Related papers: Energy dissipation in body-forced plane shear flow
A new variational problem for upper bounds on the rate of energy dissipation in body-forced shear flows is formulated by including a balance parameter in the derivation from the Navier-Stokes equations. The resulting min-max problem is…
The rate of energy dissipation in solutions of the body-forced 3-d incompressible Navier-Stokes equations is rigorously estimated with a focus on its dependence on the nature of the driving force. For square integrable body forces the high…
We present numerical solutions to the extended Doering-Constantin variational principle for upper bounds on the energy dissipation rate in plane Couette flow, bridging the entire range from low to asymptotically high Reynolds numbers. Our…
Variational turbulence is among the few approaches providing rigorous results in turbulence. In addition, it addresses a question of direct practical interest, namely the rate of energy dissipation. Unfortunately, only an upper bound is…
The background method is adapted to derive rigorous limits on surface speeds and bulk energy dissipation for shear stress driven flow in two and three dimensional channels. By-products of the analysis are nonlinear energy stability results…
We present numerical solutions to the extended Doering-Constantin variational principle for upper bounds on the energy dissipation rate in turbulent plane Couette flow. Using the compound matrix technique in order to reformulate this…
The Smagorinsky model, unmodified, is often reported to severely overdiffuse flows. Previous estimates of the energy dissipation rate of the Smagorinsky model for shear flows reflect a blow up of model energy dissipation as Re increases.…
We extend the Doering-Constantin approach to upper bounds on energy dissipation in turbulent flows by introducing a balance parameter into the variational principle. This parameter governs the relative weight of different contributions to…
Upper bounds on the bulk energy dissipation rate $\epsilon$ and enstrophy dissipation rate $\chi$ are derived for the statistical steady state of body forced two dimensional turbulence in a periodic domain. For a broad class of externally…
Extreme dissipation events in turbulent flows are rare, but they can be orders of magnitude stronger than the mean dissipation rate. Despite its importance in many small-scale physical processes, there is presently no accurate theory or…
An experiment was performed using SPIV in the LMFL boundary layer facility to determine all the derivative moments needed to estimate the average dissipation rate of the turbulence kinetic energy, $\varepsilon = 2 \nu \langle s_{ij}s_{ij}…
The shape of the turbulent energy spectrum in the dissipation range, where viscous effects dominate, remains an open question despite decades of work. We report an experimental investigation of intermediate dissipation range energy spectra…
Turbulence models, such as the Smagorinsky model herein, are used to represent the energy lost from resolved to under-resolved scales due to the energy cascade (i.e. non-linearity). Analytic estimates of the energy dissipation rates of a…
A popular method of forcing the fluid in Direct Numerical Simulations of turbulence is to take the body force proportional to the projection of the velocity of the fluid onto its lowest Fourier modes, while keeping the injected external…
Bounds on turbulent averages in shear flows can be derived from the Navier--Stokes equations by a mathematical approach called the background method. Bounds that are optimal within this method can be computed at each Reynolds number Re by…
Turbulent wall flows offer the most direct means for understanding the effects of boundaries and viscosity on turbulent fluctuations. Available data on mean-square fluctuations in these flows show apparent contradiction with classical…
We present a new rigorous method for estimating statistical quantities in fluid dynamics such as the (average) energy dissipation rate directly from the equations of motion. The method is tested on shear flow, channel flow,…
The variance and spectra of wall-normal velocities are investigated for direct numerical simulations of turbulent flow in a channel, pipe, and zero-pressure-gradient boundary layer across a decade of friction Reynolds numbers. Spectra along…
A qualitative explanation for the scaling of energy dissipation by high Reynolds number fluid flows in contact with solid obstacles is proposed in the light of recent mathematical and numerical results. Asymptotic analysis suggests that it…
Using high-resolution direct numerical simulations, the height and Reynolds number dependence of higher-order statistics of the energy dissipation rate and local enstrophy are examined in incompressible, fully-developed turbulent channel…