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We describe the general theory of anisotropic flow formation in quasi two- dimensional turbulence from the perspective on the potential vorticity (PV) transport in real space. The aim is to calculate the vorticity or PV flux. In Chapter 2, the general structure of PV flux is deduced non-perturbatively using two relaxation models : the first is a mean field theory for the dynamics of minimum enstrophy relaxation based on the requirement that the mean flux of PV dissipates total potential enstrophy but conserves total fluid kinetic energy. The analyses show that the structure of PV flux has the form of a sum of a positive definite hyper-viscous and a negative or positive viscous flux of PV. Turbulence spreading is shown to be related to PV mixing via the link of turbulence energy flux to PV flux. In the relaxed state, the ratio of the PV gradient to zonal flow velocity is homogenized. This structure of the relaxed state is consistent with PV staircases. The homogenized quantity sets a constraint on the amplitudes of PV and zonal flow in the relaxed state. The second relaxation model is derived from a joint reflection symmetry principle, which constrains the PV flux driven by the deviation from the self- organized state. The form of PV flux contains a nonlinear convective term in addition to viscous and hyper-viscous terms. The nonlinear convective term, how- ever, can be viewed as a generalized diffusion, on account of the gradient- dependent ballistic transport in avalanche-like systems. For both cases, the detailed transport coefficients can be calculated using perturbation theory in Chapter 3. For a broad turbulence spectrum, a modulational calculation of the PV flux gives both a negative viscosity and a positive hyper-viscosity. For a narrow turbulence spectrum, the result of a parametric instability analysis shows that PV transport is also convective. In both relaxation and perturbative analyses, it is shown that turbulent PV transport is sensitive to flow structure, and the transport coefficients are nonlinear functions of flow shear. In Chapter 4, the effect of mean shear flows on zonal flow formation is considered in the contexts of plasma drift wave turbulence and quasi-geostrophic turbulence models. The generation of zonal flows by modulational instability in the presence of large-scale mean shear flows is studied using the method of characteristics as applied to the wave kinetic equation. It is shown that mean shear flows reduce the modulational instability growth rate by shortening the coherency time of the wave spectrum with the zonal shear. The scalings of zonal flow growth rate and turbulent vorticity flux with mean shear are determined in the strong shear limit

Agricultural systems depend on continued inputs of phosphate fertiliser to maintain productivity. However, due to ever increasing global demand, the finite reserves of phosphate rock are being rapidly depleted. This is compounded by the fact that half of the soluble phosphate in fertiliser applied to soil is converted to sparingly-soluble minerals such as calcium phosphate which are unavailable for plant uptake. It is therefore important to investigate strategies that will improve the utilisation of phosphate in soil-plant systems. While it has been demonstrated that phosphate-solubilising bacteria can utilise sparingly-soluble phosphate minerals in soil, the mechanisms by which this occur remain unclear. In this project, 105 rhizobacteria were assessed for a number of plant growth-promoting traits, such as production of 1-aminocyclopropane-1-carboxylate deaminase, phytase, and inorganic phosphate solubilisation using plate screening assays. Ten of the most effective phosphate-solubilising isolates were further assessed using an in vitro hydroxyapatite liquid culture assay. Analysis of culture filtrates revealed that the effective phosphate-solubilising isolates, Pseudomonas spp. and Burkholderia sp., were predominantly secreting 2-keto-gluconic acid rather than the expected gluconic acid. In addition, a yet to be characterised organic acid was secreted by several Pseudomonas spp. strains which may also be involved in phosphate solubilisation. In an attempt to identify novel genes involved in phosphate solubilisation, three isolates of different bacterial genera, Enterobacter sp. Wi28, Pseudomonas sp. Ha200 and Burkholderia sp. Ha185, derived from diverse geographic locations were subjected to random transposon mutagenesis. This enabled the identification of two unique uncharacterised genes from Burkholderia sp. Ha185. One mutant, hemX::Tn5(F18), with a mutation in hemX gene involved in haem biosynthesis, exhibited an almost complete abolition in hydroxyapatite solubilisation. The second mutant bxpC::Tn5(F13) exhibited partial and delayed solubilisation. The translated product of the bxpC gene encodes a novel hypothetical protein with unknown function. However, based on a combination of organic acid, qRT-PCR and bioinformatics analysis, it is hypothesised that BxpC is a potential cargo protein involved in protection and transport of the calcium bound 2-ketogluconic acid compound. Through the use of a Burkholderia sp. Ha185 GFP-tagged strain in conjunction with a gnotobiotic in vivo plant assay developed in this study, the colonisation pattern of Burkholderia sp. Ha185 and its derivatives on ryegrass roots over three week duration was defined. The preliminary characterisation of the bxpC and hemX identified in the study and defining the interaction of Burkholderia sp. Ha185 on the plant root provides a greater understanding of phosphate cycling by bacteria and its relationship to the plant. The novel pathways and findings of this study have provided further insights into the underlying mechanisms of inorganic phosphate solubilisation in soil-plant systems.