Effects Of Large-scale Forcings On Small-scale Structures In Turbulence

Predicting turbulence is a difficult task because turbulence consists of a wide range of scales.For this reason,we have to introduce some reasonable approximations or hypotheses regarding the regimes or structure of specific turbulent flows such as the local isotropy and the self-preservation.This will significantly simplify the turbulence problems and allow some theoretical analyses.In this thesis,self-preservation(SP)analyses are firstly applied to the mean momentum and the scale-by-scale energy budget equations in the far-wake of a circular cylinder.The scale-by-scale SP analysis,which is a two-point analysis,complements the SP analysis of the mean momentum equation.Power-law variations are derived for different length scales(e.g.the Taylor microscale and the Kolmogorov length scale)and velocity scales(e.g.the root-mean-square of the streamwise velocity fluctuation the Kolmogorov velocity scale).These Power-law variations relations are well supported by hot-wire data in the far-wake at a Reynolds number of 2000 based on the free-stream velocity and the cylinder diameter.On the centreline of the far-wake,both energy spectra and structure functions exhibit an almost perfect collapse over all wavenumbers and separations,irrespectively of the set of scaling variables used for normalisation.This is consistent with a complete self-preservation(i.e.SP is satisfied at all scales of motions)in the far-wake.The transport equation for the isotropic turbulent energy dissipation rate ?isois derived by applying the limit at small separations to the two-point energy budget equation along the centreline of a far-wake and along the centreline of a fully developed channel.The results are compared to that in other flows such as the flow along the axis of a round jet,and grid turbulence.It is found along the centreline of a far-wake that the imbalance between the production and the destruction of ?isois governed by both streamwise advection and lateral turbulent diffusion(the former contributes more to the budget than the latter).This imbalance differs intrinsically from that in other flows,e.g.grid turbulence and the flow along the centreline of a fully developed channel,where either the streamwise advection or the lateral turbulent diffusion of ?isogoverns the imbalance.More importantly,the different types of imbalance represent different constraints on the relation between the skewness of the longitudinal velocity derivative S and the destruction coefficient of enstrophy G.This results in a non-universal approach of S toward a constant value as the Taylor microscale Reynolds number R?increases.For example,for the flow along the centreline in the far-wake of a circular cylinder,the magnitude of S decreases initially(R? ?40)before increasing(R?> 40)toward this constant value.For all the flows considered in the present thesis,the approach is flow-dependent and is reasonably well supported by experimental and numerical data.The constancy of S at large R?has obvious ramifications for small scale turbulence research since it violates the modified similarity hypothesis introduced by Kolmogorov in 1962 but is consistent with the original similarity hypothesis introduced by Kolmogorov in 1941.The variations of S with R?can be used to improve the standard k-?? turbulence model.The numerical values of C?2currently used in most k-?? models is 1.92.New analytical expressions are developed more rigorously than with previous ad-hoc procedures.The present analysis leads to analytical expressions for C?2which not only conform with the SP requirements but differ between different flows.They also differ between different locations in the same flow.This confirms unambiguously the non-universality of C?2.However,while its numerical value is flow-dependent,the analysis reveals that it is independent of R?in a given flow when SP is satisfied.The above analysis is then extended to the passive scalar field.An analytical expression relating the mixed velocity-temperature derivative skewness-STand the destruction coefficient of ??was derived for decaying grid turbulence and stationary forced periodic box turbulence(or SFPBT)and tested against experimental(grid turbulence)and direct numerical simulation(SFBPT)data.The available data agree well with the analytical results.In decaying grid turbulence,-STapproaches a constant value as R?increases,while for SFPBT,-STis very nearly constant(i.e.independent of R?).Finally,the present thesis examines the large turbulent scales/forcing in wake.The Proper Orthogonal Decomposition(POD)method has become a well-established tool for identifying coherent structures.The characteristic feature of the conventional POD is that the two-point space-correlation tensor should include information at least at two different space points obtained either by PIV measurements,or a hot-wire array or direct numerical simulation data.This thesis developes a new POD method for data measured from a single spatial hot-wire with good frequency response and spatial resolution.The successful development of this method may open the possibility to extend the POD analysis for the data obtained from a single point such as the vorticity and temperature data measured by the vorticity and cold-wire probes,where it would be highly challenging to measure simultaneously vorticity at two or more points.In the shear region,local isotropy is unlikely to be satisfied due the the mean shear.the departure form local isotropy can be quantified by the Lumley scaling which was obtained by a dimensional argument.From the scale-by-scale energy budget equation for the generized second order structure function,the present work derives the Lumley scaling which is more rigorous than that obtained by Lumley via a dimensional argument.