https://ogma.newcastle.edu.au/vital/access/ /manager/Index ${session.getAttribute("locale")} 5 https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:34388 1/4] and velocity scale v_K [≡(ν⋶)^1/4] also emerge as natural scaling parameters in conformity with SP, indicating that Kolmogorov's first hypothesis is subsumed under the more general hypothesis of SP. Further, the requirement for a very large Reynolds number is also relaxed, at least for the first similarity hypothesis. This requirement however is still necessary to derive the two-thirds law (or the four-fifths law) from the analysis. These analytical results are supported by experimental data in wake, jet, and grid turbulence. An expression for the fourth-order moment of the longitudinal velocity increments (δu)⁴ is derived from the analysis carried out in the inertial range. The expression, which involves the product of (δu)² and ∂δp/∂x, does not require the use the volume-averaged dissipation ⋶_r, introduced by Oboukhov [Oboukhov, Some specific features of atmospheric turbulence, J. Fluid Mech. 13, 77 (1962)] on a phenomenological basis and used by Kolmogorov to derive his refined similarity hypotheses [Kolmogorov, 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 (1962)], suggesting that ⋶_r is not, like ⋶, a quantity issuing from the Navier-Stokes equations.]]> Wed 04 Sep 2019 09:54:15 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:29592 2n+1(𝜕u∕𝜕z)=(𝜕u∕𝜕z)²ⁿ⁺¹∕(𝜕u∕𝜕z)²(2n+1)∕2 on the wake centreline, which should be zero if local isotropy is satisfied (n is a positive integer). It is found that the relation M_2n+1(𝜕u∕𝜕z) ∼ RM _𝜆̅¹ is supported reasonably well by hot-wire data up to the seventh-order (n = 3), although it is also dependent on the initial conditions. In particular, the present data show that the higher the order (e.g. fifth- or seventh-order), the higher R_𝜆 must be for local isotropy to be satisfied (i.e. M_2n+1(𝜕u∕𝜕z) = 0).]]> Sat 24 Mar 2018 07:32:09 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:55786 Sat 22 Jun 2024 12:40:13 AEST ]]>