Taylor's (1935) dissipation surrogate reinterpreted

New results from direct numerical simulation of decaying isotropic turbulence show that Taylor’s expression for the viscous dissipation rate ε = CεU3/L is more appropriately interpreted as a surrogate for the inertial energy flux. As a consequence, the well known dependence of the Taylor prefactor Cε on Reynolds number Cε(RL)→Cε,∞ can be understood as corresponding to the onset of an inertial range

Eulerian spectral closures for isotropic turbulence using a time-ordered fluctuation-dissipation relation

Procedures for time-ordering the covariance function, as given in a previous paper (K. Kiyani and W.D. McComb Phys. Rev. E 70, 066303 (2004)), are extended and used to show that the response function associated at second order with the Kraichnan-Wyld perturbation series can be determined by a local (in wavenumber) energy balance. These time-ordering procedures also allow the two-time formulation to be reduced to time-independent form by means of exponential approximations and it is verified that the response equation does not have an infra-red divergence at infinite Reynolds number. Lastly, single-time Markovianised closure equations (stated in the previous paper above) are derived and shown to be compatible with the Kolmogorov distribution without the need to introduce an ad hoc constant.Comment: 12 page

What blows in with the wind?

The shift toward renewable forms of energy for electricity generation in the electricity generation industry has clear implications for the spatial distribution of generating plant. Traditional forms of generation are typically located close to the load or population centers, while wind and solar-powered generation must be located where the energy source is found. In the case of wind, this has meant significant new investment in wind plant in primarily rural areas that have been in secular economic decline. This paper investigates the localized economic impacts of the rapid increase in wind power capacity at the county level in Texas. Unlike Input-Output impact analysis that relies primarily on levels of inputs to estimate gross impacts, we use traditional econometric methods to estimate net localized impacts in terms of employment, personal income, and property tax base. While we find evidence that both direct and indirect employment impacts are modest, significant increases in per capita income accompany wind power development. County and school property tax rolls also realize important benefits from the local siting of utility scale wind power

Non-local modulation of the energy cascade in broad-band forced turbulence

Classically, large-scale forced turbulence is characterized by a transfer of energy from large to small scales via nonlinear interactions. We have investigated the changes in this energy transfer process in broad-band forced turbulence where an additional perturbation of flow at smaller scales is introduced. The modulation of the energy dynamics via the introduction of forcing at smaller scales occurs not only in the forced region but also in a broad range of length-scales outside the forced bands due to non-local triad interactions. Broad-band forcing changes the energy distribution and energy transfer function in a characteristic manner leading to a significant modulation of the turbulence. We studied the changes in this transfer of energy when changing the strength and location of the small-scale forcing support. The energy content in the larger scales was observed to decrease, while the energy transport power for scales in between the large and small scale forcing regions was enhanced. This was investigated further in terms of the detailed transfer function between the triad contributions and observing the long-time statistics of the flow. The energy is transferred toward smaller scales not only by wavenumbers of similar size as in the case of large-scale forced turbulence, but by a much wider extent of scales that can be externally controlled.Comment: submitted to Phys. Rev. E, 15 pages, 18 figures, uses revtex4.cl

The dimensionless dissipation rate and the Kolmogorov (1941) hypothesis of local stationarity in freely decaying isotropic turbulence

An expression for the dimensionless dissipation rate was derived from the Karman-Howarth equation by asymptotic expansion of the second- and third- order structure functions in powers of the inverse Reynolds number. The implications of the time-derivative term for the assumption of local stationarity (or local equilibrium) which underpins the derivation of the Kolmogorov `4/5' law for the third-order structure function were studied. It was concluded that neglect of the time-derivative cannot be justified by reason of restriction to certain scales (the inertial range) nor to large Reynolds numbers. In principle, therefore, the hypothesis cannot be correct, although it may be a good approximation. It follows, at least in principle, that the quantitative aspects of the hypothesis of local stationarity could be tested by a comparison of the asymptotic dimensionless dissipation rate for free decay with that for the stationary case. But in practice this is complicated by the absence of an agreed evolution time for making the measurements during the decay. However, we can assess the quantitative error involved in using the hypothesis by comparing the exact asymptotic value of the dimensionless dissipation in free decay calculated on the assumption of local stationarity to the experimentally determined value (e.g. by means of direct numerical simulation), as this relationship holds for all measuring times. Should the assumption of local stationarity lead to significant error, then the `4/5' law needs to be corrected. Despite this, scale invariance in wavenumber space appears to hold in the formal limit of infinite Reynolds numbers, which implies that the `-5/3' energy spectrum does not require correction in this limit.Comment: 17 pages, no figure