Similarity equations of the spectral equations for decaying homogeneous turbulence are considered for which the similarity length scale is not allowed to grow. Two types of solutions are found: an inviscid solution and one involving viscosity. For the former, the energy decays asymptotically as t−2, while for the latter the energy decays exponentially and the ratio of integral scale to Taylor microscale is constant. For both the spectra for fixed initial conditions collapse during decay with simply the energy and a single length scale. The exponentially decaying solution appears to provide an excellent description of the turbulence generated in recent space-filling fractal grid experiments.

A simple spectral model is used to examine what is required to determine the energy and integral scale in homogeneous isotropic turbulence. The problem is that these are determined in part by the largest scales of the turbulence which are either not simulated at all by DNS or experiments, or cannot be estimated because of an insufficient statistical sample. The absence of scales an order of magnitude below the peak in the energy spectrum is shown to affect the determination significantly. Since this energy peak shifts to lower wavenumbers as the flow evolves, the problem becomes progressively worse during decay. It is suggested that almost all reported integral scales for isotropic decaying turbulence are questionable, and that the power laws fitted to them are seriously in error. Approximate correction using the spectral model shows that recent DNS data which decay as u2 ∝ tn with constant n, are also consistent with L ∝ t1/2.

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Intercropping of cereals and legumes has been used in modern agricultural systems, and the soil microorganisms associated with legumes play a vital role in organic matter decomposition and nitrogen (N) fixation. This study investigated the effect of intercropping on the rhizosphere soil microbial composition and structure and how this interaction affects N absorption and utilization by plants to improve crop productivity. Experiments were conducted to analyze the rhizosphere soil microbial diversity and the relationship between microbial composition and N assimilation by proso millet (Panicum miliaceum L.) and mung bean (Vigna radiata L.) from 2017 to 2019. Four different intercropping row arrangements were evaluated, and individual plantings of proso millet and mung bean were used as controls. Microbial diversity and community composition were determined through Illumina sequencing of 16S rRNA and internal transcribed spacer (ITS) genes. The results indicated that intercropping increased N levels in the soil–plant system and this alteration was strongly dependent on changes in the microbial (bacterial and fungal) diversities and communities. The increase in bacterial alpha diversity and changes in unique operational taxonomic unit (OTU) numbers increased the soil N availability and plant N accumulation. Certain bacterial taxa (such as Proteobacteria) and fungal taxa (such as Ascomycota) were significantly altered under intercropping and showed positive responses to increased N assimilation. The average grain yield of intercropped proso millet increased by 13.9–50.1% compared to that of monoculture proso millet. Our data clearly showed that intercropping proso millet with mung bean altered the rhizosphere soil microbial diversity and community composition; thus, this intercropping system represents a potential mechanism for promoting N assimilation and increasing grain yield.

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