The properties of turbulence subgrid-scale stresses are studied using experimental data in the far field of a round jet, at a Reynolds number of Rλ ≈ 310. Measurements are performed using two-dimensional particle displacement velocimetry. Three elements of the subgrid-scale stress tensor are calculated using planar filtering of the data. Using a priori testing, eddy-viscosity closures are shown to display very little correlation with the real stresses, in accord with earlier findings based on direct numerical simulations at lower Reynolds numbers. Detailed analysis of subgrid energy fluxes and of the velocity field decomposed into logarithmic bands leads to a new similarity subgrid-scale model. It is based on the ‘resolved stress’ tensor Lij, which is obtained by filtering products of resolved velocities at a scale equal to twice the grid scale. The correlation coefficient of this model with the real stress is shown to be substantially higher than that of the eddy-viscosity closures. It is shown that mixed models display similar levels of correlation. During the a priori test, care is taken to only employ resolved data in a fashion that is consistent with the information that would be available during large-eddy simulation. The influence of the filter shape on the correlation is documented in detail, and the model is compared to the original similarity model of Bardina et al. (1980). A relationship between Lij and a nonlinear subgrid-scale model is established. In order to control the amount of kinetic energy backscatter, which could potentially lead to numerical instability, an ad hoc weighting function that depends on the alignment between Lij and the strain-rate tensor, is introduced. A ‘dynamic’ version of the model is shown, based on the data, to allow a self-consistent determination of the coefficient. In addition, all tensor elements of the model are shown to display the correct scaling with normal distance near a solid boundary.

On the properties of similarity subgrid-scale models as deduced from measurements in a turbulent jet

The paper describes the turbulence scheme implemented in the Meso-NH community research model, and reports on some validation studies. Since the model is intended to perform both large-eddy and mesoscale simulations, we have developed a full three-dimensional scheme, based on the original method of Redelsperger and Sommeria. A prognostic equation for the turbulent kinetic energy is used, together with conservative variables for moist non-precipitating processes. A particularity of the scheme is the use of variable turbulent Prandtl and Schmidt numbers, consistently derived from the complete set of second-order turbulent-moment equations. The results of three idealized boundary-layer simulations allowing detailed comparisons with other large-eddy simulation (LES) models are discussed, and lead to the conclusion that the model is performing satisfactorily.



The vertical flux and gradient computation can be run in isolation from the rest of the scheme, providing an efficient single-column parametrization for the mesoscale configuration of the model, if an appropriate parametrization of the eddy length-scale is used. The mixing-length specification is then the only aspect of the scheme which differs from the LES to the mesoscale configuration, and the numerical constants used for the closure terms are the same in both configurations. The scheme is run in single-column mode for the same three cases as above, and a comparison of single-column and LES results again leads to satisfactory results. It is believed that this result is original, and is due to the proper formulation of the parametrized mixing length and of the turbulent Prandtl and Schmidt numbers. In fact, a comparison of the parametrized mixing length with the length-scale of the energy-containing eddies deduced by spectral analysis of the LES shows interesting similarity.

A turbulence scheme allowing for mesoscale and large‐eddy simulations

An improved Mellor–Yamada (MY) turbulence closure model (MYNN model: Mellor–Yamada– Nakanishi–Niino model) that we have developed is summarized and its performance is demonstrated against a large-eddy simulation (LES) of a convective boundary layer. Unlike the original MY model, the MYNN model considers effects of buoyancy on pressure covariances and effects of stability on the turbulent length scale, with model constants determined from a LES database. One-dimensional simulations of Day 33 of the Wangara field experiment, which was conducted in a flat area of southeastern Australia in 1967, are made by the MY and MYNN models and the results are compared with horizontal-average statistics obtained from a three-dimensional LES. The MYNN model improves several weak points of the MY model such as an insufficient growth of the convective boundary layer, and underestimates of the turbulent kinetic energy and the turbulent length scale; it reproduces fairly well the results of the LES including the vertical distributions of the mean and turbulent quantities. The improved performance of the MYNN model relies mainly on the new formulation of the turbulent length scale that realistically increases with decreasing stability, and partly on the parameterization of the pressure covariances and the expression for stability functions for third-order turbulent fluxes.

Development of an Improved Turbulence Closure Model for the Atmospheric Boundary Layer

A scale-dependent dynamic subgrid model based on Lagrangian time averaging is proposed and tested in large eddy simulations (LES) of high-Reynolds number boundary layer flows over homogeneous and heterogeneous rough surfaces. The model is based on the Lagrangian dynamic Smagorinsky model in which required averages are accumulated in time, following fluid trajectories of the resolved velocity field. The model allows for scale dependence of the coefficient by including a second test-filtering operation to determine how the coefficient changes as a function of scale. The model also uses the empirical observation that when scale dependence occurs (such as when the filter scale approaches the limits of the inertial range), the classic dynamic model yields the coefficient value appropriate for the test-filter scale. Validation tests in LES of high Reynolds number, rough wall, boundary layer flow are performed at various resolutions. Results are compared with other eddy-viscosity subgrid-scale models. Unlike the...

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A scale-dependent Lagrangian dynamic model for large eddy simulation of complex turbulent flows

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 10−6 and 10−2. The LES uses a finite-difference method to integrate the three-dimensional grid-volume-averaged Navier–Stokes equations for a Boussinesq fluid. Subgrid-scale (SGS) fluxes are determined from algebraically approximated second-order 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 × 160 × 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 three-dimensional 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.

/pdf/coherent-structure-of-the-convective-boundary-layer-derived-2q5l16fvmt.pdf

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

A Mesoscale Model for the Simulation of Turbulence, Clouds and Flow over Mountains: Formulation and Validation Examples

Newton's law of gravitation gives very accurate results for the radii r and velocities v of an orbit. However, they do not give any indication of the diameter of celestial bodies. In this respect, it is fundamental to reconsider the formula for distance laws F∝e1e2/ r a . This also means putting all the fundamental physical principles to the test, such as the theory of action at a distance, the inertial system, isotropic space, the importance of constants and dimensions in the universe, the difference between matter and antimatter. Basically, a distinction must be made between how nature works and what we, on the other hand, recognize and interpret as nature in a 3-dimensional space. This leads to a TOE with a distance law purely by mathematics, with no constants. Our idea of nature is conditioned by evolution: A 3-dimensional space. Naturally, before Einstein, physicists assumed universal time. Since the theory of relativity, however, this has been understood as a 4-dimensional space-time. This is ultimately a consequence of Newton's theory of gravitation. Since Newton, every object is associated with a mass in kg and a center of gravity. Almost all of mathematical physics is built on this notion, with calculations based on gravity. The gravitational constant has the units m/kg /s . This alone shows that the gravitation only leads to the finally observable measurements in m over several steps. Criticism of the theory of gravity: What is a mass and its center of gravity? An object's centroid is an idealized idea of its center as a point. According to quantum theory, however, the center of gravity cannot be precisely located. The center of gravity of an object can at most be a quantum. What is the mass of a celestial body even though all the particles inside it are ultimately weightless? The theory of gravitation is definitely wrong, as entangled quantum phenomena show. Criticism of the long-distance theory: The formulation of the quantum theory with the constant c contradicts itself. The interactions of particles is symmetrical. A theory of action at a distance is theoretically conceivable, but unsuitable for physical calculations and only possible over infinite series. is that a photon? The idea that a photon is a single particle is not tenable. There is no reason why a photon could be made up of an electron and its antiparticle. A photon as a single particle cannot be represented in the TOE solely by the wave property with a beginning and end in the direction of time. A photon has exactly the properties of an electron paired with an antielectron. All bosons in the TOE are composed of even numbers of particles.Kritik an der Altogether this means: An efficient physical calculation is only possible with the assumption of a universal time. Inertial systems are characterized by the fact that all objects in a system have a common center of gravity. This in turn means that classical physics is the basis for all phenomena. The speed of light is only relevant for the observer. Each interaction between 2 objects, on the other hand, always requires double the time. Every look in a mirror shows this. In the TOE there is a single type of particle, which differs from all other particles by a different location. This means that this elementary particle cannot be divided, neither can it collide directly with another particle. The electron is a suitable name for this particle. That is, a photon is made up of an electron and an antielectron. Since Newton, physical laws have been formulated with constants c, h, G with the units sec, m and kg. The first consideration is what raw data is nature giving us? Time, multiple spatial dimensions, or an energy? Time with a dimension is essential. Physics without natural numbers is also essential, as are ratios with rational numbers and algebraic numbers built from them. This allows all conceivable models for the universe to be simulated. A theory of whatever kind for the universe can only be verified on the computer through simulations and thus digitally. It is therefore not expedient to assume pi in a physical theory for the laws of nature. Integers are also the basis of atomic theory and quantum theory. The simplest model for computations in physics is a single dimension (time), a single type of particle with a universal speed, and a single law of nature. The endlessness of the universe is beyond any possible knowledge and leads to a fractal universe. The TOE assumes that nature provides a single parameter of raw data and, as the most compact piece of information, is energy. For calculations in physics, all the particles in a system must be assigned a single number. This is part of the universe. The natural numbers result in cohesion and thus replace gravity. The system has no vacuum. It's a whole. Every natural number has a particle. The structure of the system is given by dual, alternating states, matching a series of 1,1,-1,1,-1,-1. This results in an integer, binary number. The series of particles, regardless of whether it is an atom or the solar system, begins with a center and can reach as far as our horizon of knowledge. The maximum number of this system is the total energy. An object is a divider of this system. At least 2 objects and an observer are required for a system. The torque N 1/r1=N 2/r 2=N B/r B is so simple that it must apply, namely for two objects and an observer. With the assumption of a universal time, all possible states can be represented by radii from the center define. The time results solely from coincidences of the same states of three objects. For example, on Earth, a month is a part of a year. The time in this system results from the smallest possible and observable time unit and thus the alternating states of 1, -1 and back to 1. The law of the lever can also be applied to time: N B/wB=N 1/w1=N 2/w2 Every object has the same information in the radii r as in the frequencies w, if w is a complex number. Both lead to the same result. That is, potential energy is equal to kinetic energy. What is being measured when a measuring device shows a distance? A distance is always relative to another distance. There is not a single straight line in the universe. Measuring lengths is a very demanding task. As soon as a ruler is knocked over, it is subject to the Coriolis force. The Lorentz contraction is a consequence, not a cause. A transformation of time is unnecessary and so is the mass correction. Mass is the energy of its surface and is therefore proportional to R . According to Gauss's integral theorem, it is immaterial which properties the object has inside. Everything within an orbit is matter. Antimatter is anything outside of an orbit. The limit is the photon. The twin paradox thus takes care of itself. The TOE assumes a one-dimensional arrangement of particles. The orbit of one particle is the center of the next particle. The time is measured as a digital display t. Any distance between two particles in a system corresponds to the minimum circumference r = 2pi t. All calculated distances r are thus a 2pi -fold and this carries over to the energy. Nature works with binary numbers. For an observer, the base is 2pi. The raw data from nature is encrypted for observers. All possible energies E and radii of an object can be represented as a polynomial with base 2pi. Starting from the center, large radius r, small radius, hereinafter referred to as xy, and deviation z follow. This results in a clear order according to the sizes r > xy > z. This is already cheaper than 3 isotropic dimensions x, y, z. This makes Heisenberg's inequality obsolete. The 3 spatial dimensions are combined into a single dimension as a polynomial: r=r 1+2pi xy1+4pi 2 z 1 Polynomials can be treated mathematically like orthograde vectors. Schrödinger's wave theory is based on Ψ=Ae /ħ (E t+r d r =Ae (wt+r / λ)) . By the mathematical transformation with e ln(2pi )) :=2pi and the assumed digital time with the only values of 1 and -1 can be converted into rOrbit=A(2pi) (−iw t (2pi) / =±Aw (2pi) (0)+n /l λ) Apoapsis=Rcenter (2pi) (n+l+1) periapsis=Rcenter (2pi) (n+l−1) I.e. the TOE contains the quantum theory. The calculations for the solar system must include the area of the sun as a starting point. The energy of the sun can be arbitrarily defined in units of 2pi. The exponent depends on the required resolution. For the planetary system, E=RSun 2 (2pi) is sufficient for a system with integer quantum numbers. The radius of the smallest possible object is 1+2pi+(2pi) . Beginning at the surface of the sun, the quantum properties of the solar system come into play. The quantum number n starts with 0 and corresponds to its surface. The formula for the radii of objects is the same for all systems in the universe. It's just our perception of how we see objects. In nature, the orbital periods correspond to a binary number. rOrbit=rcenter n /r satellite l For an observer, a digital time applies and radii correspond to the polynomials with base 2pi: rOrbit=(Ecenter+E satellite)/(1+2pi+(2pi) ) rOrbit=((2pi) 32+(2pi)22)/(1+2pi+(2pi)) n and l apply to object 1 and m and s to object 2 As in classical mechanics, measurements arise from ratios and require a balance of the 3 objects with a common center of gravity and defines the inertial frame. All states in a closed system are occupied by all particles. These are minimum energy ground states, a common unchanging centroid. The length of the entire entire polynomial of a system with N particles has the energy E=∑ 1 N 1+2pi+(2pi)+...+(2pi)=1⁄2 (2pi) means this polynomials with a constant ratio between neighboring particles 2pi=(2pi)/(2pi) . An imbalance between 2 objects corresponds to a polynomial with two coefficients = 0 and are defects with a band gap. This causes an instability with a decay of one of the two objects and a simultaneous increase in size of the other partner in the system. The probability of the coefficients equalizing depends on the length o

Simulation of the planetary system based on a theory of everything

Newton's law of gravitation gives very accurate results for the radii r and velocities v of an orbit, but they do not give any indication of the diameter of celestial bodies or the masses of elementary particles. In contrast, the TOE is based on the simplest possible law for the energy E = 2 r i t and the torque for an observer and two objects. A common constant can be derived from h, G and c. For the system of sun, earth and moon, a formula for c results from the radius of the earth and day alone: Numerous calculations on the planetary system and elementary particles are given. For example, the exact calculation of the proton mass in relation to the electron mass. TOE gives the result

Helmut Schmidt

Papers

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

A Mesoscale Model for the Simulation of Turbulence, Clouds and Flow over Mountains: Formulation and Validation Examples

Simulation of the planetary system based on a theory of everything

Theory of everything - relation to the theory of relativity and quantum theory