Buoyancy Subrange Research Articles

Evidence of strong wave turbulence and of Bolgiano temperature spectra in katabatic winds on steep slopes

The katabatic winds on steep slopes investigated in the present study reveal a novel spectral behavior, observed in the outer part of the jet. At low wavenumbers, the one-dimensional (1D) velocity spectra show evidence of a kx−1 range for the three components of the velocity vector: Eu(kx),Ev(kx),Ew(kx)∝kx−1 [as well as for the 1D temperature spectrum Eθ(kx)∝kx−1]. This suggests the existence of strong wave turbulence. A necessary condition for strong wave turbulence to be manifest is that the flow direction wavenumber, kx, extends to much lower values than the slope normal one, kz. This is satisfied in the present field experiment where wave energy is injected at wavenumber kx=kN=(Na sin α)/uj¯, while kz∼1/Δz, with Na the ambient stratification, α the slope angle, uj¯ the maximum wind velocity, and Δz the shear layer thickness of the jet. In the inertial range, the velocity spectra exhibit a power law kx−5/3 over two decades, whereas the temperature-buoyancy spectra show evidence of a −7/5 slope in the buoyancy sub-range, followed by a −5/3 slope. The change in spectral slopes occurs at the Bolgiano scale LB that is close to the Dougherty–Ozmidov scale LOZ. The high Reynolds number based on the Taylor micro-scale, Reλ∼103, allows clear identification of the spectral laws.

On the Buoyancy Subrange in Stratified Turbulence

This study is motivated by the importance of the stratified turbulence in geophysical flows. We present a theoretical analysis of the buoyancy subrange based on the theory of strongly stratified turbulence. Some important turbulent scales and their relations are explored. Scaling constants of the buoyancy subrange scaling laws for both kinetic and potential energy spectra are derived and analyzed. It is found that these constants are functions of the horizontal Froude number F r h . For the potential energy spectrum, the scaling constant also depends on the turbulent flux coefficient of Γ .

A Model for Turbulence Spectra in the Equilibrium Range of the Stable Atmospheric Boundary Layer

AbstractStratification can cause turbulence spectra to deviate from Kolmogorov's isotropic power law scaling in the universal equilibrium range at high Reynolds numbers. However, a consensus has not been reached with regard to the exact shape of the spectra. Here we propose a shape of the turbulent kinetic energy and temperature spectra in horizontal wavenumber for the equilibrium range that consists of three regimes at small Froude number: the buoyancy subrange, a transition region, and the isotropic inertial subrange through dimensional analysis and substantial revision of previous theoretical approximation. These spectral regimes are confirmed by various observations in the atmospheric boundary layer. The representation of the transition region in direct numerical simulations will require large‐scale separation between the Dougherty‐Ozmidov scale and the Kolmogorov scale for strongly stratified turbulence at high Reynolds numbers, which is still challenging computationally. In addition, we suggest that the failure of Monin‐Obukhov similarity theory in the very stable atmospheric boundary layer is due to the fact that it does not consider the buoyancy scale that characterizes the transition region.

The life cycle of instability features measured from the Andes Lidar Observatory over Cerro Pachon on 24 March 2012

AbstractThe Aerospace Corporation's Nightglow Imager (ANI) observes nighttime OH emission (near 1.6 μm) every 2 s over an approximate 73° field of view. ANI had previously been used to study instability features seen over Maui. Here we describe observations of instabilities seen from 5 to 8 UT on 24 March 2012 over Cerro Pachon, Chile, and compare them with previous results from Maui, with theory, and with Direct Numerical Simulations (DNS). The atmosphere had reduced stability because of the large negative temperature gradients measured by a Na lidar. Thus, regions of dynamical and convective instabilities are expected to form, depending on the value of the Richardson number. Bright primary instabilities are formed with a horizontal wavelength near 9 km and showed the subsequent formation of secondary instabilities, rarely seen over Maui, consistent with the primaries being dynamical instabilities. The ratio of the primary to secondary horizontal wavelength was greater over Chile than over Maui. After dissipation of the instabilities, smaller‐scale features appeared with sizes in the buoyancy subrange between 1.5 and 6 km. Their size spectra were consistent with the model of Weinstock (1978) if the turbulence is considered to be increasing. The DNS results produce secondary instabilities with sizes comparable to what is seen in the images although their spectra are somewhat steeper than is observed. However, the DNS results also show that after the complete decay of the primary features, scale sizes considerably smaller than 1 km are produced and these cannot be seen by the ANI instrument.

An analytical theory of the buoyancy–Kolmogorov subrange transition in turbulent flows with stable stratification

The buoyancy subrange of stably stratified turbulence is defined as an intermediate range of scales larger than those in the inertial subrange. This subrange encompasses the crossover from internal gravity waves (IGWs) to small-scale turbulence. The energy exchange between the waves and small-scale turbulence is communicated across this subrange. At the same time, it features progressive anisotropization of flow characteristics on increasing spatial scales. Despite many observational and computational studies of the buoyancy subrange, its theoretical understanding has been lagging. This article presents an investigation of the buoyancy subrange using the quasi-normal scale elimination (QNSE) theory of turbulence. This spectral theory uses a recursive procedure of small-scale modes elimination based upon a quasi-normal mapping of the velocity and temperature fields using the Langevin equations. In the limit of weak stable stratification, the theory becomes completely analytical and yields simple expressions for horizontal and vertical eddy viscosities and eddy diffusivities. In addition, the theory provides expressions for various one-dimensional spectra that quantify turbulence anisotropization. The theory reveals how the dispersion relation for IGWs is modified by turbulence, thus alleviating many unique waves' features. Predictions of the QNSE theory for the buoyancy subrange are shown to agree well with various data.

An experimental study of the airside flow structure during natural convection

We report on an experimental study conducted to investigate the airside flow structure above an evaporative water surface during natural convection. Two-dimensional airside velocity fields were measured using particle image velocimetry for three different surface heat flux conditions. Detailed analysis of the turbulent velocity fields shows a complex flow structure due the local interactions of fluid motions in vertical, horizontal, and normal directions. The trends of turbulent intensity profiles on airside and waterside are found to be similar. However, the airside turbulent intensities are approximately 20 times stronger than that on the waterside. The spectral analysis of the turbulent velocities showed the existence of two distinct power law regimes. In low wavenumber range, the buoyancy subrange is observed with a slope of −3 whereas, in high wavenumber range, the inertial subrange with the classical slope of −5/3 is observed. The results also indicate that the airside turbulent velocity fields control the local evaporation rate, which in turn influences the water surface temperature field and the waterside velocity field.

The impact of air saturation on the flow structure beneath air–water interface during natural convection

We report on results from an experimental study conducted to investigate the impact of air saturation on the turbulent structure beneath air–water interface. Particle image velocimetry (PIV) was used to measure the two dimensional velocity fields beneath the water surface. The results show that air saturation has a significant impact on the waterside turbulent structure. As the air becomes saturated, the magnitudes of the horizontal and vertical turbulent velocities are decreased by factors of 5 and 2.5, respectively. It was argued that in addition to the surface heat flux, the waterside flow field is also influenced by the airside velocity via the air–water interface. The latent heat flux at the saturation state is not equal to zero. The film condensation on the tank walls at the saturation state is found to be responsible for the latent heat flux. The spectral analysis shows that both the horizontal and vertical turbulent motions are much weaker than that for the unsaturated case. For the saturated case, the range of the turbulent motions responsible for working against buoyancy forces is smaller than that for the unsaturated case. It was concluded that during natural convection, when the turbulence is relatively weak, in addition to the buoyancy subrange, another subrange exists within the inertial subrange, where the turbulent motions are simply convected by the buoyancy forces and that the energy interaction is highly dependent on the energy of the turbulent motions and the magnitude of the buoyancy forces.

Turbulent structure beneath air-water interface during natural convection

Results from an experimental study investigating the turbulent structure beneath the air-water interface during natural convection are reported. The two-dimensional velocity field beneath the surface in a plane perpendicular to the surface was measured using digital particle image velocimetry. The results show that the waterside flow field undergoes three-dimensional flow interactions forming complex flow patterns, which appear to be random. The magnitude of the turbulent velocities and turbulent kinetic energy increases with the heat flux. The profiles of the turbulent velocities are self-similar and appropriately scaled by the parameters proposed for the natural convection above a heated wall. The wave number and frequency spectra exhibit −3 slopes providing the evidence that during natural convection the buoyancy subrange exists within the inertial subrange where the energy loss is due to the work against buoyancy.

Velocity Intermittency in a Buoyancy Subrange in a Two-Dimensional Soap Film Convection Experiment

In a two-dimensional soap film convection experiment, the velocity fields are found to be strongly intermittent in the buoyancy subrange, which was reported to be nonintermittent in a recent numerical simulation. The structure functions Sq(l)(= <delta(upsilon)l(q)>) exhibit self-similar structures and can be described by power laws l(zetaq) for integers 8 > or = q < or = 1. By extending Kolmogorov's refined similarity hypothesis to our system, an analytical form is derived for the scaling exponent zeta(q) = q/2 + (mu/18)(3q - q2). Our measurements yield mu = 0.42, which is significantly greater than 0.2 found in high Reynolds number turbulence in wind tunnels.

Density Fluctuations in Strongly Stratified Two-Dimensional Turbulence

We present a study of density fluctuations in two-dimensional soap-film convection. When the temperature difference (DeltaT) imposed vertically along the film is smaller than a critical value (DeltaT(C) approximately 48 K), the convective motion is in a strongly stratified state and the frequency power spectrum of density fluctuations shows a Bolgiano-like scaling f(-7/5) in the buoyancy subrange. When DeltaT>DeltaT(C), the fluid motion crosses over to a strongly mixed state characterized by the emergence of a large-scale circulation. The density power spectrum in this state has a passive-scalar-like scaling f(-1.0).

Scaling of the velocity power spectra in turbulent thermal convection.

We report measurements of the local velocity in a convection cell filled with water. In the buoyancy subrange (the scales between the Bolgiano scale f(B) and the integral scale f(o)), two scaling regions of the velocity frequency power spectra, separated by the peak frequency f(p) of the dissipation spectra, are found. For f(p)<f<f(B), we observe a power law with the Bolgiano-Obukhov scaling exponent -11/5. For f(o)<f<f(p), an unexpected scaling with an exponent -1.35 is observed. We also found that the velocity power spectra are universal functions with respect to the characteristic scales f(p). and f(B).

Scaling properties of the temperature field in convective turbulence.

We report the scaling properties of temperature in turbulent convection in water. In the central region of the convection cell, we find that the peak frequency of the temperature dissipation spectra may be identified as the "Bolgiano frequency," with respect to which the temperature power spectra are universal functions; and that the usual inertial range is taken up entirely by the buoyancy subrange, so that a "high frequency" scaling subrange emerges only through an extended-self-similarity-type analysis. Moreover, the buoyancy subrange assumes the value of 2/5 predicted for the Bolgiano-Obukhov scaling only in the central region of the cell; in the mixing zone the exponent for the high frequency scaling exponent has a value of 2/3.

Mesospheric velocities and buoyancy subrange spectral slopes determined over Svalbard by ESR

While the European Incoherent Scatter (EISCAT) Svalbard Radar (ESR) has been in operation for some years now, it was only during the summer of 1998 that clutter contamination in mesospheric signals was successfully removed. Prior to this, it was found that one could measure velocity as low as 90 km altitude by pointing the antenna at low elevation. Subsequent to the clutter elimination we have obtained velocity information at least as low as 80 km. Using this technique to obtain horizontal velocities, we have performed tentative spectral analyses that suggest similar gravity wave energy dissipation to that reported from similar mid‐latitude observations. Although, for technical reasons, only 9 hours of data were obtained on this occasion, these latest results represent the first of their kind from Svalbard, and the spectra of horizontal mesospheric winds appear to be the first to be determined at such high latitude.

An experimental research on the instability of natural convection boundary layer around a vertical heated flat plate

Experimental results on the instability of the isothermal naturalconvection boundary layer around a vertical heated flat plate are presented. It is demonstrated that the characteristics of the instability wave in the outer layer is consistent with the calculation of Brewster & Gebhart. After an initial growth of its low frequency components at the downstream side of the turning point of the neutral curve (Gr≈120) its comparatively higher frequency components develop and become turbulent subsequently with a buoyancy subrange in its power spectra. Simultaneously, in the measurement at the inner layer near the wall a viscous instability signal the same as the Tollmien-Schlichting waves in ordinary boundary layer and its subharmonics in a much higher frequency domain is discovered and an inertial subrange can be observed in the spectra atGr≈378.6.

A height‐ and time‐dependent model of polar mesosphere summer echoes

The generation of VHF radar echoes in the polar summer mesosphere is studied with a height‐ and time‐dependent model including three mechanisms: electron scavenging by microscopic ice particles created by heterogeneous nucleation on meteoric dust, formation of steep gradients in the ice particle and electron concentrations by the Kelvin effect, and reduction of the electron diffusivity by the presence of negatively charged particles. Then turbulent mixing produces a viscous convective subrange in the variance spectrum of the electron concentration, which in turn, can give rise to strong radar echoes. Based on a gravity‐wave‐perturbed model and many sensitivity tests, several conclusions are reached. Taking into account the high variability of relevant parameters, the model can predict the wide range of reflectivities measured on the northern hemisphere and indicates that the virtual absence of detectable radar echoes on the southern hemisphere is probably due to the annual variation of the meteoric mass influx and relatively high mesopause temperatures. The frequently occurring double‐layer structure of the reflectivity is characteristic of almost unperturbed rnesospheric conditions. In the presence of weak harmonic gravity waves, the inherently strong nonlinearity of the model yields steepened and breaking reflectivity structures. In agreement with observational results, the model further predicts a positive (negative) correlation between the vertical velocity variance and the reflectivity of spectrally broad (narrow) echoes. It is suggested that the frequently measured aspect sensitivity of spectrally narrow echoes results from anisotropic turbulence in the electron gas occurring if the inertial subrange is small or absent and the viscous‐convective subrange virtually adjoins the buoyancy subrange. Even under extremely favorable conditions, the calculated reflectivities at radar frequencies near 1 GHz are much weaker than measured ones, confirming an earlier result that in the UHF range, polar mesosphwre summer echoes originate from modified Thomson scattering.

Kilometer scale kinetic energy perturbations in the mesosphere derived from EISCAT velocity data

Traditionally, radar instruments which obtain coherent echoes from structures delineated by sharp gradients in refractive index have been used as a means of determining parameters describing neutral turbulence in the middle atmosphere. In these cases the very characteristics of the coherent signals are used. An alternative, somewhat akin to using velocity estimations from meteor trails and trails of artificially introduced racers, is to determine the kinetic energy perturbation from the velocity profiles alone, the latter being available from incoherent scatter radar. Here we describe a method which assumes that the velocity fluctuations are caused by perturbations of a 1‐km scale, in the buoyancy subrange, but which still may be indicative of energy flux at the outer scale, illustrated by the remarkable similarity to energy dissipation rates determined by other measurements.

Theoretical Investigation of Energy and Thermal Intensity Spectra in Buoyancy-Driven Turbulent Flows

Buoyancy-driven turbulent flows are analyzed theoretically with the aid of a two-scale direct-interaction approximation. Special attention is paid to buoyancy effects on the spectra of the turbulent energy and thermal intensity in unstable stratified flows. Both the spectra in the buoyancy subrange are shown to be proportional to k -3 , which is in agreement with the experimental results ( k is the wavenumber.).

Stratospheric horizontal wavenumber spectra of winds, potential temperature, and atmospheric tracers observed by high‐altitude aircraft

Horizontal wavenumber power spectra of vertical and horizontal wind velocities, potential temperatures, and ozone and N2O mixing ratios, as measured in the mid‐stratosphere during 73 ER‐2 flights (altitude ≈ 20km) are presented. The velocity and potential temperature spectra in the 100 to 1‐km wavelength range deviate significantly from the uniform −5/3 power law expected for the inverse energy‐cascade regime of two‐dimensional turbulence and also for inertial‐range, three‐dimensional turbulence. Instead, steeper spectra approximately consistent with a −3 power law are observed at horizontal scales smaller than 3 km for all velocity components as well as potential temperature. Shallower spectra are observed at scales longer than 6 km. For horizontal velocity and potential temperature the spectral indices at longer scales are between −1.5 and −2.0. For vertical velocity the spectrum at longer scales becomes flat. It is argued that the observed velocity and potential temperature spectra are consistent with gravity waves. At smaller scales, the shapes are also superficially consistent with a Lumley‐Shur‐Weinstock buoyant subrange of turbulence and/or nonlinear gravity waves. Contemporaneous spectra of ozone and N2O mixing ratio in the 100 to 1‐km wavelength range do conform to an approximately uniform −5/3 power law. It is argued that this may reflect interactions between gravity wave air‐parcel displacements and laminar or filamentary structures in the trace gas mixing ratio field produced by enstrophy‐cascading two‐dimensional turbulence.

Turbulence decay in stratified and homogeneous marine layers

A spectral approach is applied to shear-induced turbulence in stratified layers. A system of spectral equations for stationary balance of turbulent energy and temperature variances was deduced in the vicinity of the local shear scale LU = (ϵ/UZ3)12. At wavenumbers between the inertial-convective (k−53) and wak turbulence (k−3) subranges, additional narrow spectral intervals—‘production’ subranges—may appear (E ∽ k−1, ET ∽ k−2). The upper boundary of these subranges is determined as LU, and the lower boundaries as LR ∽ (ϵ/UZN2)12(χ/TZ2). It is shown that the scale LU is a unique spectral scale that is uniform up to a constant value for every hydrophysical field. It appears that the spectral scale LU is equivalent to the Thorpe scale LTh for the active turbulence model. Therefore, if turbulent patches are generated in a background of permanent mean shear, a linear relation between temperature and mass diffusivities exists. In spectral terms, the fossil turbulence model corresponds to the regime of the Boldgiano-Obukhov buoyancy subrange (E ∽ k−115, ET ∽ k−75). During decay the buoyancy subrange is expanded to lower and higher wavenumbers. At lower wavenumbers the buoyancy subrange is bounded by L∗∗ = 3(χ12/N12TZ), which is equivalent to the Thorpe scale LTh. In such a transition regime only, when the viscous dissipation rate is removed from the set of main turbulence parameters, the Thorpe scale does not correlate with the buoyancy scale LN ∽ ϵ12/N32 and fossil turbulence is realized. Oceanic turbulence measurements in the equatorial Pacific near Baker Island confirm the main ideas of the active and fossil turbulence models.

Turbulent Convection with Overshooting: Reynolds Stress Approach. II.

view Abstract Citations (93) References (64) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Turbulent Convection with Overshooting: Reynolds Stress Approach. II. Canuto, V. M. Abstract We derive a new nonlocal model for turbulent convection which incorporates recent advances from laboratory, planetary, and numerical simulation of turbulence, and we show how previous prototypic models can be recovered. The new model is given by five coupled differential equations, equations (81)-(84) and (100), that yield: convective flux, temperature variance, turbulent kinetic energy in the z-direction, total turbulent kinetic energy, and (rate of) dissipation of kinetic energy. The solution of these five equations yields all the turbulent quantities as a function of the temperature gradient. The latter is then obtained by solving the flux conservation law, equation (96), which we derive anew to account for the kinetic energy flux. The main features of the new model are as follows. 1. Nonlocality. This basic feature is represented by the third-order moments that enter the governing equations (81)-(84) and (100). In all nonlocal models thus far, these moments were treated with the diffusion approximation. Since the latter yields incorrect results in the case of the convective boundary layer, we avoid it. We derive the dynamic equations for all the third-order moments and solve them analytically. 2. Gravity waves, stable stratification. The fundamental feature of the overshooting (OV) region is that the flow is stably stratified, Δ - Δad < 0. Under such circumstances, the Kolmogorov spectrum is no longer valid since eddies, working against gravity, lose a fraction of their kinetic energy which goes to generate "gravity waves." To fully account for the appearance of a "buoyancy subrange" E(k) ∼ k-3 in lieu of the Kolmogorov spectrum ∼ k-5/3, we adopt a recent model for stably stratified turbulence which has been successfully tested against convective boundary layer data. 3. Dissipation ɛ. -- The process of dissipation of turbulent kinetic energy has been neglected for many years, but is now viewed as crucial for a proper quantification of OV. The assumption ɛ = 0 not only violates the energy conservation law, but overestimates the extent of the OV region. When ɛ is included, it is generally computed locally with a mixing length l. If the description of l is difficult in the main convective region, it is all the more so in the OV region where the concept of a mixing length loses its physical content. We avoid the use of a mixing length in both the convective and the OV region by introducing a differential equation for the dissipation ɛ, equation (100), which, being nonlocal, accounts for the fact that turbulent kinetic energy created at one point in the flow may be dissipated somewhere else, in accordance with the nonlocal nature of turbulent convection. 4. Pressure forces, anisotropy. The stably stratified turbulence found in the OV region is experimentally known to be highly anisotropic since negative buoyancy suppresses the eddy vertical motion. Thus, pressure- velocity and pressure-temperature correlations, which help restore isotropy, play a crucial role. 5. The Boussinesq Approximation is avoided. 6. The turbulent kinetic energy flux. -- A new flux conservation law, equation (96), is derived which includes the turbulent kinetic energy flux recently found to be up to 50% of the total flux for Sun-like stars. 7. A new hydrostatic equilibrium equation, equation (103), is derived which, in addition to a turbulent pressure, also includes buoyancy effects. The next step is to couple the new model to a stellar structure code. Publication: The Astrophysical Journal Pub Date: October 1993 DOI: 10.1086/173238 Bibcode: 1993ApJ...416..331C Keywords: CONVECTION; STARS: INTERIORS; TURBULENCE full text sources ADS |