Temperature Structure Functions Research Articles

Small-Scale Properties of Turbulent Rayleigh-Bénard Convection

The properties of the structure functions and other small-scale quantities in turbulent Rayleigh-Bénard convection are reviewed, from an experimental, theoretical, and numerical point of view. In particular, we address the question of whether, and if so where in the flow, the so-called Bolgiano-Obukhov scaling exists, i.e., Sθ(r) ∼ r2/5 for the second-order temperature structure function and Su(r) ∼ r6/5 for the second-order velocity structure function. Apart from the anisotropy and inhomogeneity of the flow, insufficiently high Rayleigh numbers, and intermittency corrections (which all hinder the identification of such a potential regime), there are also reasons, as a matter of principle, why such a scaling regime may be limited to at most a decade, namely the lack of clear scale separation between the Bolgiano length scale LB and the height of the cell.

Open water evaporation estimation for a small shallow reservoir in winter using surface renewal

Summary Evaporation is one of the main components of the energy and water balance of reservoir water behind dams and is a major component of water loss. Measurements in winter of sensible heat ( H ) for the small and shallow reservoir of Midmar Dam, KwaZulu-Natal, South Africa were made using the surface renewal (SR) method, a renewal model method that uses the average cubic air temperature structure function and eddy covariance (EC). The small magnitude of H during winter makes it difficult to test the reliability of the H estimates obtained using instruments and sensors mounted above the water surface using the SR, renewal model and EC methods. Latent energy flux was estimated as a residual of the energy balance using additional measurements of net irradiance R n above the water surface and the water-stored heat flux. The SR sensible heat flux ( H SR ) was estimated for heights of 1.0, 1.3, 1.9 and 2.5 m above the water surface using two air temperature time lags r of 0.4 and 0.8 s of the 10-Hz measurements. The SR method depends on a weighting factor α which represents the capability of the atmospheric turbulence to mix the scalar, within the air parcel to be renewed. The factor α was determined for each measurement height and time lag from the slope of a linear regression relationship forced through the origin of measured EC sensible heat flux ( H EC ) values on the y -axis vs. H SR or renewal model H on the x -axis. All α values obtained using the renewal model method were not statistically different from that obtained using the SR method for z = 1.0 m for both time lags. Using a calibration dataset, an average α value for the 1.0- and 1.3-m heights of 0.198 for r = 0.4 s and 0.245 for r = 0.8 s for the SR and renewal model methods was obtained. The 30-min H SR , renewal model and H EC estimates were often the smallest component of the energy balance (generally −40 to 40 W m −2 ) and compared reasonably well for the validation dataset. The heat storage flux G was larger in magnitude (0–200 W m −2 ) compared to the sensible heat flux. The SR, renewal model and EC latent energy fluxes, each calculated as residuals of the energy balance, were almost the same in magnitude as the available energy flux R n − G due to the relatively small magnitude of the sensible heat flux during the winter measurement period. The daily evaporation ranged between 1.0 and 3.9 mm.

Effect of the Scalar Injection Mechanism on Passive Scalar Structure Functions in a Turbulent Flow

Higher-order passive scalar (temperature) structure functions are measured in the turbulent wake of a circular cylinder at a Taylor-microscale Reynolds number (Rlambda) of 370. The scalar is injected by two different means: (i) heating of the cylinder and (ii) use of a mandoline. Even though the second-order statistics (e.g., power spectra, second-order structure functions) of the scalar field are experimentally indistinguishable in the inertial and dissipative ranges, we observe notable differences in the inertial-range scaling exponents (xin) of the scalar structure functions at higher orders. The implication is therefore that the variations in previous estimates of xin may be attributable to differences in the scalar field initial conditions (and may not be deemed characteristic of a universal nature of the small-scale statistics of turbulent passive scalars).

Diagnostics of Near-Solar Plasma Turbulence Parameters Using the Radio Sounding Technique at Small Heliocentric Distances

We investigate the temporal correlation function and the mean intensity of monochromatic radio emission in the neighborhood of a regular caustic produced by radio sounding of near-solar plasma. Using asymptotic analysis and numerical simulation, we determine conditions under which the temporal correlation function is related to the temporal structure function by a relation similar to that used for the solar wind diagnostics (Coles and Harmon, Astrophys. J.337, 1023, 1989) in the case of weak refraction of radio waves. Information on the correlation function and on the mean intensity in the caustic shadow region can be used to determine the parameters of the electron density fluctuation spectrum at small heliocentric distances.

FADE, an instrument to measure the atmospheric coherence time

Aims. After proposing a new method of deriving the atmospheric time constant from the speed of focus variations (Kellerer & Tokovinin 2007, A&A, 461, 775), we now implement it with the new instrument, FADE. Methods. FADE uses a 36-cm Celestron telescope that is modified to transform stellar point images into a ring by increasing the central obstruction and combining defocus with spherical aberration. Sequences of images recorded with a fast CCD detector are processed to determine the defocus and its variations in time from the ring radii. The temporal structure function of the defocus is fitted with a model to derive the atmospheric seeing and time constant. We investigated by numerical simulation the data reduction algorithm and instrumental biases. Bias caused by instrumental effects, such as optical aberrations, detector noise, acquisition frequency, etc., is quantified. The ring image must be well-focused, i.e. must have a sufficiently sharp radial profile, otherwise, scintillation seriously affects the results. An acquisition frequency of 700 Hz appears adequate. Results. FADE was operated for 5 nights at the Cerro Tololo observatory in parallel with the regular site monitor. Reasonable agreement between the results from the two instruments has been obtained.

Scaling laws in the central region of confined turbulent thermal convection

In confined turbulent thermal convection, the velocity is separated into two parts: one that is correlated with some function of the temperature fluctuations, and thus associated with the plume velocity, and the other part, the background velocity, which is uncorrelated with any function of the temperature fluctuations. As a result, one should focus on the plume velocity, and not the whole velocity, and the temperature when studying the scaling behavior. In this paper, a phenomenological theory for the scaling behavior in the central region of confined turbulent thermal convection is presented. The spatial (temporal) plume velocity structure functions are found to have the same scaling behavior as the spatial (temporal) temperature structure functions. For tau> or = taub, where the buoyant scale taub is determined in terms of measurable quantities, the scaling exponents of the temporal temperature structure functions and hence those of the temporal plume velocity structure functions are obtained. These results are checked against experimental measurements, and good agreement is found.

A comparison of new and existing equations for estimating sensible heat flux using surface renewal and similarity concepts

This paper describes two approaches for estimating sensible heat flux, using surface renewal and similarity concepts. One approach depends on a temperature structure function parameter and is valid in the inertial sublayer. The other approach depends on the temperature standard deviation and operates when measurements are made above the canopy top, either in the roughness or inertial sublayer. The approaches were tested over grass, rangeland grass, wheat, grape vineyard, and nectarine and olive orchards. It is shown that the free convection limit expression for the standard deviation method holds for slightly unstable conditions. When surface homogeneity and fetch requirements are not fully met in the field, the results show that the equations based on surface renewal principles are more robust and accurate than equations exclusively based on similarity backgrounds. It is likely that the two methods are less sensitive to site‐specific adjustment of the similarity relationships unless the canopy is rather heterogeneous. Under unstable conditions, the free convection limit equation, which depends on the temperature standard deviation, can provide online sensible heat flux estimates using affordable battery‐powered data logger with temperature data as the only input. The approach performed well when measuring above the canopy in the roughness and inertial sublayers, thus suggesting that the method is useful for long‐term monitoring over growing vegetation.

Optical Turbulence Profiling with Balloons Relevant to Astronomy and Atmospheric Physics

ABSTRACTWe present here an in situ technique to measure the microstructure of the temperature field in our atmosphere. It consists of an autonomous payload that computes the structure function of the temperature, along with an off‐the‐shelf meteorological sonde that gives air pressure, temperature, humidity, and wind speed. This technique, which has been intensively cross‐calibrated, gives a high spatiotemporal resolution, allowing us to achieve an optical turbulence profile C2N(h) with a better than 6 m vertical resolution. It has been designed to allow simultaneous measurements of the temperature structure function in various geometrical configurations. Its versatility, reliability, and accuracy helped us to successfully undertake many astronomical site testing campaigns, as well as offer new insights into the physics of the optical turbulence.

Statistical Characteristics of atmospheric phase fluctuations observed by a VLBI system using a beacon wave from a geostationary Satellite

This paper reports the statistical characteristics of phase fluctuations obtained by a very long baseline interferometry, which received beacon waves from a geostationary satellite. Observations were made in different weather conditions by the 6-m Kagoshima and the 10-m Mizusawa radio telescopes, which were 1284 km apart from one another. Atmospheric phase fluctuations ranging from 0.2 to about 1000 s were detected. To study a variety of statistical characteristics of these phase fluctuations, the Allan standard deviation, /spl sigma//sub y/(/spl tau/), the temporal structure function, D/sub /spl phi//(/spl tau/), and the square root of power spectrum, G/sub /spl phi//(f), were calculated from the observation results. These qualities were found to depend on the time interval /spl tau/ or the frequency f (f=1/2/spl tau/) as follows: /spl sigma//sub y/(/spl tau/)/spl prop//spl tau//sup -0.6/, /spl tau//sup -0.3/, D/sub /spl phi//(/spl tau/)/spl prop//spl tau//sup 0.9/, /spl tau//sup 1.3/ for 0.2 s f>0.33 Hz and G/sub /spl phi//(f)/spl prop/f/sup -1.3/ for 0.33 Hz>f>0.00125 Hz. The curves of /spl sigma//sub y/(/spl tau/) and D/sub /spl phi//(/spl tau/) exhibited shifts whose magnitudes followed the weather order clear, cloudy, and rainy. For /spl tau/>1.5 s (or f 0.33 Hz), the model has to be modified to explain the experimental results.

Eulerian short-time statistics of turbulent flow at large Reynolds number

An asymptotic analysis is presented of the short-time behavior of second-order temporal velocity structure functions and Eulerian acceleration correlations in a frame that moves with the local mean velocity of the turbulent flow field. Expressions in closed-form are derived which cover the viscous and inertial subranges. They apply to general anisotropic turbulence at a large Reynolds number obeying the Kolmogorov theory. Previously published results for isotropic turbulence emerge as special cases. In the derivation use is made of the approximation of temporarily frozen turbulence proposed by Tennekes. It is shown to be valid under conditions not other than those for which the Kolmogorov hypotheses hold. The effects of intermittency appear to be marginal.

Inverse structure functions of temperature in grid-generated turbulence

Jensen [Phys. Rev. Lett. 83, 76 (1999)] proposed a new technique to study the scaling behavior of turbulent velocity fields. Inverse structure functions—defined as average moments of distances (or times) corresponding to a specified difference of a turbulent quantity—were used to investigate the intermittency of the turbulent velocity field. The present Brief Communication employs inverse structure functions to study the behavior of a passive scalar (temperature) in high-Reynolds-number grid-generated turbulence. It is shown that the scaling exponents of inverse structure functions of temperature are significantly different than those of the longitudinal and transverse velocity. Such a result is attributed to the higher level of intermittency associated with passive scalar fields.

Similarity solution of temperature structure functions in decaying homogeneous isotropic turbulence

An equilibrium similarity analysis is applied to the transport equation for <(deltatheta)(2)>, the second-order temperature structure function, for decaying homogeneous isotropic turbulence. A possible solution is that the temperature variance <theta(2)> decays as x(n), and that the characteristic length scale, identifiable with the Taylor microscale lambda, or equivalently the Corrsin microscale lambda(theta), varies as x(1/2). The turbulent Reynolds and Péclet numbers decay as x((m+1)/2) when m<-1, where m is the exponent which characterizes the decay of the turbulent energy <q(2)>, viz., <q(2)> approximately x(m). Measurements downstream of a grid-heated mandoline combination show that, like <(deltaq)(2)>, <(deltatheta)(2)> satisfies similarity approximately over a significant range of scales r, when lambda, lambda(theta), <q(2)>, and <theta(2)> are used as the normalizing scales. This approximate similarity is exploited to calculate the third-order structure functions. Satisfactory agreement is found between measured and calculated distributions of <deltau(deltaq)(2)> and <deltau(deltatheta)(2)>, where deltau is the longitudinal velocity increment.

Characterization of Atmospheric Parameters using a Ground Based GPS Network in North Europe

We characterize the temporal and spatial variation of the Zenith Wet Delay (ZWD) and the Zenith Total Delay (ZTD), estimated using a network of Global Positioning System (GPS) receivers. This characterization is important for the improvement and validation of atmospheric water vapor models, applicable in GPS meteorology, as well as in the navigation. We treat the estimates of Zenith Hydrostatic Delay (ZHD) and ZWD as realizations of random walk stochastic processes and we derive the corresponding parameters for different locations and measurement techniques for data acquired at intervals of 1 to 3 hours. The monthly standard deviation (StD) of the ZTD is less than 50 mm and does not exhibit a strong seasonal signature over the period 1997-1998 for any of the studied GPS sites. However, the StDs of the pairwise-differenced ZTD time series show a seasonal dependence, mainly due to the spatial variations of the ZWD, which should be considered when GPS data are assimilated in weather prediction models. We show the differences in typical spatial characteristics of ZHD and ZWD for the winter and summer seasons in North Europe. Finally, we describe the use of temporal structure functions for detection of rapid changes in ZTD.

Intermittency and scaling in turbulent convection

Both the velocity and temperature measurements taken in turbulent Rayleigh-B'enard convection experiments have been analyzed. It is found that both the velocity and temperature fluctuations are intermittent and can be well-described by the She-Leveque hierarchical structure. A positive correlation between the vertical velocity and the temperature differences is found both at the center, near the sidewall and near the bottom of the convection cell, supporting that buoyancy is significant in the Bolgiano regime. Moreover, the intermittent nature of the temperature fluctuations in the Bolgiano regime can be attributted to the variations in the temperature dissipation rate. However, the relations between the velocity and temperature structure functions and their correlations implied by the Bolgiano-Obukhov scaling are not supported by experimental measurements.

Spatial and temporal fluctuations of atmospheric microwave emission

Characteristics of spatial and temporal fluctuations of atmospheric absorption and emission at millimeter and centimeter wavelengths are presented. Theoretical relations and experimental data are given on structure functions of absorption and brightness temperature at wavelengths of 0.8 and 1.35 cm. It is shown that in cloudless weather the intensity of fluctuations at these wavelengths is determined mainly by random fluctuations of the humidity field. Under cloudy conditions the intensity of fluctuations of microwave atmospheric radiation grows, with stratiform and cumuliform clouds differently affecting the character of the space‐time dependency of fluctuations.

Structure and Evolution of the Transition Region Network Observed in he ii λ304

The length scale and life time of the transition region network cells were studied using He ii λ304 filtergrams. The temporal structure function was calculated from spatially aligned He ii λ304 images. The estimated life time of the network cell was about 27 hr. We compared this life time with the life time of photospheric magnetic network and of the extrapolated magnetic network. The spatial structure function was calculated from the He ii λ304 filtergrams. The calculated spatial structure function saturates at ∼ 25 000 km. The transition region network elements are bigger in size than the photospheric magnetic network element. The magnetic network element equals the size of the He ii λ304 network element when the photospheric magnetic field is extrapolated to a height of 3000 km above the photosphere where the magnetic fluxes are deployed. The derived value of the diffusion speed of the network elements was 0.098 km s−1.

Plume statistics in thermal turbulence: mixing of an active scalar.

Statistical properties of the temperature field in turbulent convection are studied experimentally. We show that the skewness of the plus and minus temperature increments can be used to quantitatively characterize the mixing zone in the convective flow and the result reveals how the mixing zone evolves with the Rayleigh number. We also present evidence for the saturation of the temperature structure function exponent and that the saturation is related to thermal plumes. A more direct study of the thermal plumes suggests that their sizes have a distribution that is approximately log-normal.

Temperature structure functions for air flow over moderately heated ground

We study temperature structure functions of second, fourth, and sixth orders at heights of up to 2 m above the ground in moderately heated atmosphere. Most of the data come from measurements over salt flats of the Utah desert, with well-defined wind direction and uniform temperature boundary conditions. As in high-Rayleigh-number convection in a closed container, a thermal boundary layer develops near the ground, its thickness here being of the order of 50 cm. We demonstrate the coexistence of two scaling ranges, one of which corresponds to the classical inertial range and the other to the buoyant range influenced by thermal convection. The determination of scaling exponents in the two ranges is facilitated by the use of a scaling function. We present the variations with height of scaling exponents in both ranges, as well as the crossover scales from one range to another.

Ionospheric irregularity diagnostics from the phase structure functions of MF/HF radio echoes

We present a new approach to investigating ionospheric irregularities, using the temporal structure function of totally reflected radio echo phase variations. Modern digital ionosondes (e.g., the dynasonde) measure the echo phase with very high resolution and precision, at closely spaced antennas, frequencies, and times. A “stringing” procedure gives continuous and unambiguous phase variation data for time intervals of any desired length. Quasi‐periods of tens of seconds up through several minutes are caused by large‐scale movements of the ionospheric plasma, while shorter‐period phase variations result from the interaction of the sounding signal with small‐scale irregularities. The relevant irregularity spatial domain extends from decameter radio wavelengths to the first Fresnel scale, a few kilometers. We obtain a theoretical relation between structure functions of the temporal phase variations and spatial irregularities with a simple model of frozen horizontal drift. The relation permits solutions of both the direct and inverse problems. Although long‐period phase measurements are practicable and essential to exploring larger irregularity scales, they require observing modes dedicated to multiple fixed‐frequency time series, and this undesirably limits the number of altitudes that can be monitored simultaneously. An alternative “rudimentary structure function” is obtainable from standard dynasonde “B‐mode” ionograms; it offers good altitude and time resolution for irregularity studies while permitting other established diagnostics (electron density profiles, vector velocities, critical frequencies, etc.) with the same data. We show some example analyses by these methods as applied to auroral and magnetic‐equatorial dynasonde observations. We find irregularity amplitudes in the range 0.001 &lt; ΔN/N &lt; 0.1 (for a nominal scale of 1 km) and spectral indices in the range 2 &lt; v &lt; 4, with evidence of diurnal variation in both quantities at both locations.

Conditional statistics of temperature fluctuations in turbulent convection.

We find that the conditional statistics of temperature difference at fixed values of the locally averaged temperature dissipation rate in turbulent convection become Gaussian in the regime where the mixing dynamics is expected to be driven by buoyancy. Hence, intermittency of the temperature fluctuations in this buoyancy-driven regime can be solely attributed to the variation of the locally averaged temperature dissipation rate. We further obtain the functional behavior of these conditional temperature structure functions. This functional form demonstrates explicitly the failure of dimensional arguments and enhances the understanding of the temperature structure functions.