On the initiation of surface waves by turbulent shear flow

An analytical model is developed for the initial stage of surface wave generation at an air-water interface by a turbulent shear flow in either the air or in the water. The model treats the problem of wave growth departing from a flat interface and is relevant for small waves whose forcing is dominated by turbulent pressure fluctuations. The wave growth is predicted using the linearised and inviscid equations of motion, essentially following Phillips [Phillips, O.M., 1957. On the generation of waves by turbulent wind. J. Fluid Mech. 2, 417-445], but the pressure fluctuations that generate the waves are treated as unsteady and related to the turbulent velocity field using the rapid-distortion treatment of Durbin [Durbin, P.A., 1978. Rapid distortion theory of turbulent flows. PhD thesis, University of Cambridge]. This model, which assumes a constant mean shear rate F, can be viewed as the simplest representation of an oceanic or atmospheric boundary layer. For turbulent flows in the air and in the water producing pressure fluctuations of similar magnitude, the waves generated by turbulence in the water are found to be considerably steeper than those generated by turbulence in the air. For resonant waves, this is shown to be due to the shorter decorrelation time of turbulent pressure in the air (estimated as proportional to 1/Gamma), because of the higher shear rate existing in the air flow, and due to the smaller length scale of the turbulence in the water. Non-resonant waves generated by turbulence in the water, although being somewhat gentler, are still steeper than resonant waves generated by turbulence in the air. Hence, it is suggested that turbulence in the water may have a more important role than previously thought in the initiation of the surface waves that are subsequently amplified by feedback instability mechanisms.

Turbulent flow at 190 m height above London during 2006-2008: A climatology and the applicability of similarity theory

Flow and turbulence above urban terrain is more complex than above rural terrain, due to the different momentum and heat transfer characteristics that are affected by the presence of buildings (e.g. pressure variations around buildings). The applicability of similarity theory (as developed over rural terrain) is tested using observations of flow from a sonic anemometer located at 190.3 m height in London, U.K. using about 6500 h of data. Turbulence statistics—dimensionless wind speed and temperature, standard deviations and correlation coefficients for momentum and heat transfer—were analysed in three ways. First, turbulence statistics were plotted as a function only of a local stability parameter z/Λ (where Λ is the local Obukhov length and z is the height above ground); the σ_i/u_* values (i = u, v, w) for neutral conditions are 2.3, 1.85 and 1.35 respectively, similar to canonical values. Second, analysis of urban mixed-layer formulations during daytime convective conditions over London was undertaken, showing that atmospheric turbulence at high altitude over large cities might not behave dissimilarly from that over rural terrain. Third, correlation coefficients for heat and momentum were analyzed with respect to local stability. The results give confidence in using the framework of local similarity for turbulence measured over London, and perhaps other cities. However, the following caveats for our data are worth noting: (i) the terrain is reasonably flat, (ii) building heights vary little over a large area, and (iii) the sensor height is above the mean roughness sublayer depth.

A method for estimating the turbulent kinetic energy dissipation rate from a vertically pointing Doppler lidar, and independent evaluation from balloon-borne in situ measurements

A method of estimating dissipation rates from a vertically pointing Doppler lidar with high temporal and spatial resolution has been evaluated by comparison with independent measurements derived from a balloon-borne sonic anemometer. This method utilizes the variance of the mean Doppler velocity from a number of sequential samples and requires an estimate of the horizontal wind speed. The noise contribution to the variance can be estimated from the observed signal-to-noise ratio and removed where appropriate. The relative size of the noise variance to the observed variance provides a measure of the confidence in the retrieval. Comparison with in situ dissipation rates derived from the balloon-borne sonic anemometer reveal that this particular Doppler lidar is capable of retrieving dissipation rates over a range of at least three orders of magnitude. This method is most suitable for retrieval of dissipation rates within the convective well-mixed boundary layer where the scales of motion that the Doppler lidar probes remain well within the inertial subrange. Caution must be applied when estimating dissipation rates in more quiescent conditions. For the particular Doppler lidar described here, the selection of suitably short integration times will permit this method to be applicable in such situations but at the expense of accuracy in the Doppler velocity estimates. The two case studies presented here suggest that, with profiles every 4 s, reliable estimates of ϵ can be derived to within at least an order of magnitude throughout almost all of the lowest 2 km and, in the convective boundary layer, to within 50%. Increasing the integration time for individual profiles to 30 s can improve the accuracy substantially but potentially confines retrievals to within the convective boundary layer. Therefore, optimization of certain instrument parameters may be required for specific implementations.

Particle image velocimetry measurements of turbulent flow within outdoor and indoor urban scale models and flushing motions in urban canopy layers

We investigate the spatial characteristics of urban-like canopy flow by applying particle image velocimetry (PIV) to atmospheric turbulence. The study site was a Comprehensive Outdoor Scale MOdel (COSMO) experiment for urban climate in Japan. The PIV system captured the two-dimensional flow field within the canopy layer continuously for an hour with a sampling frequency of 30 Hz, thereby providing reliable outdoor turbulence statistics. PIV measurements in a wind-tunnel facility using similar roughness geometry, but with a lower sampling frequency of 4 Hz, were also done for comparison. The turbulent momentum flux from COSMO, and the wind tunnel showed similar values and distributions when scaled using friction velocity. Some different characteristics between outdoor and indoor flow fields were mainly caused by the larger fluctuations in wind direction for the atmospheric turbulence. The focus of the analysis is on a variety of instantaneous turbulent flow structures. One remarkable flow structure is termed 'flushing', that is, a large-scale upward motion prevailing across the whole vertical cross-section of a building gap. This is observed intermittently, whereby tracer particles are flushed vertically out from the canopy layer. Flushing phenomena are also observed in the wind tunnel where there is neither thermal stratification nor outer-layer turbulence. It is suggested that flushing phenomena are correlated with the passing of large-scale low-momentum regions above the canopy.

Determination of turbulent heat fluxes using a large aperture scintillometer over undulating mixed agricultural terrain

Scintillometry is an established technique for determining large areal average sensible heat fluxes. The scintillometer measurement is related to sensible heat flux via Monin–Obukhov similarity theory, which was developed for ideal homogeneous land surfaces. In this study it is shown that judicious application of scintillometry over heterogeneous mixed agriculture on undulating topography yields valid results when compared to eddy covariance (EC). A large aperture scintillometer (LAS) over a 2.4 km path was compared with four EC stations measuring sensible (H) and latent (LvE) heat fluxes over different vegetation (cereals and grass) which when aggregated were representative of the LAS source area. The partitioning of available energy into H and LvE varied strongly for different vegetation types, with H varying by a factor of three between senesced winter wheat and grass pasture. The LAS derived H agrees (one-to-one within the experimental uncertainty) with H aggregated from EC with a high coefficient of determination of 0.94. Chronological analysis shows individual fields may have a varying contribution to the areal average sensible heat flux on short (weekly) time scales due to phenological development and changing soil moisture conditions. Using spatially aggregated measurements of net radiation and soil heat flux with H from the LAS, the areal averaged latent heat flux (LvELAS) was calculated as the residual of the surface energy balance. The regression of LvELAS against aggregated LvE from the EC stations has a slope of 0.94, close to ideal, and demonstrates that this is an accurate method for the landscape-scale estimation of evaporation over heterogeneous complex topography.

Turbulence dynamics near a turbulent/non-turbulent interface

The characteristics of the boundary layer separating a turbulence region from an irrotational (or non-turbulent) flow region are investigated using rapid distortion theory (RDT). The turbulence region is approximated as homogeneous and isotropic far away from the bounding turbulent/non-turbulent (T/NT) interface, which is assumed to remain approximately flat. Inviscid effects resulting from the continuity of the normal velocity and pressure at the interface, in addition to viscous effects resulting from the continuity of the tangential velocity and shear stress, are taken into account by considering a sudden insertion of the T/NT interface, in the absence of mean shear. Profiles of the velocity variances, turbulent kinetic energy (TKE), viscous dissipation rate (epsilon), turbulence length scales, and pressure statistics are derived, showing an excellent agreement with results from direct numerical simulations (DNS). Interestingly, the normalized inviscid flow statistics at the T/NT interface do not depend on the form of the assumed TKE spectrum. Outside the turbulent region, where the flow is irrotational (except inside a thin viscous boundary layer), epsilon decays as z^{-6}, where z is the distance from the T/NT interface. The mean pressure distribution is calculated using RDT, and exhibits a decrease towards the turbulence region due to the associated velocity fluctuations, consistent with the generation of a mean entrainment velocity. The vorticity variance and epsilon display large maxima at the T/NT interface due to the inviscid discontinuities of the tangential velocity variances existing there, and these maxima are quantitatively related to the thickness delta of the viscous boundary layer (VBL). For an equilibrium VBL, the RDT analysis suggests that delta ~ eta (where eta is the Kolmogorov microscale), which is consistent with the scaling law identified in a very recent DNS study for shear-free T/NT interfaces.

Case study modeling of turbulent and mesoscale fluxes over the BOREAS region

Results from aircraft and surface observations provided evidence for the existence of mesoscale circulations over the Boreal Ecosystem-Atmosphere Study (BOREAS) domain. Using an integrated approach that included the use of analytical modeling, numerical modeling, and data analysis, we have found that there are substantial contributions to the total budgets of heat over the BOREAS domain generated by mesoscale circulations. This effect is largest when the synoptic flow is relatively weak, yet it is present under less favorable conditions, as shown by the case study presented here. While further analysis is warranted to document this effect, the existence of mesoscale flow is not surprising, since it is related to the presence of landscape patches, including lakes, which are of a size on the order of the local Rossby radius and which have spatial differences in maximum sensible heat flux of about 300 W m−2. We have also analyzed the vertical temperature profile simulated in our case study as well as high-resolution soundings and we have found vertical profiles of temperature change above the boundary layer height, which we attribute in part to mesoscale contributions. Our conclusion is that in regions with organized landscapes, such as BOREAS, even with relatively strong synoptic winds, dynamical scaling criteria should be used to assess whether mesoscale effects should be parameterized or explicitly resolved in numerical models of the atmosphere.

Spectral nonlocality, absolute equilibria and Kraichnan-Leith-Batchelor phenomenology in two-dimensional turbulent energy cascades

We study the degree to which Kraichnan–Leith–Batchelor (KLB) phenomenology describes two-dimensional energy cascades in α turbulence, governed by ∂θ/∂t+J(ψ,θ)=ν∇2θ+f, where θ=(−Δ)α/2ψ is generalized vorticity, and ψ^(k)=k−αθ^(k) in Fourier space. These models differ in spectral non-locality, and include surface quasigeostrophic flow (α=1), regular two-dimensional flow (α=2) and rotating shallow flow (α=3), which is the isotropic limit of a mantle convection model. We re-examine arguments for dual inverse energy and direct enstrophy cascades, including Fjørtoft analysis, which we extend to general α, and point out their limitations. Using an α-dependent eddy-damped quasinormal Markovian (EDQNM) closure, we seek self-similar inertial range solutions and study their characteristics. Our present focus is not on coherent structures, which the EDQNM filters out, but on any self-similar and approximately Gaussian turbulent component that may exist in the flow and be described by KLB phenomenology. For this, the EDQNM is an appropriate tool. Non-local triads contribute increasingly to the energy flux as α increases. More importantly, the energy cascade is downscale in the self-similar inertial range for 2.5<α<10. At α=2.5 and α=10, the KLB spectra correspond, respectively, to enstrophy and energy equipartition, and the triad energy transfers and flux vanish identically. Eddy turnover time and strain rate arguments suggest the inverse energy cascade should obey KLB phenomenology and be self-similar for α<4. However, downscale energy flux in the EDQNM self-similar inertial range for α>2.5 leads us to predict that any inverse cascade for α≥2.5 will not exhibit KLB phenomenology, and specifically the KLB energy spectrum. Numerical simulations confirm this: the inverse cascade energy spectrum for α≥2.5 is significantly steeper than the KLB prediction, while for α<2.5 we obtain the KLB spectrum.

Irreversible compressible work and APE dissipation in turbulent stratified fluid

Although it plays a key role in the theory of stratified turbulence, the concept of available potential energy (APE) dissipation has remained until now a rather mysterious quantity, owing to the lack of rigorous result about its irreversible character or energy conversion type. Here, we show by using rigorous energetics considerations rooted in the analysis of the Navier-Stokes for a fully compressible fluid with a nonlinear equation of state that the APE dissipation is an irreversible energy conversion that dissipates kinetic energy into internal energy, exactly as viscous dissipation. These results are established by showing that APE dissipation contributes to the irreversible production of entropy, and by showing that it is a part of the work of expansion/contraction. Our results provide a new interpretation of the entropy budget, that leads to a new exact definition of turbulent effective diffusivity, which generalizes the Osborn-Cox model, as well as a rigorous decomposition of the work of expansion/contraction into reversible and irreversible components. In the context of turbulent mixing associated with parallel shear flow instability, our results suggests that there is no irreversible transfer of horizontal momentum into vertical momentum, as seems to be required when compressible effects are neglected, with potential consequences for the parameterisations of momentum dissipation in the coarse-grained Navier-Stokes equations.

Thermodynamics/dynamics coupling in weakly compressible turbulent stratified fluids

In traditional and geophysical fluid dynamics, it is common to describe stratified turbulent fluid flows with low Mach number and small relative density variations by means of the incompressible Boussinesq approximation. Although such an approximation is often interpreted as decoupling the thermodynamics from the dynamics, this paper reviews recent results and derive new ones that show that the reality is actually more subtle and complex when diabatic effects and a nonlinear equation of state are retained. Such an analysis reveals indeed: (1) that the compressible work of expansion/contraction remains of comparable importance as the mechanical energy conversions in contrast to what is usually assumed; (2) in a Boussinesq fluid, compressible effects occur in the guise of changes in gravitational potential energy due to density changes. This makes it possible to construct a fully consistent description of the thermodynamics of incompressible fluids for an arbitrary nonlinear equation of state; (3) rigorous methods based on using the available potential energy and potential enthalpy budgets can be used to quantify the work of expansion/contraction B in steady and transient flows, which reveals that B is predominantly controlled by molecular diffusive effects, and act as a significant sink of kinetic energy.

Aircraft-based observations of air–sea turbulent fluxes around the British Isles

Observations of turbulent fluxes of momentum, heat and moisture from low-level aircraft data are presented. Fluxes are calculated using the eddy covariance technique from flight legs typically ∼40 m above the sea surface. Over 400 runs of 2 min (∼12 km) from 26 flights are evaluated. Flight legs are mainly from around the British Isles although a small number are from around Iceland and Norway. Sea-surface temperature (SST) observations from two on-board sensors (the ARIES interferometer and a Heimann radiometer) and a satellite-based analysis (OSTIA) are used to determine an improved SST estimate. Most of the observations are from moderate to strong wind speed conditions, the latter being a regime short of validation data for the bulk flux algorithms that are necessary for numerical weather prediction and climate models. Observations from both statically stable and unstable atmospheric boundary-layer conditions are presented. There is a particular focus on several flights made as part of the DIAMET (Diabatic influence on mesoscale structures in extratropical storms) project. Observed neutral exchange coefficients are in the same range as previous studies, although higher for the momentum coefficient, and are broadly consistent with the COARE 3.0 bulk flux algorithm, as well as the surface exchange schemes used in the ECMWF and Met Office models. Examining the results as a function of aircraft heading shows higher fluxes and exchange coefficients in the across-wind direction, compared to along-wind (although this comparison is limited by the relatively small number of along-wind legs). A multi-resolution spectral decomposition technique demonstrates a lengthening of spatial scales in along-wind variances in along-wind legs, implying the boundary-layer eddies are elongated in the along-wind direction. The along-wind runs may not be able to adequately capture the full range of turbulent exchange that is occurring because elongation places the largest eddies outside of the run length.