Roddam Narasimha

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An event-based description of the heat-flux time
series in an atmospheric boundary layer
Roddam Narasimha Jawaharlal Nehru Centre for
Advanced Scientific Research, Bangalore Internat
ional Workshop Wall Bounded Shear Flows
Transition and Turbulence Isaac Newton Institute
for Mathematical Sciences 11 September 2008
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FLUX TIME SERIES

• Unlike energy, dissipation, flux is not
  sign-definite
• Great interest in contribution to mean flux,
  rather than to mean squared fluctuation
• Generalized harmonic analysis, wavelets cannot
  handle problem
• Attempt event-based episodic description
  through extended point process analysis

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DATA ANALYSED

• Monsoon Trough Boundary Layer Experiment
  (MONTBLEX 90)\
• (Goel Srivastav 1990 BAMS Narasimha, Sikka
  Prabhu 1997 Ind. Acad. Sci.)
• Boulder Atmospheric Observatory, 300 m tower
  (Courtesy J C Kaimal)
• KNMI Cabauw, 200 m tower (courtesy KNMI)

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THE MONSOON TROUGH
----- mean position, active - - - -
mean position, weak -------envelope
of l.s.d. around
mean
Rajkumar, R Narasimha 1995 Paul Sikka 1976
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MONTBLEX 90
30 m mast with 6 booms at 1, 2, 4, 8, 15, 30 m
respectively
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BASIC DATA FOR JODHPUR
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WIND SPEEDS
Wind speed records from cup anemometers mounted
on the Jodhpur mast at 1, 2, 4, 8, 15 and 30 m
above ground (file J6261400).
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LARGE MEAN FLUX, HUGE FLUCTUATIONS
Typical traces of horizontal and vertical
fluctuations and their product the mean value of
the product is shown by the full line in the top
panel R Narasimha 1995 Curr. Sci.
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EVENT DETECTION
Event markers from different methods of event
detection.
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EXTENDED POINT PROCESS

• Point process (Cox Isham 1980)
• In the simplest case, a point process is a
  series of points (e.g. instants of time) that can
  be marked on a line (representing running time),
  each point denoting the occurrence of one of the
  events under study (e.g. failure of bulbs in a
  lab, arrival of bus at a stop).
• For flux events we introduce the concept of
  extended point processes. Here the event at
  each occurrence is characterized by additional
  variables, including
• the sign of the event
• its amplitude (max. flux value, e.g.)
• its magnitude (total contribution to mean flux)
• its duration

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AGENDA

• Suitable event detection procedure
• Classification of events into types
• Event characterization
• Representation of flux time series as extended
  point process
• Determination of EPP statistical parameter
• Dynamical implication

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EVENT PARAMETERS
Sketch defining event parameters. R Narasimha et
al. 2007, Phil. Trans.
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DETECTION CRITERIA

• Lu Willmarth (1973) hyperbolic hold in u?w?
  plane fluctuations in u?w ? can be huge multiple
  of mean
• Present method
• Event occurs if
• f gt kf f
• where f instantaneous flux
• f rms fluctuation
• kf threshold number
• Wavelets
• Identify local maxima of absolute value of WTC
  at each scale
• Event if peak flux gt f

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FLUX FLUCTUATION
Variation of fractional contribution to flux and
fractional cumulative duration of corresponding
flux events as function of threshold for event
detection in multiples of r.m.s. value of flux
fluctuation. Measurement at height above ground
of 4 m at Jodhpur, 10 m at Boulder and 20 m at
Cabauw. .
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FLUX FLUCTUATION
Normalized signatures of positive (upper) and
negative (lower) events with threshold technique.
Dotted line is a mirror reflection of the
negative event about the horizontal axis. .
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QUADRANT STATISTICS
Jodhpur
Bangalore
Cabauw
Wind tunnel
Momentum flux events All numbers as per cent
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MOMENTUM EVENT STATISTICS
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FREQUENCY DISTRIBUTION
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AMPLITUDE VERSUS DURATION
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FLUX SIGNAL TIME SERIES
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CUMULATIVE FLUX
Burstiness area AOC area ADC concentration
index (cf. Gini index) R Narasimha, Kailas
(1990)
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BURSTINESS CURVES
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HEAT FLUX EVENT PROFILES
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HEAT FLUX EVENT PROFILES
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FLUX TIME SERIES
Events
Raw signal
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EVENT PARAMETER DISTRIBUTIONS
Event magnitudes
Event duration
Mean time between event occurrences
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Quadrantal Occupancy
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CONTRIBUTION TO FLUX
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MEAN AMPLITUDE
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MEAN DURATION
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NUMBER OF EVENTS
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BURSTINESS DIAGRAMS
Burstiness curves for heat flux events in
near-neutral case
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EFFECT OF STABILITY
Actual flux vs. fractional quadrant time (l. to
r.) stable, neutral, unstable
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EFFECT OF STABILITY
Actual heat flux
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THRESHOLD EFFECT OF STABILITY
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EFFECT OF STABILITY
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EFFECT OF STABILITY
Heat flux Event Parameters For and events
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CO-OCCURRENCE COEFFICIENTS
no. of w?T? events that occur during a u?w?
event Chm

89.8 total number of momentum flux
events
no. of u?w? events that occur during a w?T?
event Cmh

79.6 total number of momentum flux
events
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TABLE 1
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COMPARISON OF HEAT FLUX DATA
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FLUX EVENT PARAMETERS STABLE CASE
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FLUX EVENT PARAMETERS NEAR-NEUTRAL CASE
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FLUX EVENT PARAMETERS UNSTABLE CASE
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CONCLUSIONS

• Momentum flux
• Analysis at z 1.1 x 105, Jodhpur
• Flux events with instantaneous flux exceeding 1
  s.d. account for virtually all flux
• Feasible to identify normalized event signatures
  (both and )
• Flux time series can be represented by chronicle
  of signed events with magnitude and duration as
  parameters
• Flow is flux-productive 36 of time
• counter-productive 15
• idle 49

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CONCLUSIONS

• Compared lab Re
• higher ejection quadrant occupancy
• lower sweep quadrant occupancy
• lower ejection quadrant contribution to flux
• higher sweep quadrant contribution to flux

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CONCLUSIONS

• Heat flux
• Co-occurrence
• heat flux event 89.8 of momentum flux events
• momentum flux event 79.6 of heat flux events
• Effect of stability

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THANK YOU
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