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Abstract The spectral model turbulence analysis technique is widely used to derive kinetic energy dissipation rates of turbulent structures (ɛ) from different in situ measurements in the Earth's atmosphere. The essence of this method is to fit a model spectrum to measured spectra of velocity or scalar quantity fluctuations and thereby to deriveɛonly from wavenumber dependence of turbulence spectra. Owing to the simplicity of spectral model of Heisenberg (1948),https://doi.org/10.1007/bf01668899its application dominates in the literature. Making use of direct numerical simulations which are able to resolve turbulence spectra down to the smallest scales in dissipation range, we advance the spectral model technique by quantifying uncertainties for two spectral models, the Heisenberg (1948),https://doi.org/10.1007/bf01668899and the Tatarskii (1971) model, depending on (a) resolution of measurements, (b) stage of turbulence evolution, (c) model used. We show that the model of Tatarskii (1971) can yield more accurate results and reveals higher sensitivity to the lowestɛ‐values. This study shows that the spectral model technique can reliably deriveɛif measured spectra only resolve half‐decade of power change within the viscous (viscous‐convective) subrange. In summary, we give some practical recommendations on how to derive the most precise and detailed turbulence dissipation field from in situ measurements depending on their quality. We also supply program code of the spectral models used in this study in Python, IDL, and Matlab.
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Travelling pulses on three spatial scales in a Klausmeier-type vegetation-autotoxicity model
Abstract Reaction-diffusion models describing interactions between vegetation and water reveal the emergence of several types of patterns and travelling wave solutions corresponding to structures observed in real-life. Increasing their accuracy by also considering the ecological factor known asautotoxicityhas lead to more involved models supporting the existence of complex dynamic patterns. In this work, we include an additional carrying capacity for the biomass in a Klausmeier-type vegetation-water-autotoxicity model, which induces the presence of two asymptotically small parameters:ɛ, representing the usual scale separation in vegetation-water models, andδ, directly linked to autotoxicity. We construct three separate types of homoclinic travelling pulse solutions based on two different scaling regimes involvingɛandδ, with and without a so-calledsuperslow plateau. The relative ordering of the small parameters significantly influences the phase space geometry underlying the construction of the pulse solutions. We complement the analysis by numerical continuation of the constructed pulse solutions, and demonstrate their existence (and stability) by direct numerical simulation of the full partial differential equation model.
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- Award ID(s):
- 2105816
- PAR ID:
- 10524637
- Publisher / Repository:
- IOP Publishing
- Date Published:
- Journal Name:
- Nonlinearity
- Volume:
- 37
- Issue:
- 9
- ISSN:
- 0951-7715
- Format(s):
- Medium: X Size: Article No. 095008
- Size(s):
- Article No. 095008
- Sponsoring Org:
- National Science Foundation
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