mountain-wave momentum flux in an evolving synoptic-scale flow
DESCRIPTION
Mountain-Wave Momentum Flux in an Evolving Synoptic-Scale Flow. Chih-Chieh Chen, Dale R. Durran and Gregory J. Hakim Department of Atmospheric Sciences University of Washington. : maximum mean flow. : period. : half width of mountain. Transient Mountain Waves. - PowerPoint PPT PresentationTRANSCRIPT
May 2005 ICAM - MAP 1
Mountain-Wave Momentum Flux in an Mountain-Wave Momentum Flux in an Evolving Synoptic-Scale FlowEvolving Synoptic-Scale Flow
Chih-Chieh Chen,Dale R. Durran and Gregory J. Hakim
Department of Atmospheric SciencesUniversity of Washington
May 2005 2ICAM - MAP
Transient Mountain WavesTransient Mountain Waves
Lott and Teitelbaum (1993)
: maximum mean flow
: period
: half width of mountain
• U = U(t)
• 2D configuration
• large-scale dynamics unspecified
May 2005 ICAM - MAP 3
How does the domain-averaged momentum flux vary with time and
height?
Lott and Teitelbaum: when 1, “roughly the momentum flux remains that predicted by the
stationary theory.”
May 2005 4ICAM - MAP
Nonlinearly Balanced Barotropic SynoptiNonlinearly Balanced Barotropic Synoptic-Scale Flowc-Scale Flow
doubly periodic
May 2005 5ICAM - MAP
Hypothetical Hypothetical z-tz-t Momentum Flux Distribution Momentum Flux Distribution
under linear theory:
t
z
/2
- - + +
May 2005 6ICAM - MAP
Horizontally Averaged Momentum Flux Horizontally Averaged Momentum Flux ((hh = 250 m) = 250 m)
Constant U of 10 ms-1
Constant U of 20 ms-1
May 2005 7ICAM - MAP
WKB Ray Tracing for U = U(t)U increasing with time
t = t1t = t2t = t3
U decreasing with time
t = t4t = t5t = t6
May 2005 8ICAM - MAP
Conservation of Wave ActionConservation of Wave Action
Wave action density changes when neighboring rays converge or diverge
May 2005 9ICAM - MAP
Momentum Flux Changes Along a RayMomentum Flux Changes Along a Ray
Ways to change momentum flux:• change wave action (convergence or divergence of
neighboring rays)• change intrinsic frequency and/or local wavenumbers
And for hydrostatic Boussinesq gravity waves:
May 2005 10ICAM - MAP
Comparison of Momentum Fluxes from the Model and the WKB Reconstructon (h=125 m)model output WKB solution
May 2005 11ICAM - MAP
Change of intrinsic frequencyChange of intrinsic frequency
k increases k decreases
x
y
Accelerating Phase
x
y
Decelerating Phase
May 2005 12ICAM - MAP
Influence of Confluence and Difluence (h=125 m)Translating square wave Uniform westerly flow
May 2005 13ICAM - MAP
Momentum Flux for Higher MountainsMomentum Flux for Higher Mountains
h = 250 m h = 500 m h = 1 km
Linear (h2) contour scaling
May 2005 14ICAM - MAP
Pressure Drag Pressure Drag EvolutionEvolution
From steady-state linear theory: drag U
min(Nh/U)=0.0625min(Nh/U)=0.50min(Nh/U)=0.125min(Nh/U)=0.25min(Nh/U)=0.375
May 2005 15ICAM - MAP
SummarySummary• On a time-scale of 2 days, transience renders the steady-state solution almost irrelevant.• In an accelerating flow, wave packets tend to accumulate above the mountain, enhancing wave activity aloft.• Large-scale confluence and difluence also affect the momentum flux.• Momentum flux distribution:
• Largest momentum fluxes are found in the mid and upper troposphere before the time of maximum cross-mountain flow.• Low-level convergence of momentum flux produces an surprising acceleration of low-level cross-mountain flow during the accelerating phase.
May 2005 16ICAM - MAP
Summary ContinuedSummary Continued
• For almost-linear flows:• The momentum flux distribution may be understood using WKB ray tracing theory. • The instantaneous drag (but not the momentum flux aloft) is given by the steady linear solution.
• For nonlinear flows • The instantaneous drag is not determined by the instantaneous value of Nh/U.
May 2005 17ICAM - MAP
Average Average Momentum Momentum Flux Profile Flux Profile over One over One
PeriodPeriod
May 2005 18ICAM - MAP
Group Velocity of Mountain-Wave PacketsGroup Velocity of Mountain-Wave Packets
Dispersion relation for 2D gravity waves
For stationary waves at
Vertical group velocity of mountain wave packet launched at time
May 2005 19ICAM - MAP
Construction of the Synoptic-Scale Construction of the Synoptic-Scale FlowFlow
doubly periodic
May 2005 20ICAM - MAP
Momentum Flux and Pressure DragMomentum Flux and Pressure Drag
Breaking
U
pressure drag<uw>
<uw>
<uw>
<uw>
a sink for momentum
H L
May 2005 21ICAM - MAP
Ray Paths and Momentum Flux in the Ray Paths and Momentum Flux in the z-t z-t planeplane