Brief Survey of Studies Related to the Appearance of the Problem of Chaotic and Stochastic Motions and to Turbulence Theory

Abstract Relational turbulence theory (RTT) proposes causal relationships across cognitive, emotional and communicative variables. Although many tenets of this theory have been tested individually, there has not yet been a comprehensive, predictive examination of RTT. Using structural equation modelling, this study longitudinally tested several propositions and axioms of RTT. Results are largely in line with many of RTT's predictions. Time 1 relational uncertainty predicted time 2 biased cognitions. Time 1 facilitation from a partner predicted time 2 negative emotions. Negative emotions cross-sectionally related to both the enactment and valence of relational communication episodes. Relational turbulence theory's proposed feedback loop received partial support, such that time 1 communication valence (but not engagement) predicted time 2 partner uncertainty, relationship uncertainty and partner facilitation. Results are discussed in terms of theory expansion and refinement.

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Observations of Small-Scale Turbulence and Energy Dissipation Rates in the Cloudy Boundary Layer

Journal of the Atmospheric Sciences ◽

10.1175/jas3687.1 ◽

2006 ◽

Vol 63 (5) ◽

pp. 1451-1466 ◽

Cited By ~ 75

Author(s):

Holger Siebert ◽

Katrin Lehmann ◽

Manfred Wendisch

Keyword(s):

Boundary Layer ◽

Energy Dissipation ◽

Wind Velocity ◽

Turbulence Theory ◽

Horizontal Wind ◽

Inertial Subrange ◽

Intermittent Flow ◽

Small Scale ◽

Dissipation Rates ◽

Wide Range

Abstract Tethered balloon–borne measurements with a resolution in the order of 10 cm in a cloudy boundary layer are presented. Two examples sampled under different conditions concerning the clouds' stage of life are discussed. The hypothesis tested here is that basic ideas of classical turbulence theory in boundary layer clouds are valid even to the decimeter scale. Power spectral densities S( f ) of air temperature, liquid water content, and wind velocity components show an inertial subrange behavior down to ≈20 cm. The mean energy dissipation rates are ∼10−3 m2 s−3 for both datasets. Estimated Taylor Reynolds numbers (Reλ) are ∼104, which indicates the turbulence is fully developed. The ratios between longitudinal and transversal S( f ) converge to a value close to 4/3, which is predicted by classical turbulence theory for local isotropic conditions. Probability density functions (PDFs) of wind velocity increments Δu are derived. The PDFs show significant deviations from a Gaussian distribution with longer tails typical for an intermittent flow. Local energy dissipation rates ɛτ are derived from subsequences with a duration of τ = 1 s. With a mean horizontal wind velocity of 8 m s−1, τ corresponds to a spatial scale of 8 m. The PDFs of ɛτ can be well approximated with a lognormal distribution that agrees with classical theory. Maximum values of ɛτ ≈ 10−1 m2 s−3 are found in the analyzed clouds. The consequences of this wide range of ɛτ values for particle–turbulence interaction are discussed.

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