Numerical evidence of anomalous energy dissipation in incompressible Euler flows: towards grid-converged results for the inviscid Taylor–Green problem

The well-known energy dissipation anomaly in the inviscid limit, related to velocity singularities according to Onsager, still needs to be demonstrated by numerical experiments. The present work contributes to this topic through high-resolution numerical simulations of the inviscid three-dimensional Taylor–Green vortex problem using a novel high-order discontinuous Galerkin discretisation approach for the incompressible Euler equations. The main methodological ingredient is the use of a discretisation scheme with inbuilt dissipation mechanisms, as opposed to discretely energy-conserving schemes, which – by construction – rule out the occurrence of anomalous dissipation. We investigate effective spatial resolution up to $8192^3$ (defined based on the $2{\rm \pi}$ -periodic box) and make the interesting phenomenological observation that the kinetic energy evolution does not tend towards exact energy conservation for increasing spatial resolution of the numerical scheme, but that the sequence of discrete solutions seemingly converges to a solution with non-zero kinetic energy dissipation rate. Taking the fine-resolution simulation as a reference, we measure grid-convergence with a relative $L^2$ -error of $0.27\,\%$ for the temporal evolution of the kinetic energy and $3.52\,\%$ for the kinetic energy dissipation rate against the dissipative fine-resolution simulation. The present work raises the question of whether such results can be seen as a numerical confirmation of the famous energy dissipation anomaly. Due to the relation between anomalous energy dissipation and the occurrence of singularities for the incompressible Euler equations according to Onsager's conjecture, we elaborate on an indirect approach for the identification of finite-time singularities that relies on energy arguments.

Control efficiency improvement of an electro-hydraulic winch

The paper presents a study regarding electro-hydraulic control systems for drive winches, a structural part of LARS (Launch and Recovery Systems). In the Introduction section of the paper, the authors present the domains of the research vessel. Furthermore, there is presented the importance of launch and recovery systems (LARS) and drive winches on the deck of a research vessel. The launch and recovery systems (LARS) using drive winches are installed on the stern of the research vessel. Further in the paper, the authors present the results of studying three simplified systems that use electric, hydraulic and electro-hydraulic driving solutions. Furthermore, there are presented comparative advantages of using this three types of drive winches. At the end of the paper, the authors perform an analysis of the electro-hydraulic systems for the drive winch, using a modelling and simulation software. Each schematic is presented along with its components. Moreover, the authors mention that all the schematics presented in this paper are modelled using FluidSim software from FESTO. In this case, only three mathematic relations are used in the paper: the Cauchy momentum (convective form), the incompressible Euler relations and the pressure losses in the hydraulic and electro-hydraulic drive winch.

On the approximation of vorticity fronts by the Burgers–Hilbert equation

This paper proves that the motion of small-slope vorticity fronts in the two-dimensional incompressible Euler equations is approximated on cubically nonlinear timescales by a Burgers–Hilbert equation derived by Biello and Hunter (2010) using formal asymptotic expansions. The proof uses a modified energy method to show that the contour dynamics equations for vorticity fronts in the Euler equations and the Burgers–Hilbert equation are both approximated by the same cubically nonlinear asymptotic equation. The contour dynamics equations for Euler vorticity fronts are also derived.