An analysis of intermittency, scaling, and surface renewal in atmospheric surface layer turbulence. (English) Zbl 1171.86338
Summary: Turbulent velocity and scalar concentration time series were collected in the atmosphere above an ice sheet, a mesic grassland, and a temperate pine forest, thereby encompassing a wide range of roughness conditions encountered in nature. Intermittency and scaling properties of such series were then analyzed using Tsallis’s non-extensive thermostatistics. While theoretical links between the Tsallis’s non-extensive thermostatistics and Navier–Stokes turbulence remain questionable, the Tsallis distribution (a special interpretation of Student’s t-distribution) provides a unifying framework to investigate two inter-connected problems: similarity between scalars and velocity statistics within the inertial subrange and “contamination” of internal intermittency by “external” factors. In particular, we show that “internal” intermittency models, including the She–Leveque, Lognormal, and Log-stable, reproduce the observed Tsallis parameters well for velocities within the inertial subrange, despite the differences in surface roughness conditions, but fail to describe the fluctuations for the scalars (e.g., air temperature CO\(_{2}\) and water vapor). Such scalars appear more intermittent than velocity when the underlying surface is a large source or sink. The dissimilarity in statistics between velocity and scalars within the inertial subrange is shown to be strongly dependent on “external” intermittency. The genesis of “external” intermittency for scalars is linked to the classical Higbie surface renewal process and scalar source strength. Surface renewal leads to a ramp-like pattern in the scalar concentration (or temperature) time series with a gradual increase (rise-phase) associated with sweeping motion from the atmosphere onto the surface or into the canopy and a sharp drop associated with an ejection phase from the surface (or the canopy) back into the atmosphere. The duration of the rise-phase is on the order of the integral time scale, while the duration of the ejection phase is much shorter and is shown to impact the distributional tails at the small scales. Implications for “scalar turbulence” models are also discussed in the context of biosphere–atmosphere CO\(_{2}\) exchange.
Keywords:
Antartica; grassland; pine forest; atmosphere turbulence; intermittency; scalar transfer; surface renewal; Tsallis statisticsReferences:
| [1] | Warhaft, Z., Passive scalars in turbulent flows, Annu. Rev. Fluid Mech., 32, 203-240 (2000) · Zbl 0988.76042 |
| [2] | Warhaft, Z., Turbulence in nature and in the laboratory, Proc. Nat. Acad. Sci. USA, 99, 2481-2486 (2002) |
| [3] | Warhaft, Z.; Shen, X., Some comments on the small scale structure of turbulence at high Reynolds number, Phys. Fluids, 13, 5, 1532-1533 (2001) · Zbl 1184.76584 |
| [4] | Gylfason, A.; Warhaft, Z., On higher order passive scalar structure functions in grid turbulence, Phys. Fluids, 16, 11, 4012-4019 (2004) · Zbl 1187.76198 |
| [5] | Pumir, A.; Shraiman, B. I.; Siggia, E. D., Turbulent mixing of a passive scalar, Physica A, 263, 1-4, 95-103 (1999) |
| [6] | Shraiman, B. I.; Siggia, E. D., Scalar turbulence, Nature, 405, 6787, 639-646 (2000) |
| [7] | Sreenivasan, K.; Antonia, R., The phenomenology of small-scale turbulence, Annu. Rev. Fluid Mech., 29, 435-472 (1997) |
| [8] | Ramos, F. M., Generalized thermostatistics description of probability densities of turbulent temperature fluctuations, Comput. Phys. Comm., 147, 1-2, 556-558 (2002) · Zbl 1074.76566 |
| [9] | Ramos, F. M., Atmospheric turbulence within and above an Amazon forest, Physica D, 193, 1-4, 278-291 (2004) · Zbl 1076.76534 |
| [10] | Gotoh, T.; Kraichnan, R. H., Turbulence and Tsallis statistics, Physica D, 193, 1-4, 231-244 (2004) · Zbl 1060.76064 |
| [11] | Tsallis, C., Possible generalization of the Boltzmann-Gibbs statistics, J. Stat. Phys., 52, 479-487 (1988) · Zbl 1082.82501 |
| [12] | Beck, C., Generalized statistical mechanics and fully developed turbulence, Physica A, 306, 189-198 (2002) · Zbl 0994.76039 |
| [13] | Ramos, F. M., Non-extensive statistics and three-dimensional fully developed turbulence, Physica A, 295, 1-2, 250-253 (2001) · Zbl 0978.76036 |
| [14] | Bolzan, M. J.A., Analysis of fine-scale canopy turbulence within and above an Amazon forest using Tsallis’ generalized thermostatistics, J. Geophys. Res.-Atmos., 107, D20 (2002) |
| [15] | Arimitsu, T.; Arimitsu, N., Tsallis statistics and fully developed turbulence, J. Phys. A, 33, 27, L235-L241 (2000) · Zbl 1005.76038 |
| [16] | Arimitsu, T.; Arimitsu, N., Analysis of turbulence by statistics based on generalized entropies, Physica A, 295, 1-2, 177-194 (2001) · Zbl 0978.76034 |
| [17] | Arimitsu, T.; Arimitsu, N., Analysis of fully developed turbulence by a generalized statistics, Progr. Theoret. Phys., 105, 2, 355-360 (2001) · Zbl 1005.76038 |
| [18] | Arimitsu, N.; Arimitsu, T., Analysis of velocity derivatives in turbulence based on generalized statistics, Europhys. Lett., 60, 1, 60-65 (2002) · Zbl 1051.82002 |
| [19] | Arimitsu, T.; Arimitsu, N., Analysis of velocity fluctuation in turbulence based on generalized statistics, J. Phys. Condens. Matter., 14, 9, 2237-2246 (2002) · Zbl 1051.82002 |
| [20] | Arimitsu, T.; Arimitsu, N., Tsallis statistics and turbulence, Chaos Solitons Fractals, 13, 3, 479-489 (2002) · Zbl 1051.82002 |
| [21] | Frisch, U., Turbulence (1995), Cambridge University Press, p. 296 · Zbl 0727.76064 |
| [22] | Cava, D.; Giostra, U.; Tagliazucca, M., Spectral analysis of a perturbed stable boundary layer, Nuovo Cimento Soc. Ital. Fis. C, 22, 5, 693-704 (1999) |
| [23] | Cava, D.; Giostra, U.; Tagliazucca, M., Spectral maxima in a perturbed stable boundary layer, Bound. Layer Meteorol., 100, 3, 421-437 (2001) |
| [24] | Giostra, U.; Cava, D.; Schipa, S., Structure functions in a wall-turbulent shear flow, Bound. Layer Meteorol., 103, 3, 337-359 (2002) |
| [25] | Cava, D.; Schipa, S.; Giostra, U., Investigation of low-frequency perturbations induced by a steep obstacle, Bound. Layer Meteorol., 115, 1, 27-45 (2005) |
| [26] | Katul, G.; Hsieh, C. I.; Sigmon, J., Energy-inertial scale interactions for velocity and temperature in the unstable atmospheric surface layer, Bound. Layer Meteorol., 82, 1, 49-80 (1997) |
| [27] | Katul, G.; Vidakovic, B.; Albertson, J., Estimating global and local scaling exponents in turbulent flows using discrete wavelet transformations, Phys. Fluids, 13, 1, 241-250 (2001) · Zbl 1184.76274 |
| [28] | Cava, D., Organised motion and radiative perturbations in the nocturnal canopy sublayer above an even-aged pine forest, Bound. Layer Meteorol., 112, 1, 129-157 (2004) |
| [29] | Katul, G. G.; Albertson, J. D., An investigation of higher-order closure models for a forested canopy, Bound. Layer Meteorol., 89, 1, 47-74 (1998) |
| [30] | Katul, G. G.; Albertson, J. D., Modeling \(CO_2\) sources, sinks, and fluxes within a forest canopy, J. Geophys. Res. Atmos., 104, D6, 6081-6091 (1999) |
| [31] | Katul, G., Multiscale analysis of vegetation surface fluxes: from seconds to years, Adv. Water Resour., 24, 9-10, 1119-1132 (2001) |
| [32] | Siqueira, M.; Katul, G., Estimating heat sources and fluxes in thermally stratified canopy flows using higher-order closure models, Bound. Layer Meteorol., 103, 1, 125-142 (2002) |
| [33] | Hsieh, C. I.; Katul, G. G., Dissipation methods, Taylor’s hypothesis, and stability correction functions in the atmospheric surface layer, J. Geophys. Res. Atmos., 102, D14, 16391-16405 (1997) |
| [34] | Cleve, J., Intermittency exponent of the turbulent energy cascade, Phys. Rev. E, 69 (2004), Art. No. 066316 |
| [35] | Meneveau, C., Joint multifractal measures: Theory and applications to turbulence, Phys. Rev. A, 41, 894-913 (1990) |
| [36] | Katul, G. G.; Parlange, M. B., On the active-role of temperature in surface-layer turbulence, J. Atmospheric Sci., 51, 15, 2181-2195 (1994) |
| [37] | Aivalis, K., Temperature structure functions for air flow over moderately heated ground, Phys. Fluids, 14, 2439-2446 (2002) · Zbl 1185.76023 |
| [38] | Higbie, R., The rate of absorption of a pure gas into a still liquid during short periods of exposure, Trans. Amer. Inst. Chem. Eng., 31, 365-388 (1935) |
| [39] | Perlmutter, D. D., Surface renewal models in mass transfer, Chem. Eng. Sci., 16, 287-296 (1961) |
| [40] | Castellvi, F.; Perez, P. J.; Ibanez, M., A method based on high-frequency temperature measurements to estimate the sensible heat flux avoiding the height dependence, Water Resour. Res., 38, 6 (2002) |
| [41] | Castellvi, F., Combining surface renewal analysis and similarity theory: A new approach for estimating sensible heat flux, Water Resour. Res., 40, 5 (2004) |
| [42] | Snyder, R. L.; Spano, D.; Pawu, K. T., Surface renewal analysis for sensible and latent heat flux density, Bound. Layer Meteorol., 77, 3-4, 249-266 (1996) |
| [43] | Spano, D., Surface renewal analysis for sensible heat flux density using structure functions, Agr. Forest Meteorol., 86, 3-4, 259-271 (1997) |
| [44] | Spano, D., Estimating sensible and latent heat flux densities from grapevine canopies using surface renewal, Agr. Forest Meteorol., 104, 3, 171-183 (2000) |
| [45] | Katul, G., Latent and sensible heat flux predictions from a uniform pine forest using surface renewal and flux variance methods, Bound. Layer Meteorol., 80, 3, 249-282 (1996) |
| [46] | Paw-U, K. T., Surface renewal analysis: A new method to obtain scalar fluxes, Agri. Forest Meteorol., 74, 119-137 (1995) |
| [47] | Katul, G. G., One and two equation models for canopy turbulence, Bound. Layer Meteorol., 113, 1, 81-109 (2004) |
| [48] | Katul, G. G.; Parlange, M. B.; Chu, C. R., Intermittency, local isotropy, and non-Gaussian statistics in atmospheric surface-layer turbulence, Phys. Fluids, 6, 7, 2480-2492 (1994) |
| [49] | Katul, G.; Vidakovic, B., Identification of low-dimensional energy containing flux transporting eddy motion in the atmospheric surface layer using wavelet thresholding methods, J. Atmospheric Sci., 55, 3, 377-389 (1998) |
| [50] | Deschatres, F.; Sornette, D., The dynamics of book sales: Endogenous versus exogenous shocks in complex networks, Phys. Rev. Lett. E, 72, 1 (2005), Art. No. 016112 |
| [51] | Sornette, D.; Helmstetter, A., Endogenous versus exogenous shocks in systems with memory, Physica A, 318, 3-4, 577-591 (2003) · Zbl 1010.37017 |
| [52] | Kolmogorov, A. N., The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers, Dokl Akad. Nauk. SSSR, 30, 9-13 (1941) · Zbl 1142.76389 |
| [53] | Kolmogorov, A. N., A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number, J. Fluid Mech., 13, 82-86 (1962) · Zbl 0112.42003 |
| [54] | Renner, C.; Peinke, J.; Friedrich, R., Experimental indications for Markov properties of small-scale turbulence, J. Fluid Mech., 433, 383-409 (2001) · Zbl 0968.76504 |
| [55] | Leveque, E.; She, Z. S., Cascade structures and scaling exponents in a dynamical model of turbulence: Measurements and comparison, Phys. Rev. E, 55, 2789-2799 (1997) |
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