Dispersion due to meandering Dean Vickers, Larry Mahrt COAS, Oregon State University Danijel Belušić AMGI, Department of Geophysics, University of Zagreb

Overview Introduction (long) Introduction (long) Particle model Particle model Dispersion due to meandering Dispersion due to meandering Meandering vs. turbulence Meandering vs. turbulence

Meandering intro Meandering = mesoscale wind direction variation Meandering = mesoscale wind direction variation Usually recognized by and studied in terms of its effects on dispersion in stable weak-wind ABL Usually recognized by and studied in terms of its effects on dispersion in stable weak-wind ABL Unknown dynamics Unknown dynamics

Turbulence vs. mesoscale

Modeling transient mesoscale motions Regional models, LES models, etc. do not include the common transient mesoscale motions: 1. Not resolved 2. Physics missing 3. Eliminated by explicit or implicit numerical diffusion.

Types of small mesoscale motions 1. Gravity flows (sometimes multiple flows superimposed) 2. Flow distortion by terrain/obstacles 3. Transient mesoscale motions (gravity waves, meandering) 4. Nonstationary low-level jets 5. Solitons

Based on 14 eddy-correlation datasets, the strength of mesoscale motions are: Not related to u *, z/L, Ri or wind speed Not related to u *, z/L, Ri or wind speed Can be greater in complex terrain although less in thermally generated circulations. Can be greater in complex terrain although less in thermally generated circulations. Different types of mesoscale motions may have quite different dispersive behavior. Different types of mesoscale motions may have quite different dispersive behavior. NOT PREDICTABLE NOT PREDICTABLE

Effects on dispersion (1) To a first approximation, the variation of wind direction σ θ is inversely proportional to the mean wind speed: To a first approximation, the variation of wind direction σ θ is inversely proportional to the mean wind speed: and is usually parameterized in models as:

Indeed…

Effects on dispersion (2) Therefore, σ θ (i.e. meandering) is significant only in weak winds Therefore, σ θ (i.e. meandering) is significant only in weak winds The lateral dispersion is then: The lateral dispersion is then:

Effects on dispersion (3) Now, the parameterizations actually state that the variability of cross-wind component σ v is constant  not completely true, but it is independent of V and stability Now, the parameterizations actually state that the variability of cross-wind component σ v is constant  not completely true, but it is independent of V and stability

Effects on dispersion (4) What does that actually mean? What does that actually mean? The dispersion due to meandering does NOT depend on wind speed and stability?! The dispersion due to meandering does NOT depend on wind speed and stability?!

Effects on dispersion (5) Let’s compare the two expressions: Let’s compare the two expressions: Space or time?? In time, the dispersion due to meandering does NOT depend on wind speed nor stability. In time, the dispersion due to meandering does NOT depend on wind speed nor stability.

Particle model Lagrangian stochastic particle model Lagrangian stochastic particle model Particle position updated as Xp(t+dt) = Xp(t) + (U+u’)dt Particle position updated as Xp(t+dt) = Xp(t) + (U+u’)dt Turbulence described by a Markov Chain Monte Carlo process with one step memory: Turbulence described by a Markov Chain Monte Carlo process with one step memory:

Wind field for particle models Observed from single mast (assume spatially homogeneous) Observed from single mast (assume spatially homogeneous) Mesoscale model Mesoscale model LES model LES model Observed using a tower network (this study) Observed using a tower network (this study)

Observations CASES-99 Grassland in rural Kansas in October Grassland in rural Kansas in October Seven towers inside circle of radius 300 m Seven towers inside circle of radius 300 m 13 sonic anemometers  20-hz (u,v,w,T) 13 sonic anemometers  20-hz (u,v,w,T) Site has weak meandering (ranked 8 th out of 9 sites studied) Site has weak meandering (ranked 8 th out of 9 sites studied)

CASES-99 network

Wind field High temporal resolution (no interpolation required) High temporal resolution (no interpolation required) Meandering wind components and the turbulence velocity variances are spatially interpolated in 3-D every time step Meandering wind components and the turbulence velocity variances are spatially interpolated in 3-D every time step Meandering resolved! Meandering resolved!

Decomposition Velocity variances are partitioned into meandering and turbulence based on the time scale associated with the gap region in the heat flux multiresolution cospectra Velocity variances are partitioned into meandering and turbulence based on the time scale associated with the gap region in the heat flux multiresolution cospectra Turbulence and meandering are generated by different physics and have different influences on the plume Turbulence and meandering are generated by different physics and have different influences on the plume

Animations

Case studies show Spatial streaks and bimodal patterns in the 1-h average distribution Spatial streaks and bimodal patterns in the 1-h average distribution Double maximum patterns with higher C on the plume edges and minimum C on plume centerline Double maximum patterns with higher C on the plume edges and minimum C on plume centerline Wind direction often jumps between preferred modes rather than oscillate back and forth Wind direction often jumps between preferred modes rather than oscillate back and forth Time series are highly non-stationary even when 1-h average distribution is ~ Gaussian Time series are highly non-stationary even when 1-h average distribution is ~ Gaussian

Removing record-mean flow Particles leave the tower network domain too quickly with any significant mean wind, so the record-mean wind is removed Particles leave the tower network domain too quickly with any significant mean wind, so the record-mean wind is removed Removing mean wind has a huge impact on the spatial distribution, however, it has little impact on the travel-time dependence of particle dispersion (verified using particle simulator) Removing mean wind has a huge impact on the spatial distribution, however, it has little impact on the travel-time dependence of particle dispersion (verified using particle simulator) This allows us to look at all the records including the stronger wind speeds This allows us to look at all the records including the stronger wind speeds

Measure of particle dispersion Travel time dependence of particle dispersion computed as Travel time dependence of particle dispersion computed as σ x 2 = [(X p (t) - [X p (t)]) 2 ], where t is travel time and brackets denote an average over all particles E.g., for 1-h records there are 72,000 samples of X p for all travel times E.g., for 1-h records there are 72,000 samples of X p for all travel times σ xy = (σ x 2 + σ y 2 ) ½ σ xy = (σ x 2 + σ y 2 ) ½

The entire dataset shows The meandering motions, not the turbulence, are primarily responsible for the horizontal dispersion, and streaks, bimodal patterns and non-stationary time series are a consequence The meandering motions, not the turbulence, are primarily responsible for the horizontal dispersion, and streaks, bimodal patterns and non-stationary time series are a consequence Meandering dominates in weak winds, strong winds, stable and unstable conditions Meandering dominates in weak winds, strong winds, stable and unstable conditions Tracer experiments cannot measure the travel time dependence and therefore they suggest that meandering is only important in weak winds Tracer experiments cannot measure the travel time dependence and therefore they suggest that meandering is only important in weak winds

Problems Horizontal dispersion is parameterized in terms of turbulence, while meandering dominates horizontal dispersion (and has different properties than the turbulence) Horizontal dispersion is parameterized in terms of turbulence, while meandering dominates horizontal dispersion (and has different properties than the turbulence) Regional models under-represent meandering motions Regional models under-represent meandering motions While σ xy = f(σ uvM ) works well, such a velocity scale is not available in models, nor does it appear predictable, nor is it very useful since distributions are highly non-Gaussian While σ xy = f(σ uvM ) works well, such a velocity scale is not available in models, nor does it appear predictable, nor is it very useful since distributions are highly non-Gaussian