of Georgia) and Stathis Michaelides
(Tulane University) are taking advantage of this new
code. Collaborations with John Finnigan (CSIRO, Australia)
and Shaw are further improving this SGS model by deriving
the canopy influence on dissipation from first principles.
Subfilter scale motions in LES
Sullivan, Lenschow, Moeng,
Thomas Horst (ATD), and Jeffrey
Weil (MMM visitor, University of Colorado/CIRES)
published a manuscript (JFM 482) describing their
analysis
of
the field
data collected
from the Horizontal Array Turbulence Study (HATS).
One of the major highlights from this work exposed
the shortcomings of current subgrid scale modeling
in situations where large amounts of momentum and scalar
flux are transmitted by unresolved motions in LES.
New anisotropic subgrid scale models for LES are needed
near boundaries and in cases with strong stable stratification.
The HATS datasets were shared with John Wyngaard (Pennsylvania
State University), Chenning Tong (Clemson University),
and Ronald Adrian (University Illinois, Urbana-Champagne).
Mechanisms of up-valley winds
Richard Rotunno in
collaboration with Gabriele Rampanelli and Dino Zardi
(both of the University of Trento, Italy)
investigated the basic physical mechanisms governing
the daytime evolution of up-valley winds in mountain
valleys using a series of numerical simulations of
thermally driven flow over idealized three-dimensional
topography. As in previous studies of two-dimensional
circulations in valleys, the heated valley side walls
require a compensating subsidence in the valley core
which brings potentially warmer air from the stable
free atmosphere into the valley core. In the context
of the three-dimensional valley-plain simulations,
they found that the subsidence heating in the valley
core is the main contributor to the valley-plain temperature
contrast along the valley axis and, under the hydrostatic
approximation, the pressure difference that accelerates
the up-valley wind (see Figure 40, below).
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| Figure
40: The Physical mechanisms governing
the daytime evolution of up-valley winds in mountain
valleys using a series of numerical simulations of
thermally driven flow over idealized three-dimensional
topography. |
The foregoing theory improves on the standard textbook
explanation that assumes zero heat transfer between
the free atmosphere and the air within the valley.
Moist neutral flow over a ridge
Although moist neutral flow over a ridge is a fairly
common atmospheric condition in orographic-rain scenarios,
relatively little is known about it from theory and
modeling. Marcello Miglietta (Consiglio Nazionale della
Ricerca, Italy) and Rotunno carried
out numerical simulations of the orographic-flow modification
occurring for a
two-dimensional moist neutral flow over a ridge. If
an initially saturated moist neutral flow were to remain
everywhere saturated as it flows over an obstacle,
then the expected solution would be the linear solution
because the moist stability is small. However, Miglietta
and Rotunno found
that the numerical solutions indicate the development
of areas of unsaturated air, with correspondingly
larger values of local static stability. For certain
parameter settings, the subsaturated zone may even
propagate upwind (see Figure 41, below).
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| Figure
41: Numerical simulations of the orographic-flow
modification occurring for a
two-dimensional moist neutral flow over a ridge. |
This internal switching from small to large values
of static stability is an inherent nonlinearity of
moist airflow, which has far-reaching consequences
for understanding the orographic-flow modification
and predictability of rainfall in this regime.
Lee vortex formation related to upstream blocking
Craig Epifanio (Texas A&M University) and Rotunno explored
the basic fluid mechanics of orographic wake formation
using simple scaling arguments and diagnostic
vorticity inversion techniques. Their work pinpoints
upstream blocking as the key process associated with
lee-side mountain wake formation at the surface. Upstream
blocking causes the descent of warm air over the lee
slope to replace the colder surface air blocked upstream.
The result is a temperature gradient along the lee
slope that quickly collapses into a front. The colder
surface air downstream of the front tends to propagate
upstream into the lee-side warm anomaly, and for sufficiently
large temperature difference,
the flow behind the front stagnates and reverses to
form a wake at the surface. In three dimensions the
flow wraps around the lateral edges of the wake as
suggested by the tilting of horizontal vortex lines
to produce vertical vorticity (see Figure 42, below).
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| Figure
42: Basic fluid mechanics of orographic wake formation
using simple scaling arguments and diagnostic
vorticity inversion techniques pinpoints
upstream blocking as the key process associated with
lee-side mountain wake formation at the surface. |
This work provides a conceptual model to describe
surface wake formation downstream of mountains and
clarifies the previously observed association between
orographic wake formation and upstream blocking.
An all-scale anelastic model for geophysical flows:
dynamic grid deformation
Joseph Prusa (Iowa State University) and Smolarkiewicz continued
the development of an adaptive grid-refinement approach,
embedded in the framework of a nonhydrostatic
anelastic model for simulating a broad range of geophysical
flows using nonoscillatory forward-in-time (NFT) numerical
methods. The focus of the past year was the extension
of the generalized coordinate technique into the viscous
portions of the model. This required a rigorous development
of the higher order differential operators for scalar
and vector diffusion, as well as development of the
accompanying boundary conditions along deformable surfaces.
These developments have been coded into the numerical
model, and are currently being tested in preliminary
simulations. Additional refinements were also developed
regarding the use of analytically specified transformations
for grid adaptation, and are currently being tested
in the context of idealized Held-Suarez climates with
orographic forcing as well as oceanic flows in channels
with irregular coastlines (Figure 43). It is expected
that the former experiments will clarify to what extent
local grid adaptation can enhance the accuracy of climate
statistics. The experiments with irregular channel
geometry open new opportunities for studies of valley
and canyon flows.
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| Figure
43: Continued development of an adaptive grid-refinement
approach, embedded in the framework of a nonhydrostatic
anelastic model for simulating a broad range of geophysical
flows using nonoscillatory forward-in-time (NFT) numerical
methods, have been coded into the numerical model and
are currently being tested in the context of
idealized Held-Suarez climates with
orographic forcing as well as oceanic flows in channels
with irregular coastlines. |
Multidimensional Positive Definite Advection Transport
Algorithm
(MPDATA): an edge-based unstructured-data formulation
Joanna Szmelter (Cranfield University, Srivenham,
UK) and Smolarkiewicz developed
the iterative upwind scheme MPDATA in a Finite Volume
framework with an
edge-based data structure and arbitrary hybrid mesh.
MPDATA has proven successful in simulations of geophysical
flows using single-block, structured, topologically
rectangular meshes employing continuous time-dependent
curvilinear mapping approach (see Smolarkiewicz and
Margolin, J. Comput. Phys., 1998 for a comprehensive
review). The motivation for the finite-volume formulation
and the choice of unstructured meshes is to facilitate
the use of MPDATA schemes for a wider range of applications
involving complex geometries and/or inhomogeneous anisotropic
flows where mesh adaptivity is advantageous. Their
new development preserves the signature benefits of
the standard, Cartesian-mesh MPDATA scheme; i.e., second-order
accuracy, sign preservation, and a full multidimensionality
free of directional-splitting errors (see Fig.
44).
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| Figure
44: Development
of an iterative upwind scheme MPDATA in a Finite
Volume framework with an
edge-based data structure and arbitrary hybrid mesh
has proven successful in simulations of geophysical
flows using single-block, structured, topologically
rectangular meshes employing continuous time-dependent
curvilinear mapping approach. |
Laboratory for internal-gravity-wave dynamics: the
numericale equivalent to the quasi-biennial oscillation (QBO)
analogue
Nils Wedi (European Center for Medium-range Weather
Forecasting) and Smolarkiewicz extended
the classical terrain-following
coordinate
transformation of Gal-Chen and Somerville (J. Comput.
Phys., 1974) to a broad class of time-dependent curvilinear
vertical domains. In particular, their development
allows the simulation of stratified flows with intricate
geometric, time-dependent boundary forcings, either
at the top or bottom of the domain. They applied their
mathematical/numerical framework to the direct numerical
simulation of the celebrated laboratory experiment
of Plumb and McEwan (J. Atmos. Sci, 1978) thereby creating
the numerical equivalent to the laboratory quasi-biennial
oscillation (QBO) analogue. The QBO represents a conspicuous
example of a fundamental dynamical mechanism with challenging
detail, but it is difficult to identify all the physical
mechanisms from experimental evidence alone. A series
of 2D and 3D simulations demonstrate their ability
to reproduce the laboratory experiment (Fig.
45) and
to associate reversing flow patterns as an entirely
wave-driven phenomena.
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| Figure
45: A
series of 2D and 3D simulations demonstrate the
ability to reproduce the laboratory experiment
of classical terrain-following coordinate transformation
of Gal-Chen and Somerville, and to extend it
to a broad class of time-dependent curvilinear
vertical
domains. |
Their results enhance the confidence in the numerical
approach and further elevate the importance of the
laboratory setup for its fundamental similarity to
the atmosphere, while allowing study of the principal
atmospheric mechanisms and their numerical realization
in a well-suited environment.
Ocean-atmosphere interaction
at turbulence- and mesoscales (TOP)
A new method to measure oceanic waves from a moving
platform
Jeilun Sun, in collaboration
with Sean
Burns, Douglas
Vandemark (NASA Goddard Space Flight Center), and Mark
Donelan (University of Miami), continued efforts at
retrieving two-dimensional wave spectra using three
laser altimeters on board the LongEZ aircraft. Sun found that a wavelet analysis method is able to retrieve
wave propagation direction and wavenumber using datasets
collected from the Shoaling Waves Experiment (SHOWEX,
http://www.mmm.ucar.edu/science/abl/showex/showex.html)
and Coupled Boundary-Layers/Air-Sea Transfer (CBLAST-low,
http://www.mmm.ucar.edu/science/abl/cblast/).
This wave analysis method provides a new capability
to efficiently
and economically measure waves and atmospheric turbulence
gathered from a moving platform.
Air-sea interactions under weak wind conditions
Sun, in collaboration
with Haflidi H. Jonsson (Navy Postgraduate School),
Djamal Khelif (University of
California, Irvine), Larry Mahrt and Dean Vickers
(both of Oregon State University), participated in
the ONR-sponsored CBLAST-low experiment off the coast
of Martha's Vineyard, Massachusetts. Sun and
colleagues planned the scientific missions and detailed
flight
plans for the Pelican research aircraft from the Navy
Postgraduate School. Preliminary data analysis showed
the existence of complex internal boundary layer structures
associated with spatial variations in sea surface temperature
(Figure 46).
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| Figure
46: Preliminary
data analysis showing the existence of complex
internal boundary layer structures associated
with spatial variations in sea surface temperature,
as studied in teh CBLAST-low experiment off the
coast of Martha's Vineyard, Massachusetts. |
LES of marine boundary layers with swell
Recent observations in the marine surface layer provide
evidence that swell (fast moving waves) can generate
spectacular behavior in the low-wind neutral planetary
boundary layer (PBL). Low-level jets, positive (upward)
vertical momentum flux, and negative mean gradient
profiles are often observed. To model the impact of
surface waves on the PBL, Peter
Sullivan,
James McWilliams (University of California, Los Angeles),
and Chin-Hoh Moeng recently
developed a new large-eddy simulation (LES) code with
the capability of imposing a moving sinusoidal
wave at its lower boundary. Preliminary simulations
focused on PBLs with light winds, neutral stratification,
and different surface conditions.
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| Figure
47: Snapshot of the instantaneous velocities over
swell
in neutrally
stratified winds of 5ms-1 from
LES. The wave age c/U10 > 2.2, where
U10 is the wind at z=10m and c is
the wave phase
speed. The properties of the imposed wave are amplitude
= 1.6m, waveslope = 0.1, wavelength = 100m, and
wave phase speed c = 12.5m/s. Upper panel u and
lower panel w. Note the strong positive
correlation between u and w on
the downwind side of each wave crest which leads
to a positive
upward
momentum
flux for z > 10m. The color bar, located in
the lower right portion of each figure, shows the
variation in units of m/s. |
Flow visualization of the LES solutions (see Figure
xx, above) shows that in the case of fast moving swell
a coherent pattern of accelerated winds occurs downwind
of each wave crest. At the same time, the vertical
velocity is biased towards negative (positive) values
upstream (downstream) of the wave crest, respectively.
This organization induces positive vertical momentum
flux that accelerates the
near surface winds. The LES is thus able to replicate
important features of a wave-driven boundary layer.
The appearance of a low-level jet and vertically varying
vertical momentum flux makes surface layer measurements
dependent on wave state and vertical distance above
the surface, and invalidates the use of Monin-Obukhov
similarity theory most often used to predict air-sea
fluxes.
Turbulence simulations of ocean boundary layers
Sullivan, James
McWilliams (University of California, Los Angeles),
and Ken Melville (Scripps Institute of
Oceanography) are developing a stochastic model for
the effects of breaking waves for use in turbulence-resolving
simulations of the ocean boundary layer (OBL). The
breaking parameterization, based on laboratory and
field data, is being evaluated in direct numerical
simulation (DNS) with large-eddy simulation (LES) implementations
expected in the next fiscal year. They found that DNS
with wave breaking generates long-lived vortices close
to the water surface that are effective in energizing
the surface region of oceanic boundary layers. A comparison
of idealized oceanic boundary layers driven by constant
current, constant stress, or a mixture of constant
stress plus stochastic breakers provides evidence that
intermittent stress transmission from breaking waves
significantly alters the instantaneous flow patterns
(see Movie 5, below) as well
as the ensemble statistics. Analysis of the mean current
profiles shows that breaking
effectively increases the surface roughness zo by more
than a factor of 30 (see also Figure 48,
below).
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| Movie
5: Animation
of the spanwise vorticity for an OBL simulation
with 100% breaking waves. Note the difference in
flow structure near the no-slip lower boundary
and the uppoer boundary where breaking waves are
present. Near the top of the water the usual turbulence
production mechanism associated with low-speed
streaks and hairpin vortices is disrupted by intermittent
breaking. The highly energized ocean surface layer
enhances turbulence mixing which leads to an increase
in surface roughness. In the above animation, time
is made dimensionless by a large scale turnover
time. |
Mouse over
image to begin movie. Alternately, you may download
the animation.
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| Figure
48: Vertical profiles of the mean current
in wall coordinates with wave breaking. The dotted
line
is the linear
curve u+ = -z+;
the thick solid line is the log-linear law u+ =
ln(-z+)/k +
b valid for smooth walls with (k,
b) = (0.41,5); and the thin solid line is the log-linear
law for
fully rough walls with b = (0.41,-2.1).
The different simulations, indicated by dots, are:
Couette flow (red); stress driven OBL with no breaking
(pink); 25% breaking (green); 80% breaking (blue);
100% breaking (black). Notice how the effective
surface roughness z0 deduced from
the current profiles, increases with the amount
of breaking. |
Compared to a flow driven by a constant current, the
extra mixing from breakers increases the mean eddy
viscosity by more than a factor of ten near the water
surface. Breaking waves alter the usual balance of
production equals dissipation in the turbulent kinetic
energy (TKE) budget. Turbulent boundary layers driven
by constant current and constant stress (i.e. with
no breaking) are also found to differ in fundamental
ways.
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