Nonlinear interfacial waves in a constant-vorticity planar flow over variable depth

Exact Lagrangian in compact form is derived for planar internal waves in a two-fluid system with a relatively small density jump (the Boussinesq limit taking place in real oceanic conditions), in the presence of a background shear current of constant vorticity, and over arbitrary bottom profile. Long-wave asymptotic approximations of higher orders are derived from the exact Hamiltonian functional in a remarkably simple way, for two different parametrizations of the interface shape.Comment: revtex, 4.5 pages, minor corrections, summary added, accepted to JETP Letter

BOUT++ : Recent and current developments

BOUT++ is a 3D nonlinear finite-difference plasma simulation code, capable of solving quite general systems of PDEs, but targeted particularly on studies of the edge region of tokamak plasmas. BOUT++ is publicly available, and has been adopted by a growing number of researchers worldwide. Here we present improvements which have been made to the code since its original release, both in terms of structure and its capabilities. Some recent applications of these methods are reviewed, and areas of active development are discussed. We also present algorithms and tools which have been developed to enable creation of inputs from analytic expressions and experimental data, and for processing and visualisation of output results. This includes a new tool Hypnotoad for the creation of meshes from experimental equilibria. Algorithms have been implemented in BOUT++ to solve a range of linear algebraic problems encountered in the simulation of reduced MHD and gyro-fluid models: A preconditioning scheme is presented which enables the plasma potential to be calculated efficiently using iterative methods supplied by the PETSc library, without invoking the Boussinesq approximation. Scaling studies are also performed of a linear solver used as part of physics-based preconditioning to accelerate the convergence of implicit time-integration schemes

Lattice kinetic simulations of 3-D MHD turbulence

A recently proposed lattice Boltzmann kinetic scheme offers a promising tool for simulating complex 3-D MHD flows. The algorithm is based on the BGK modeling of the collision term. The conventional approach for implementing magnetic behavior in LBM methods is based on one tensor-valued distribution function to present both the fluids variables (density and momentum) and the magnetic field. This formulation, however, has been proven a rather inefficient approach. The present scheme calls for a separate BGK-like evolution equation for the magnetic field which models the induction equation and enhances simplicity while allowing for the independent adjustment of the magnetic resistivity. Furthermore the algorithm correctly recovers the macroscopic dissipative MHD equations. Numerical results for the 3-D Taylor-Green vortex problem are presented with corresponding results computed with a pseudo-spectral code used as benchmark. (C) 2005 Elsevier Ltd. All rights reserved

Lattice kinetic simulations in three-dimensional magnetohydrodynamics

A lattice kinetic algorithm to simulate three-dimensional (3D) incompressible magnetohydrodynamics is presented. The fluid is monitored by a distribution function, which obeys a scalar kinetic equation, subject to an external force due to the imposed magnetic field. Following the work of Dellar [J. Comput. Phys. 179, 95 (2002)] , the magnetic field is represented by a different three-component vector distribution function, which obeys a corresponding vector kinetic equation. Discretization of the 3D phase space is based on a 19-bit scheme for the hydrodynamic part and on a 7-bit scheme for the magnetic part. Numerical results for magnetohydrodynamic (MHD) flow in a rectangular duct with insulating and conducting walls provide excellent agreement with corresponding analytical solutions. The scheme maintains in all cases tested the MHD constraint del.B=0 within machine round-off error

Lattice kinetic schemes in toroidal geometry

Lattice kinetic schemes has been consistently developed for the last 15 years as a tool to tackle complicated problems from a mesoscopic perspective. The system is described by a velocity distribution function, which follows a BGK kinetic type equation and is evolved under specific constrains in order to ensure a desired macroscopic behavior. This mesoscale scheme has been recently extended to MHD configurations with noticeable success. In the present work the in-house 3D MHDlattice kinetic code is properly modified to simulate dissipative flows in a toroidal geometry. The evolution of the MHD field is followed in time via the aforementioned lattice kinetic solver and numerical results are reported for space dependent and overall quantities

Lattice kinetic schemes in fusion plasmas

Lattice Boltzmann Methods (LBM) are an established alternative approach for numerical simulations of a large spectrum of physical processes. They are based on a mesoscopic analysis of the underlying physics through a velocity distribution function f(x,ξ,t) which obeys the Boltzmann Equation (BE). Furthermore, it has been argued that a number of macroscopic processes can be modeled through a mesoscopic evolution equation similar to BE appropriately tuned to recover the desired macroscopic behavior while retaining the multi-scale characteristics of LBM. Such an approach can be utilized to analyze a magnetohydrodynamic (MHD) system via lattice kinetic schemes [1,2]. All macroscopic quantities are given as moments of f and the algorithm is seen to solve consistently the hydrodynamic and magnetic induction dissipative equations in generalized 3D geometry [3]. We examine the potential of such an algorithm for large-scale fusion simulations. Initial conditions may be provided by the Integrated Tokamak Modelling (ITM) mdsplus server in ENEA frascati, Rome, for ITER related scenarios [4]. The case considered is the evolution of continuous shear Alfvén waves in a plasma [5]

Rarefied gas flow in concentric annular tube: Estimation of the Poiseuille number and the exact hydraulic diameter

The fully developed flow of rarefied gases through circular ducts of concentric annular cross sections is solved via kinetic theory. The flow is due to an externally imposed pressure gradient in the longitudinal direction and it is simulated by the BGK kinetic equation, subject to Maxwell diffuse-specular boundary conditions. The approximate principal of the hydraulic diameter is investigated for first time in the field of rarefied gas dynamics. For the specific flow pattern, in addition to the flow rates, results are reported for the Poiseuille number and the exact hydraulic diameter. The corresponding parameters include the whole range of the Knudsen number and various values of the accommodation coefficient and the ratio of the inner over the outer radius. The accuracy of the results is validated in several ways, including the recovery of the analytical solutions at the hydrodynamic and free molecular limits. (C) 2007 Elsevier Masson SAS. All rights reserved

AN INVISCID INVESTIGATION OF THE INITIATION OF ROLL WAVES IN HORIZONTAL GAS-LIQUID FLOWS

A model with constant vorticity in the liquid phase has been applied to the study of interfacial waves between two inviscid fluids in relative motion, in order to take into account the shear induced into the liquid by the concurrent gas flow. For a range of values of gas velocity and vorticity in the liquid phase a new wave pattern is calculated, consisting of a recirculating eddy below the wave crest. It is suggested that, under certain conditions, the onset of this new type of waves (rather than the classical Kelvin-Helmholtz instability mechanism) provides the inviscid analog to the experimentally observed transition to roll waves

Towards robust pan-European storm surge forecasting

Operational forecasting systems are important for disaster risk reduction. In this work we implement a coupled storm surge and tidal model on an unstructured grid over Europe towards the development of a pan-European Storm Surge Forecasting System (EU-SSF). The skill to predict tidal, surge and total water levels was evaluated based on measurements from 208 tidal gauge stations. Results show satisfactory performance for the two atmospheric forcing datasets tested, a High Resolution Forecast and ERA-INTERIM reanalysis, both provided by the European Center for Medium range Weather Forecast. For tidal predictions, the total RSS is equal to 0.197 m, lower than the values estimated by the global tidal model FES2004, and outperformed only by FES2012 (RSS = 0.05 m), which however is a product of data assimilation. Storm surge validation results show good predictive skill, with 0.04 m < RMSE < 0.21 m and %RMSE within 4%–22%. Coupling with tides results in improved storm surge level predictions, with RMSE reducing by up to 0.033 m. The areas benefiting most from the coupling are the North Sea and the English Channel, resulting in up to 2% reduction of the %RMSE. Increasing the resolution of atmospheric forcing also improves the predictive skill, leading to a reduction of RMSE up to 0.06 m in terms of the extremes, especially in shallow areas where wind is the main driver for surge production. We propose a setup for operational pan-European storm surge forecasting combining tidal levels from the FES2012 model and storm surge residuals from the EU-SSF setup which couples meteorological and astronomic tides