F. T. M. Nieuwstadt

Temperature measurement with a sonic anemometer and its application to heat and moisture fluxes

The possibility of measuring heat and moisture fluxes using sonic anemometer data is investigated. Theoretical relations for the temperature variance and heat flux are derived. In the first part of this paper, these relations are verified by experimental data, involving a sonic anemometer, a fast thermocouple and a Lyman-α hygrometer. In the second part we propose two simple procedures to estimate heat flux from sonic anemometer data. The first one requires a rough estimate of the Bowen ratio; for the second one the net radiation is needed. Using the last method, a good estimate of the moisture flux is also obtained.

The Turbulent Structure of the Stable, Nocturnal Boundary Layer

Abstract A large number of turbulence observations were made under stable conditions along a meteorological mast at Cabauw, The Netherlands. To present and organize these data we turn to the parameterized equations for the turbulent variances and covariances. In a dimensionless form these equations lead to a local scaling hypothesis. According to this hypothesis, dimensionless combinations of variables which are measured at the same height can be expressed as a function of a single parameter z/Λ. Here, Λ is called a local Obukhov length and is defined as Λ=−τ3/2T/(kgwθ) where τ and wθ) are the kinematic momentum and heat flux, respectively. Note that, in general, Λ may vary across the boundary layer, because τ and wθ are still unknown functions of height. The observations support local scaling. In particular, they agree with the limit condition for z/Λ→∞, which predicts that locally scaled variables approach a constant value. The latter result is called z-less stratification. An important application of z...

Scaling the atmospheric boundary layer

We review scaling regimes of the idealized Atmospheric Boundary Layer. The main emphasis is given on recent findings for stable conditions. We present diagrams in which the scaling regimes are illustrated as a function of the major boundary-layer parameters. A discussion is given on the different properties of the scaling regimes in unstable and stable conditions.

Large-Eddy Simulation of the Convective Boundary Layer: A Comparison of Four Computer Codes

To test the consistency of large-eddy simulation we have run four existing large-eddy codes for the same case of the convective atmospheric boundary layer. The four models differ in various details, such as: the subgrid model, numerics and boundary conditions.

Random walk models for particle displacements in inhomogeneous unsteady turbulent flows

First a small time analysis is developed for the first and second moments of the velocity (W) and displacement (Z) in one direction of particles marked at a given point in an inhomogeneous unsteady turbulent flow, in terms of the local energy dissipation rate, and the local derivatives of the second and third moments of the vertical component of the velocity field, ∂∼(u23)/∂z and ∼(∂u33)/∂z. Then the appropriate form of a Langevin equation in inhomogeneous turbulence is suggested, namely, dW=(−W/TL+a1)dt+a1/22 dωt where a1, a2, and TL are functions of the particle position and time, and dωt is a random Gaussian velocity increment with ∼(dωt)=0 and ∼((dωt))2=dt. For simplicity, only one component of the particle motion, W(t), is considered. The functions a1 and a2 are determined by relating the random walk model to the Eulerian conservation equations for the mass of the contaminant and volume of the flow (i.e., the continuity equation), using the Fokker–Planck equation and the Eulerian equations for the mo...

Some Aspects of the Turbulent Stable Boundary Layer

We consider the structure of the stable boundary layer using the concept of local scaling. In this scaling approach turbulence variables, non-dimensionalized with measurements taken at the same height, can be expressed as a function of a single parameter z/Λ, where z is the height and Λ a local Obukhov length. One of the consequences is that locally scaled variables become constant above the surface layer. This behavior is illustrated with observations of the Richardson number. With local scaling as a closure hypothesis we then formulate a model of the stable boundary layer. Its solution for steady-state conditions is given. One result we obtain is the well-known Zilitinkevich equation for the boundary-layer height. A comparison of this equation with observations results in a reasonable agreement. Also we discuss some alternative expressions for the stable boundary-layer height and compare them with observations. Another result of our model is an explicit profile for the K-coefficient as a quadratic function of height. We discuss the consequences of this expression for the dispersion of a point source emission. We find that the time scale of diffusion in this case is about 5 hours.

The steady-state height and resistance laws of the nocturnal boundary layer: Theory compared with cabauw observations

An expression is derived for the height of the stationary boundary layer during stable lapse rate conditions. It satisfies the conventional limits for neutral conditions and for large values of stability. Comparison with acoustic sounder observations near the meteorological mast at Cabauw (the Netherlands) shows that the steady-state height is not attained for large stability values. The observations are also used to investigate how the similarity functions A and B in the resistance laws depend on the stability parameters μ0 = u*/fL and Μ = h/L. The function B shows a clear trend as a function of stability, which can be described in terms of μ. The dependence of A is masked by scatter in the data points. The general conclusion leads to the concept of a non-steady boundary layer during stable lapse rate conditions.

The computation of the friction velocity u* and the temperature scale T* from temperature and wind velocity profiles by least-square methods

A method is given to calculate the surface layer parameters: u* (friction velocity) and T* (temperature scale) from wind speed and temperature profiles.The problem is formulated as a minimization of a least-square function, which is constructed from the difference between the measured profiles and the well-known Kansas profile relations.The wind speed and temperature profiles are treated simultaneously in this procedure. All the available wind speed and temperature measurements are used in order to reduce the effect of measurement errors.Estimates of the goodness of fit and confidence limits on the estimated parameters are discussed.The method has been applied to data obtained during experiments in a wide variety of conditions: Project Prairie Grass, experiments over Lake Flevo and experiments at the meteorological tower at Cabauw, the last two in the Netherlands.

DIRECT NUMERICAL SIMULATION OF PARTICLE DEPOSITION ONTO A FREE-SLIP AND NO-SLIP SURFACE

We consider here the direct numerical simulation (DNS) of channel flow with two different surfaces: a no-slip, fixed wall and on the opposite side a free-slip, free surface. The simulated velocity field agrees well with the experimental data for a free-surface flow obtained by Komori et al. [Int. J. Heat Mass Transf. 25, 513 (1982)]. The DNS is used to simulate particle trajectories, which are computed with a dynamic particle equation in which only the drag force given by the Stokes law is taken into account. For the particle time scale, nondimensionalized in terms of the fixed-wall friction velocity and the kinematic viscosity, we use the values τ+=5 and τ+=15. A statistically stationary condition is studied that is obtained by the introduction of a uniform distribution of particles at the beginning of the channel and by continuous removal through deposition at the two walls. The steady-state concentration distribution is nonuniform across the channel width, primarily due to the process whereby particles...

NUMERICAL STUDY OF TRANSIENT AND STEADY LAMINAR BUOYANCY-DRIVEN FLOWS AND HEAT TRANSFER IN A SQUARE OPEN CAVITY

Numerical simulations are presented for transient and steady laminar buoyancy-driven flows and heat transfer in a square cavity open on one side. Computations were performed within the domain of the cavity. Vorticity transport and energy equations were solved using the alternating direction implicit scheme, and a successive overrelaxation method was employed to obtain solutions for the streamfunction. A range of values were considered for Gr and Pr. The results indicate that natural convection in the cavity does not depend on the computational domain or on the boundary conditions at the open side, which influence only a small region nearby. Heat transfer from the cavity is calculated, and flow and transport characteristics are discussed