Entropy and Turbulence Structure

Abstract

Some new perspectives are offered on the spectral and spatial structure of turbulent flows, in the context of conservation principles and entropy. In recent works, we have shown that the turbulence energy spectra are derivable from the maximum entropy principle, with good agreement with experimental data across the entire wavenumber range. Dissipation can also be attributed to the Reynolds number effect in wall-bounded turbulent flows. Within the global energy and dissipation constraints, the gradients (d/dy+ or d2/dy+2) of the Reynolds stress components neatly fold onto respective curves, so that function prescriptions (dissipation structure functions) can serve as a template to expand to other Reynolds numbers. The Reynolds stresses are fairly well prescribed by the current scaling and dynamical formalism so that the origins of the turbulence structure can be understood and quantified from the entropy perspective.

Using Different Classic Turbulence Closure Models to Assess Salt and Temperature Modelling in a Lagunar System: A Sensitivity Study

“…Figure 6 presents model results for the temperature for similar conditions as Figure 5. The agreement appears to be less good due to scale resolution, but the temperature range for both data and simulation is constrained within (13,16) An objective evaluation of the model skill predictivity relative to data can be achieved through the target diagrams for salinity (Figure 7a-d) and temperature (Figure 8a-d The diagrams for the salinity confirm that the model prediction for St1, St5, and St6, can be considered satisfactory. Indeed, the dots in Figure 7a-d, for, respectively, St1, St2, St5, and St6, are situated very close to the axis origins, corresponding to low values of the bias: the absolute values of the bias are of the order or smaller than 5 PSU, which indicates a small deviation of the simulations relative to the data.…”

“…Typical summer salinity values, as in June 2001, were in the range of (30-34) PSU (which are values close to the ocean salinity), whereas low values (<5 PSU) were found close to the major river boundaries (stations 3, and 4) or at the far end areas (stations 6, 7 and 8) (30-33) PSU. The water temperature was in the range of (13)(14)(15)(16)(17)(18) • C for spring and (18-24) • C for summer, typical values for those seasons. The model used in this work is the baseline Mike3-HD [50,61], which is based on the numerical solution of the two/three-dimensional incompressible Reynolds-averaged Navier-Stokes equations, subject to the assumptions of Boussinesq and of hydrostatic pressure and consists in a system of continuity, momentum, temperature, and salinity equations.…”

“…Turbulence has been studied for nearly a hundred years. Despite numerous experimental and computational advances, it remains an enigmatic topic in fluid mechanics and physics [13]. Among three significant challenges posed by turbulence [13], which are the dynamical closure of the turbulence, the structural scaling, and the energy spectra, the first is the most crucial when dealing with modelling studies.…”

“…Despite numerous experimental and computational advances, it remains an enigmatic topic in fluid mechanics and physics [13]. Among three significant challenges posed by turbulence [13], which are the dynamical closure of the turbulence, the structural scaling, and the energy spectra, the first is the most crucial when dealing with modelling studies. Indeed, the closure of the turbulence allows for determining the turbulent eddy viscosity and diffusion coefficients, which are fundamental parameters for numerically solving the hydrodynamic and the transport equations.…”

“…Figure6presents model results for the temperature for similar conditions as Figure5. The agreement appears to be less good due to scale resolution, but the temperature range for both data and simulation is constrained within(13,16) °C. The simulation underestimates the maximum temperature value for St6 by nearly 1 °C.…”