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- Author or Editor: H. Tennekes x
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Abstract
This paper deals with the problem of fully developed free convection in the atmospheric boundary layer. In free convection, the height of the Ekman layer is much larger than the absolute value of the Monin-Oboukhov length. The kinetic energy budget of the turbulence above the surface layer shows that the standard deviations of vertical velocity and of temperature are related to h/L by σ w /u *∝(−h/L)⅓ and σθ/θ*∝(−h/L)⅓. Because convection has no natural length scale, the height of the neutral Ekman layer (h∝u */f) is used to explore the consequences of the proposed expressions for σ w and σθ. The dissimilarity between the heat flux and the momentum flux is studied in terms of time- and length-scale ratios and in terms of a flux Richardson number. A definitive solution of the problem, however, cannot be formulated until an expression for the height of unstable Ekman layers, as a function of the time of day and the stability conditions at the top of the boundary layer, can he found.
Abstract
This paper deals with the problem of fully developed free convection in the atmospheric boundary layer. In free convection, the height of the Ekman layer is much larger than the absolute value of the Monin-Oboukhov length. The kinetic energy budget of the turbulence above the surface layer shows that the standard deviations of vertical velocity and of temperature are related to h/L by σ w /u *∝(−h/L)⅓ and σθ/θ*∝(−h/L)⅓. Because convection has no natural length scale, the height of the neutral Ekman layer (h∝u */f) is used to explore the consequences of the proposed expressions for σ w and σθ. The dissimilarity between the heat flux and the momentum flux is studied in terms of time- and length-scale ratios and in terms of a flux Richardson number. A definitive solution of the problem, however, cannot be formulated until an expression for the height of unstable Ekman layers, as a function of the time of day and the stability conditions at the top of the boundary layer, can he found.
Abstract
The differential equations governing the strength Δ (a potential temperature difference) and the height h of inversions associated with dry penetrative convection are considered. No assumptions on the magnitude of the downward heat flux at the inversion base are needed to obtain an algebraic equation that relates h and Δ to the heating history of the boundary layer and to the initial conditions. After the nocturnal inversion has been filled in by heating, the inversion base generally grows linearly with time in the morning, but is proportional to the square root of time in the afternoon. The variation of Δ with time differs greatly from case to case.
Abstract
The differential equations governing the strength Δ (a potential temperature difference) and the height h of inversions associated with dry penetrative convection are considered. No assumptions on the magnitude of the downward heat flux at the inversion base are needed to obtain an algebraic equation that relates h and Δ to the heating history of the boundary layer and to the initial conditions. After the nocturnal inversion has been filled in by heating, the inversion base generally grows linearly with time in the morning, but is proportional to the square root of time in the afternoon. The variation of Δ with time differs greatly from case to case.
Abstract
This paper explores the practical consequences of the asymptotic nature of the logarithmic wind profile in neutral, barotropic, planetary boundary layers. Recent developments in boundary-layer theory have shown that the von Kármán constant is a universal constant only in a very specific asymptotic sense; in typical atmospheric conditions its value is probably about 10% larger than the asymptotic one. Pending the development of a second-order theory, the value κ = 0.35 ± 0.02 is recommended for micrometeorological applications over smooth terrain. It is shown that K theory cannot be used in attempts to detect any trends of deviations from the logarithmic law.
Abstract
This paper explores the practical consequences of the asymptotic nature of the logarithmic wind profile in neutral, barotropic, planetary boundary layers. Recent developments in boundary-layer theory have shown that the von Kármán constant is a universal constant only in a very specific asymptotic sense; in typical atmospheric conditions its value is probably about 10% larger than the asymptotic one. Pending the development of a second-order theory, the value κ = 0.35 ± 0.02 is recommended for micrometeorological applications over smooth terrain. It is shown that K theory cannot be used in attempts to detect any trends of deviations from the logarithmic law.
Abstract
Since eddies in turbulent flows are a dense collection of very short wave packets, their position and wavenumber (or lifetime and frequency) cannot be determined without ambiguity. The spectral width of eddies is about an octave, but the effects of resolution limitations on the formulation of dynamically consistent turbulence models are largely unknown. Fourier transforms are inefficient at high wavenumbers; more efficient decomposition schemes sacrifice the capability to describe the microstructure of turbulent flows.
Abstract
Since eddies in turbulent flows are a dense collection of very short wave packets, their position and wavenumber (or lifetime and frequency) cannot be determined without ambiguity. The spectral width of eddies is about an octave, but the effects of resolution limitations on the formulation of dynamically consistent turbulence models are largely unknown. Fourier transforms are inefficient at high wavenumbers; more efficient decomposition schemes sacrifice the capability to describe the microstructure of turbulent flows.
Abstract
It is likely that several features of the mid-latitude circulation in the earth's atmosphere wig also be observed in two-dimensional, nondivergent flow with buoyant forcing and surface friction. Properly scalled, buoyancy effects are surprisingly similar to baroclinic effects. A linear stability analysis shows that the growth rate of unstable disturbances depends on zonal wavenumber in much the same way as that of baroclinic waves, except for the absence of a high-wavenumber cutoff related to the Rossby radius of deformation. The energy conversion mechanisms in buoyancy-driven two-dimensional flow closely resemble those in the atmosphere: eddy kinetic energy is maintained primarily by conversion of eddy potential energy, the kinetic energy of the mean zonal flow is maintained primarily by a reverse energy cascade, and the flow owes its existence and dynamics to the mean temperature contrast between latitude circles. The equations studied in this paper include these for enstrophy and temperature variance; the spectral fluxes of these quantities are taken into account. The maintenance of the general circulation in two-dimensional flow is described in part by a system of flux-maintenance equations. These shed light on such issues as the magnitude of the poleward eddy heat flux in developing storms and the countergradient eddy momentum flux in middle latitudes.
Abstract
It is likely that several features of the mid-latitude circulation in the earth's atmosphere wig also be observed in two-dimensional, nondivergent flow with buoyant forcing and surface friction. Properly scalled, buoyancy effects are surprisingly similar to baroclinic effects. A linear stability analysis shows that the growth rate of unstable disturbances depends on zonal wavenumber in much the same way as that of baroclinic waves, except for the absence of a high-wavenumber cutoff related to the Rossby radius of deformation. The energy conversion mechanisms in buoyancy-driven two-dimensional flow closely resemble those in the atmosphere: eddy kinetic energy is maintained primarily by conversion of eddy potential energy, the kinetic energy of the mean zonal flow is maintained primarily by a reverse energy cascade, and the flow owes its existence and dynamics to the mean temperature contrast between latitude circles. The equations studied in this paper include these for enstrophy and temperature variance; the spectral fluxes of these quantities are taken into account. The maintenance of the general circulation in two-dimensional flow is described in part by a system of flux-maintenance equations. These shed light on such issues as the magnitude of the poleward eddy heat flux in developing storms and the countergradient eddy momentum flux in middle latitudes.
Three-dimensional turbulence occurs mainly in convective clouds and in the atmospheric boundary layer. Two-dimensional turbulence is a model for the statistical features of large-scale flows in the atmosphere. The differences between two- and three-dimensional turbulence are discussed, with a minimum of mathematics, in terms of elementary vorticity dynamics. The influence of the microstructure on the evolution of the large-scale features of the flow field is explored in some detail. A simple rationale is given for ignoring subgrid scale fluxes in numerical weather prediction.
Three-dimensional turbulence occurs mainly in convective clouds and in the atmospheric boundary layer. Two-dimensional turbulence is a model for the statistical features of large-scale flows in the atmosphere. The differences between two- and three-dimensional turbulence are discussed, with a minimum of mathematics, in terms of elementary vorticity dynamics. The influence of the microstructure on the evolution of the large-scale features of the flow field is explored in some detail. A simple rationale is given for ignoring subgrid scale fluxes in numerical weather prediction.
Abstract
The budget of turbulent kinetic energy at the base of the inversion which caps the daytime atmospheric boundary layer depends on the lapse rate of potential temperature in the air aloft. The principal gain term in the energy budget is turbulent transport of kinetic energy, the principal loss term is buoyant conversion of kinetic energy into potential energy. The contributions made by these and other terms in the energy budget need to be parameterized for applications to inversion-rise prediction schemes. This paper contains a detailed analysis of the effects of dissipation near the inversion base, which leads to reduced entrainment if the air aloft is very stable. The parameterized energy budget also includes the Zilitinkevich correction, the influence of mechanical energy production near the inversion base, and modifications needed to incorporate cases in which the surface heat flux is negligible. Extensive comparisons of the theoretical model with experimental data indicate that a simplified treatment of the energy budget is adequate for forecasts of the development of convective mixed layers. The parameterization scheme is also applicable to thermocline erosion in the ocean; in that case, however, some of the minor terms in the energy budget often play a major role.
Abstract
The budget of turbulent kinetic energy at the base of the inversion which caps the daytime atmospheric boundary layer depends on the lapse rate of potential temperature in the air aloft. The principal gain term in the energy budget is turbulent transport of kinetic energy, the principal loss term is buoyant conversion of kinetic energy into potential energy. The contributions made by these and other terms in the energy budget need to be parameterized for applications to inversion-rise prediction schemes. This paper contains a detailed analysis of the effects of dissipation near the inversion base, which leads to reduced entrainment if the air aloft is very stable. The parameterized energy budget also includes the Zilitinkevich correction, the influence of mechanical energy production near the inversion base, and modifications needed to incorporate cases in which the surface heat flux is negligible. Extensive comparisons of the theoretical model with experimental data indicate that a simplified treatment of the energy budget is adequate for forecasts of the development of convective mixed layers. The parameterization scheme is also applicable to thermocline erosion in the ocean; in that case, however, some of the minor terms in the energy budget often play a major role.
Abstract
In this paper we develop an abbreviated model for the pressure-gradient velocity correlation terms in the equations for the Reynolds-stress components in the neutral boundary layer. The model contains three terms: a nonlinear return-to-isotropy term, a mean strain-rate term, and a mean vorticity term. There are three free constants in the model, which are determined with the aid of experimental results on the ratios between the Reynolds-stress components in the neutral surface layer. Since three independent equations are involved, the model is self-contained. Through its mean vorticity term, the model incorporates the effects of a rotating coordinate system. The application of the model to a neutral Ekman layer gives realistic results.
Abstract
In this paper we develop an abbreviated model for the pressure-gradient velocity correlation terms in the equations for the Reynolds-stress components in the neutral boundary layer. The model contains three terms: a nonlinear return-to-isotropy term, a mean strain-rate term, and a mean vorticity term. There are three free constants in the model, which are determined with the aid of experimental results on the ratios between the Reynolds-stress components in the neutral surface layer. Since three independent equations are involved, the model is self-contained. Through its mean vorticity term, the model incorporates the effects of a rotating coordinate system. The application of the model to a neutral Ekman layer gives realistic results.
