TY  - RPRT
A1  - Drescher, Hans Paul
T1  - The irreversible thermodynamic’s theorem of minimum entropy production applied to the laminar and the turbulent Couette flow
N2  - Analyzing thermodynamic non-equilibrium processes, like the laminar and turbulent fluid flow, the dissipation is a key parameter with a characteristic minimum condition. That is applied to characterize laminar and turbulent behaviour of the Couette flow, including its transition in both directions. The Couette flow is chosen as the only flow form with constant shear stress over the flow profile, being laminar, turbulent or both. The local dissipation defines quantitative and stable criteria for the transition and the existence of turbulence. There are basic results: The Navier Stokes equations cannot describe the experimental flow profiles of the turbulent Couette flow. But they are used to quantify the dissipation of turbulent fluctuation. The dissipation minimum requires turbulent structures reaching maximum macroscopic dimensions, describing turbulence as a “non-local” phenomenon. At the transition the Couette flow profiles and the shear stress change by a factor ≅ 5 due to a change of the “apparent” turbulent viscosity by a calculated factor ≅ 27. The resulting difference of the laminar and the turbulent profiles results in two different Reynolds numbers and different loci of transition, which are identified by calculation.
KW  - Turbulence
KW  - Transition
KW  - Minimum dissipation
Y1  - 2018
ER  - 
TY  - JOUR
A1  - Harris, Isaac
A1  - Kleefeld, Andreas
T1  - The inverse scattering problem for a conductive boundary condition and transmission eigenvalues
JF  - Applicable Analysis
N2  - In this paper, we consider the inverse scattering problem associated with an inhomogeneous media with a conductive boundary. In particular, we are interested in two problems that arise from this inverse problem: the inverse conductivity problem and the corresponding interior transmission eigenvalue problem. The inverse conductivity problem is to recover the conductive boundary parameter from the measured scattering data. We prove that the measured scatted data uniquely determine the conductivity parameter as well as describe a direct algorithm to recover the conductivity. The interior transmission eigenvalue problem is an eigenvalue problem associated with the inverse scattering of such materials. We investigate the convergence of the eigenvalues as the conductivity parameter tends to zero as well as prove existence and discreteness for the case of an absorbing media. Lastly, several numerical and analytical results support the theory and we show that the inside–outside duality method can be used to reconstruct the interior conductive eigenvalues.
KW  - Transmission eigenvalues
KW  - Conductive boundary condition
KW  - Inverse scattering
Y1  - 2018
U6  - https://doi.org/10.1080/00036811.2018.1504028
SN  - 1563-504X
VL  - 99
IS  - 3
SP  - 508
EP  - 529
PB  - Taylor & Francis
CY  - London
ER  -