https://nova.newcastle.edu.au/vital/access/ /manager/Index ${session.getAttribute("locale")} 5 https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:26107 -4 (x is the streamwise direction). It is important to stress that this derivation does not use the constancy of the non-dimensional dissipation rate parameter C_∊ = ⋷u^'3/L_u (L_u and u' are the integral length scale and root mean square of the longitudinal velocity fluctuation respectively). We show, in fact, that the constancy of C_∊ is simply a consequence of complete SP (i.e. SP at all scales of motion). The significance of the analysis relates to the fact that the SP requirements for the mean velocity and mean turbulent kinetic energy (i.e. U ~ x^-1 and k ~ x^-2 respectively) are derived without invoking the transport equations for and . Experimental hot-wire data along the axis of a turbulent round jet show that, after a transient downstream distance which increases with Reynolds number, the turbulence statistics comply with complete SP. For example, the measured ⋷ agrees well with the SP prediction, i.e. ⋷ ~ x^-4, while the Taylor microscale Reynolds number Reλ remains constant. The analytical expression for the prefactor A_∊ for ⋷ ~ (x - X₀)^-4(where x₀ is a virtual origin), first developed by Thiesset et al. (J. Fluid Mech., vol. 748, 2014, R2) and rederived here solely from the SP analysis of the s.b.s. energy budget, is validated and provides a relatively simple and accurate method for estimating ⋷ along the axis of a turbulent round jet.]]> Sat 24 Mar 2018 07:39:53 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:37033 θ, the mean dissipation rate of θ̅²/2, where θ̅² is the temperature variance. The analytical approach follows that of Thiesset et al. (J. Fluid Mech., vol. 748, 2014, R2) who developed an expression for ϵ_κ, the mean turbulent kinetic energy dissipation rate, using the transport equation for (δu)², the second-order velocity structure function. Experimental data show that complete self-preservation for all scales of motion is very well satisfied along the jet axis for streamwise distances larger than approximately 30 times the nozzle diameter. This validation of the analytical results is of particular interest as it provides justification and confidence in the analytical derivation of power laws representing the streamwise evolution of different physical quantities along the axis, such as: η, λ, λθ, R_U, R_Θ (all representing characteristic length scales), the mean temperature excess Θ₀, the mixed velocity–temperature moments uθ², vθ² and θ² and ∈_θ. Simple models are proposed for uθ² and vθ² in order to derive an analytical expression for A_∈θ, the prefactor of the power law describing the streamwise evolution of ∈θ. Further, expressions are also derived for the turbulent Péclet number and the thermal-to-mechanical time scale ratio. These expressions involve global parameters that are most likely to be influenced by the initial and/or boundary conditions and are therefore expected to be flow dependent.]]> Fri 07 Aug 2020 10:22:14 AEST ]]>