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The Interaction between Meso- and Sub-mesoscale Gravity Waves
No full textAs present weather forecast codes and increasingly many atmospheric climate models resolve at least part of the mesoscale flow, and hence also internal gravity waves (GWs), it is natural to ask whether even in such configurations subgrid-scale GWs might impact the resolved flow and how their effect could be taken into account. This motivates a theoretical and numerical investigation of the interactions between unresolved submesoscale and resolved mesoscale GWs, using Boussinesq dynamics for simplicity. By scaling arguments, first a subset of submesoscale GWs that can indeed influence the dynamics of mesoscale GWs is identified. Therein, hydrostatic GWs with wavelengths corresponding to the largest unresolved scales of present-day limited-area weather forecast models are an interesting example. A large-amplitude WKB theory, allowing for a mesoscale unbalanced flow, is then formulated, based on multiscale asymptotic analysis utilizing a proper scale-separation parameter. Purely vertical propagation of submesoscale GWs is found to be most important, implying inter alia that the resolved flow is only affected by the vertical flux convergence of submesoscale horizontal momentum at leading order. In turn, submesoscale GWs are refracted by mesoscale vertical wind shear while conserving their wave-action density. An efficient numerical implementation of the theory uses a phase-space ray tracer, thus handling the frequent appearance of caustics. The WKB approach and its numerical implementation are validated successfully against submesoscale-resolving simulations of the resonant radiation of mesoscale inertia GWs by a horizontally as well as vertically confined submesoscale GW packet
A dimensionally split Cartesian cut cell method for the compressible Navier-Stokes equations
No full textWe present a dimensionally split method for computing solutions to the compressible Navier-Stokes equations on Cartesian cut cell meshes. The method is globally second order accurate in the L1 norm, fully conservative, and allows the use of time steps determined by the regular grid spacing. We provide a description of the three-dimensional implementation of the method and evaluate its numerical performance by computing solutions to a number of test problems ranging from the nearly incompressible to the highly compressible flow regimes. All the computed results show good agreement with reference results from theory, experiment and previous numerical studies. To the best of our knowledge, this is the first presentation of a dimensionally split cut cell method for the compressible Navier-Stokes equations in the literature
Large-scale secondary circulations in a limited area model - the impact of lateral boundaries and resolution
No full textWithin their domain, regional climate and weather forecasting models deviate from the driving data. Small-scale deviations are a desired effect of adding regional details. There are, however, also deviations of the large-scale circulation, which can be caused by orographic effects and depend on the large-scale flow condition. These ‘secondary circulations’ (SCs) are confined to the model domain due to the prescribed boundary conditions. Here, the impact of different regional model configurations on the SC is analysed in a case study for the European region using an ensemble approach. It is shown that at 500 hPa, vortices of the SC have diameters on the order of several thousand kilometres and are related to wind speed anomalies of more than 5 m/s and geopotential height anomalies of more than 5 dam. The spatial structure and the amplitude of the SC strongly depend on the location of the lateral boundaries. The impact of the boundary location on the anomalies is on the same order of magnitude as the anomalies themselves. The resolution of the regional model, as well as the application of spectral nudging and a smoothed topography, affects mainly the amplitude of the SC, but not the spatial structure
Calcium Ions in Aqueous Solutions: Accurate Force Field Description Aided by Ab Initio Molecular Dynamics and Neutron Scattering
No full textWe present a combination of force field and ab initio molecular dynamics simulations together with neutron scattering experiments with isotopic substitution that aim at characterizing ion hydration and pairing in aqueous calcium chloride and formate/acetate solutions. Benchmarking against neutron scattering data on concentrated solutions together with ion pairing free energy profiles from ab initio molecular dynamics allows us to develop an accurate calcium force field which accounts in a mean-field way for electronic polarization effects via charge rescaling. This refined calcium parameterization is directly usable for standard molecular dynamics simulations of processes involving this key biological signaling ion
Signatures of air-waves interactions over a large lake
No full textThe air–water exchange of momentum and scalars (temperature and water vapour) is investigated using the Lake-Atmosphere Turbulent EXchange (LATEX) dataset. The wind waves and swell are found to affect the coupling between the water surface and the air differently. The surface-stress vector aligns with the wind velocity in the presence of wind waves, but a wide range of stress–wind misalignment angles is observed during swell. The momentum transport efficiency decreases when significant stress–wind misalignment is present, suggesting a strong influence of surface wave properties on surface drag. Based on this improved understanding of the role of wave–wind misalignment, a new relative wind speed for surface-layer similarity formulations is proposed and tested using the data. The new expression yields a value of the von Kármán constant (κ) of 0.38, compared to 0.36 when using the absolute wind speed, as well as reduced data fitting errors. Finally, the ratios of aerodynamic to scalar roughness lengths are computed and various existing models in the literature are tested using least-square fitting to the observed ratios. The tests are able to discriminate between the performance of various models; however, they also indicate that more investigations are required to understand the physics of scalar exchanges over waves
Convergences of the squareroot approximation scheme to the Fokker–Planck operator
Get PDFWe study the qualitative convergence properties of a finite volume scheme that recently was proposed by Lie, Fackeldey and Weber [SIAM Journal on Matrix Analysis and Applications 2013 (34/2)] in the context of conformation dynamics. The scheme was derived from physical principles and is called the squareroot approximation (SQRA) scheme. We show that solutions to the SQRA equation converge to solutions of the Fokker-Planck equation using a discrete notion of G-convergence. Hence the squareroot approximation turns out to be a usefull approximation scheme to the Fokker-Planck equation in high dimensional spaces. As an example, in the special case of stationary Voronoi tessellations we use stochastic two-scale convergence to prove that this setting satisfies the G-convergence property. In particular, the class of tessellations for which the G-convergence result holds is not trivial
Instabilities and small-scale waves within the Stewartson layers of a thermally driven rotating annulus
No full textWe report on small-scale instabilities in a thermally driven rotating annulus filled with a liquid with moderate Prandtl number. The study is based on direct numerical simulations and an accompanying laboratory experiment. The computations are performed independently with two different flow solvers, that is, first, the non-oscillatory forward-in-time differencing flow solver EULAG and, second, a higher-order finite-difference compact scheme (HOC). Both branches consistently show the occurrence of small-scale patterns at both vertical sidewalls in the Stewartson layers of the annulus. Small-scale flow structures are known to exist at the inner sidewall. In contrast, short-period waves at the outer sidewall have not yet been reported. The physical mechanisms that possibly trigger these patterns are discussed. We also debate whether these small-scale structures are a gravity wave signal
Function space bases in the dune-functions module
Get PDFThe dune-functions Dune module provides interfaces for functions and function space bases. It forms one abstraction level above grids, shape functions, and linear algebra, and provides infrastructure for full discretization frameworks like dune-pdelab and dune-fem. This document describes the function space bases provided by dune-functions. These are based on an abstract description of bases for product spaces as trees of simpler bases. From this description, many different numberings of degrees of freedom by multi-indices can be derived in a natural way. We describe the abstract concepts, document the programmer interface, and give a complete example program that solves the stationary Stokes equation using Taylor-Hood elements