Ulrich Schumann

Coherent structure of the convective boundary layer derived from large-eddy simulations

Turbulence in the convective boundary layer (CBL) uniformly heated from below and topped by a layer of uniformly stratified fluid is investigated for zero mean horizontal flow using large-eddy simulations (LES). The Rayleigh number is effectively infinite, the Froude number of the stable layer is 0.09 and the surface roughness height relative to the height of the convective layer is varied between lo- and The LES uses a finite-difference method to integrate the threedimensional grid-volume-averaged Navier-Stokes equations for a Boussinesq fluid. Subgrid-scale (SGS) fluxes are determined from algebraically approximated secondorder closure (SOC) transport equations for which all essential coefficients are determined from the inertial-range theory. The surface boundary condition uses the Monin-Obukhov relationships. A radiation boundary condition at the top of the computational domain prevents spurious reflections of gravity waves. The simulation uses 160 x 160 x 48 grid cells. In the asymptotic state, the results in terms of vertical mean profiles of turbulence statistics generally agree very well with results available from laboratory and atmospheric field experiments. We found less agreement with respect to horizontal velocity fluctuations, pressure fluctuations and dissipation rates, which previous investigations tend to overestimate. Horizontal spectra exhibit an inertial subrange. The entrainment heat flux at the top of the CBL is carried by cold updraughts and warm downdraughts in the form of wisps at scales comparable with the height of the boundary layer. Plots of instantaneous flow fields show a spoke pattern in the lower quarter of the CBL which feeds large-scale updraughts penetrating into the stable layer aloft. The spoke pattern has also been found in a few previous investigations. Small-scale plumes near the surface and remote from strong updraughts do not merge together but decay while rising through large-scale downdraughts. The structure of updraughts and downdraughts is identified by threedimensional correlation functions and conditionally averaged fields. The mean circulation extends vertically over the whole boundary layer. We find that updraughts are composed of quasi-steady large-scale plumes together with transient rising thermals which grow in size by lateral entrainment. The skewness of the vertical velocity fluctuations is generally positive but becomes negative in the lowest mesh cells when the dissipation rate exceeds the production rate due to buoyancy near the surface, as is the case for very rough surfaces. The LES results are used to determine the root-mean-square value of the surface friction velocity and the mean temperature difference between the surface and the mixed layer as a function of the roughness height. The results corroborate a simple model of the heat transfer in the surface layer.

Numerical simulation of turbulent convection over wavy terrain

Thermal convection of a Boussinesq fluid in a layer confined between two infinite horizontal walls is investigated by direct numerical simulation (DNS) and by large-eddy simulation (LES) for zero horizontal mean motion. The lower-surface height varies sinusoidally in one horizontal direction while remaining constant in the other. Several cases are considered with amplitude δ up to 0.15 H and wavelength λ of H to 8 H (inclination up to 43°), where H is the mean fluid-layer height. Constant heat flux is prescribed at the lower surface of the initially at rest and isothermal fluid layer. In the LES, the surface is treated as rough surface ( z 0 = 10 −4 H ) using the Monin-Oboukhov relationships. At the flat top an adiabatic frictionless boundary condition is applied which approximates a strong capping inversion of an atmospheric convective boundary layer. In both horizontal directions, the model domain extends over the same length (either 4 H or 8 H ) with periodic lateral boundary conditions. We compare DNS of moderate turbulence (Reynolds number based on H and on the convective velocity is 100, Prandtl number is 0.7) with LES of the fully developed turbulent state in terms of turbulence statistics and Characteristic large-scale-motion structures. The LES results for a flat surface generally agree well with the measurements of Adrian et al. (1986). The gross features of the flow statistics, such as profiles of turbulence variances and fluxes, are found to be not very sensitive to the variations of wavelength, amplitude, domain size and resolution and even the model type (DNS or LES), whereas details of the flow structure are changed considerably. The LES shows more turbulent structures and larger horizontal scales than the DNS. To a weak degree, the orography enforces rolls with axes both perpendicular and parallel to the wave crests and with horizontal wavelengths of about 2 H to 4 H . The orography has the largest effect for λ = 4 H in the LES and for λ = 2 H in the DNS. The results change little when the size of the computational domain is doubled in both horizontal directions. Most of the motion energy is contained in the large-scale structures and these structures are persistent in time over periods of several convective time units. The motion structure persists considerably longer over wavy terrain than over flat surfaces.

Lightning: Principles, Instruments and Applications

Lightning is a natural phenomenon that has always produced much impact on nhumans and their societies, mainly because of its impressive appearance and the threats imposed on life and structures. As one consequence, modern lightning research continues to develop effective tools and procedures suited to recognize severe thunderstorms and to generate reliable alert. During the long time of past lightning investigation, much understanding of the discharge processes has been gathered and efficient detection techniques have been implemented. Today, numerous institutions all over the world deal with unraveling the numerous questions about lightning that have remained open, with much success, but as is typical for research in subjects of natural science, the complexity of the phenomena defies fast and comprehensive clarification. Meanwhile, the many competent research efforts and their impressive results render it impossible to present the gathered knowledge in na single book. Thus, the present monograph is designed to describe in 27 chapters. nmerely some of the highlights of current research. Moreover, the topics have been nselected to elucidate the lightning phenomena that are readily understandable by na general, educated readership, rather than addressing only specialists in the field. nAccordingly, a more deeply interested reader is referred to the ample reports in nliterature. nAt first,

Potential to reduce the climate impact of aviation by flight level changes

Aircraft contribute to global and regional climate changes by contrail formation and by emissions of carbon dioxide and others species. Among these, contrails are considered to have the largest warming contribution on short time scales (up to order of decades) while carbon dioxide may cause the largest warming effect globally at long time scales (order of a century). Contrails warm generally during night. During day contrails may cause a cooling. This paper discusses various strategies to reduce the global warming from aircraft by contrail formation and carbon dioxide emissions. In particular, we discuss the impact of changes of the flight level, typically 2000 ft (610 m) up or down. Previous studies suggested reducing contrail formation by flying lower generally or by flying higher or lower at the actual level with minimum relative humidity. This paper introduces a more efficient strategy which selects optimized routes based on the climate impact of contrails and fuel consumption along these routes. By preferred flights in atmospheric regions where contrails cool, an aircraft routing can be designed with minimum or even negative climate impact. For the fleet as a whole the climate impact is measured in terms of its radiative forcing RF. For individual flights, the climate impact is measured by the amount of energy induced into the Earth-atmosphere system per unit flight distance, which we call the energy forcing EF. Both RF and EF for contrails and CO2 can be combined into a global mean surface temperature increase for a given time horizon. This paper describes the basic principles and quantifies the potential impacts using the recently developed Contrail Cirrus Simulation Prediction tool (CoCiP).

Lightning and NOX Production in Global Models

In the upper troposphere lightning is the major contributor to the production of nitric oxide, which is a critical precursor gas for ozone production. It is therefore important that this source is simulated with a high accuracy in global chemical transport models and global chemistry/climate models. This chapter reviews development of the parameterization of lightning-produced nitric oxide in such models and the various components required such as flash rate distribution, NO production per flash and its vertical distribution. The results from simulations with different global models, the uncertainties and the impact on ozone are discussed.

Comparison of Static Pressure from Aircraft Trailing Cone Measurements and Numerical Weather Prediction Analysis

Accurate static pressure measurements are a prerequisite for safe navigation and precise air data measurements on aircraft. Pressure is also fundamental to assess winds and air temperature and, hence, important for meteorology. The direct static pressure measurement by aircraft is ndisturbed by the aircraft aerodynamics and needs to be corrected using proper calibration. In this paper we compare static pressure measured by means of a trailing cone (TC) in the undisturbed atmosphere behind two different jet aircraft (Dassault FALCON 20E and Gulfstream 550 “HALO”) at flight levels (FL) from 40 to 450 during 6 flights on different days with data from numerical weather predictions (NWP). The height is derived from differential Global Navigation Satellite System (GNSS) measurements. The GNSS height is compared to NWP geopotential height. nThe NWP data were provided by the Integrated Forecast System (IFS) of the European Centre for Medium-Range Weather Forecasts (ECMWF). The IFS model assumes constant gravity g. For constant g, the pressure differences (at same height) have mean values and standard deviations of 0.40±0.17 hPa for 159 individual measurements of 43±31 s duration each. The respective height differences (at same pressure) are -10±5 m on average over the same measurements. When computing the geopotential with latitude/height dependent gravity (which is 0.4 % smaller at FL 450 than at 0 km) the agreement becomes significantly better: -0.01±0.15 hPa for pressure, 0.6±2.8 m for height. This pressure accuracy implies NWP temperature errors <0.1 K on average below 10 km altitude. Standard deviations of random errors in the TC-NWP difference are 0.06 hPa and 1 m. The TC measurements provide a first quantification of the case-specific accuracy of NWP pressure geopotential relationships. The method of comparing operational pressure/GNSS measurements on aircraft with NWP analysis or predictions can be used to test the height keeping performance of aircraft after or during operation.