Spectral Budget Research Articles

Wavelet-based wavenumber spectral estimate of eddy kinetic energy: Application to the North Atlantic

An ensemble of eddy-rich North Atlantic simulations is analyzed, providing estimates of eddy kinetic energy (EKE) wavenumber spectra and spectral budgets below the mixed layer where energy input from surface convection and wind stress are negligible. A wavelet transform technique is used to estimate a spatially localized ‘pseudo-Fourier’ spectrum (Uchidaet al., 2023b), permitting comparisons to be made between spectra at different locations in a highly inhomogeneous and anisotropic environment. The EKE spectra tend to be stable in time but the spectral budgets are highly time dependent. We find evidence of a Gulf Stream imprint on the near Gulf Stream eddy field appearing as enhanced levels of EKE in the (nominally) North–South direction relative to the East–West direction. Surprisingly, this signature of anisotropy holds into the quiescent interior with a tendency of the orientation aligned with maximum EKE being associated with shallower spectral slopes and elevated levels of inverse EKE cascade. Conversely, the angle associated with minimum EKE is aligned with a steeper spectral slope and forward cascade of EKE. Our results also indicate that vertical motion non-negligibly affects the direction of EKE cascade. A summary conclusion is that the spectral characteristics of eddies in the wind-driven gyre below the mixed layer where submesoscale dynamics are expected to be weak tend to diverge from expectations built on inertial-range assumptions, which are stationary in time and horizontally isotropic in space.

An Analysis of Various Design Pathways Towards Multi-Terabit Photonic On-Interposer Interconnects

In the wake of dwindling Moore’s Law, to address the rapidly increasing complexity and cost of fabricating large-scale, monolithic systems-on-chip (SoCs), the industry has adopted dis-aggregation as a solution, wherein a large monolithic SoC is partitioned into multiple smaller chiplets that are then assembled into a large system-in-package (SiP) using advanced packaging substrates such as silicon interposer. For such interposer-based SiPs, there is a push to realize on-interposer inter-chiplet communication bandwidth of multi-Tb/s and end-to-end communication latency of no more than 10 ns. This push comes as the natural progression from some recent prior works on SiP design, and is driven by the proliferating bandwidth demand of modern data-intensive workloads. To meet this bandwidth and latency goal, prior works have focused on a potential solution of using the silicon photonic interposer (SiPhI) for integrating and interconnecting a large number of chiplets into an SiP. Despite the early promise, the existing designs of on-SiPhI interconnects still have to evolve by leaps and bounds to meet the goal of multi-Tb/s bandwidth. However, the possible design pathways, upon which such an evolution can be achieved, have not been explored in any prior works yet. In this paper, we have identified several design pathways that can help evolve on-SiPhI interconnects to achieve multi-Tb/s aggregate bandwidth. We perform an extensive link-level and system-level analysis in which we explore these design pathways in isolation and in different combinations of each other. From our link-level analysis, we have observed that the design pathways that simultaneously enhance the spectral range and optical power budget available for wavelength multiplexing can render aggregate bandwidth of up to 4 Tb/s per on-SiPhI link. We also show that such high-bandwidth on-SiPhI links can substantially improve the performance and energy-efficiency of the state-of-the-art CPU and GPU chiplets based SiPs.

Exploring the Differences in Kinetic Energy Spectra between the NCEP FNL and ERA5 Datasets

Abstract Two global atmospheric circulation datasets (ERA5 and NCEP FNL) with horizontal resolutions of 0.25° × 0.25° are investigated in terms of kinetic energy (KE) spectra at 200 hPa (roughly between 11 and 12 km). The horizontal KE (HKE) in NCEP FNL is larger and flatter than that in ERA5 at subsynoptic scales and mesoscales. Restoring the energy of this wavenumber range to the physical space shows that the HKE in NCEP FNL is larger than that in ERA5 over most areas but smaller mainly in the Indo-Pacific warm pool. The spectral budgets show that at these scales, the positive contribution from net vertical flux in ERA5 is stronger than that in NCEP FNL, while the negative contribution from available potential energy (APE) conversion is smaller; assuming that the atmosphere is in a quasi-stationary state, more dissipation is found in ERA5 than in NCEP FNL, which should be responsible for the HKE spectrum in ERA5 to be steeper and weaker than that in NCEP FNL. Our formulation shows that the APE conversion and net vertical flux are related to the pressure vertical velocity (PVV). The APE conversion and net vertical flux differences between the two datasets, like the PVV difference, are mainly from the tropical region. At large scales, the vertical motion in ERA5 is larger than that in NCEP FNL. The amplitude differences of the PVV spectra between two datasets are consistent with those of the large-scale precipitation spectra associated with microphysics parameterizations. These results support that vertical motion is a key dynamical factor explaining energy discrepancies at mesoscales. Significance Statement The atmospheric kinetic energy spectrum reflects energy distribution characteristics in atmospheric motion at different scales. According to the Helmholtz decomposition, the horizontal wind field can be decomposed into two parts: rotational wind field and divergent wind field. We explore the dynamical causes of the atmospheric energy spectra differences among different datasets from the perspective of rotational and divergent components of motion. Our results reveal that the differences in energy spectra and their energy budget at scales below a few hundred kilometers are relatively significant in tropical regions and are closely related to vertical motion. A better understanding of the differences in kinetic energy spectra will contribute to the improvement of atmospheric models.

Kinetic Energy Spectra and Spectral Budget of Radiative–Convective Equilibrium

Abstract The atmospheric kinetic energy spectrum and energy cascade are investigated in idealized simulations of radiative–convective equilibrium (RCE). WRF is employed to perform cloud-resolving simulations of an idealized radiative–convective equilibrium with and without aggregation with Δx = 4 km. The horizontal kinetic energy (HKE) spectrum for the aggregated simulation in the upper troposphere is steeper than the nonaggregated case and closer to −5/3. The HKE spectra for the nonaggregated simulation in the upper troposphere and the lower stratosphere are much shallower than the −5/3 spectrum. In the upper troposphere, the divergent kinetic energy has a similar magnitude to the rotational kinetic energy in both the nonaggregated simulation and aggregated simulation. Energy is mainly gained from the buoyancy flux and mainly lost from the vertical energy flux for scales larger than 20 km. Downscale energy transfer is found in the upper troposphere. Numerical dissipation is the main source of energy loss at small scales. In the lower stratosphere, the divergent kinetic energy dominates the kinetic energy spectrum in both simulations. Energy is mainly gained from the vertical energy flux and is balanced by the loss from the buoyancy flux term, transfer term, and dissipation. An Eliassen–Palm flux analysis suggests that wave–mean-flow interaction may be responsible for the upscale energy transfer found in the lower stratosphere. The magnitudes of our kinetic energy spectra are similar to spectra calculated from aircraft data. Rotation is found to promote aggregation and steepen the energy spectrum.

Mesoscale Spectra of Vertical Vorticity and Horizontal Divergence in an Idealized Baroclinic Wave Simulation

Abstract A new formulation of the spectral budget of vertical vorticity and horizontal divergence suitable for the mesoscale atmosphere on an f plane is derived. Compared to previous formulations in large-scale studies, there are three main improvements: (i) both the squared vorticity (SV; i.e., enstrophy as usual) and squared divergence (SD) spectra are taken into account, (ii) the spectral transfers of SV and SD between scales are exactly constructed under the nonlinear advection of the full horizontal velocity, and (iii) the general relationship between spectral energy and SV/SD transfers is derived. With this new formulation, the atmospheric spectra of divergent and rotational motion components are investigated through numerical simulation of idealized dry baroclinic waves. Spectral budget analysis shows that, in the present dry simulation, the upper troposphere is almost completely dominated by the downscale SV transfer at all scales, while the lower stratosphere is dominated by the downscale SV transfer at synoptic scales and by the downscale SD transfer at mesoscales. The pressure-related term is largely cancelled out by the conversion term between SV and SD at both levels, but at the small-scale end of lower-stratospheric mesoscales there exists a significant net positive forcing, accounting for the distinct spectral transition of the total spectrum there. An explicit association between spectral energy and SV/SD transfers is further made. In the upper troposphere, the downscale energy cascade is mainly governed by the downscale SV transfer, while in the lower stratosphere, it is mainly governed by the residual term related to nonuniformly distributed vertical velocity. Significance Statement The purpose of this study is to explore the dynamics underlying the atmospheric spectra of divergent and rotational motion components. The traditional analysis of enstrophy is first extended to include both squared vertical vorticity (SV) as usual and squared horizontal divergence (SD), and then a new formulation of the spectral SV and SD budget suitable for the mesoscale atmosphere is derived, with application to the dry baroclinic waves simulation. Our results clearly reveal the different physical processes governing the vorticity and divergence spectra at different heights. We also derive the general relationship between spectral energy and SV/SD transfers, which allows explicitly associating spectral energy and SV/SD fluxes and thus provides additional physical views on the mesoscale energy cascade. Further work should consider the effects of other physical processes neglected here.

Spectral Budget of Rotational and Divergent Kinetic Energy in Global Analyses

Abstract To study the multiscale interactions between rotational and divergent components of atmospheric motion, a new formulation of spectral budget of rotational kinetic energy (RKE) and divergent kinetic energy (DKE) based on the primitive equations in the pressure coordinate is derived, with four main characteristics: 1) horizontal kinetic energy (HKE) spectral transfer is exactly divided into spectral transfer of RKE and DKE, 2) the exact spectral conversion term between DKE and RKE is constructed, 3) the Coriolis term is considered, and 4) both the baroclinic conversion from available potential energy (APE) and the vertical flux of HKE act only on DKE. With this new formulation, outputs from ERA5 global reanalysis are investigated. At planetary scales, HKE spectral transfer, mainly attributed to β effect, is dominated by downscale DKE transfer. At synoptic scales, it is dominated by an upscale transfer of RKE energized by conversion of DKE mainly due to the Coriolis effect. The ultimate source of DKE in the upper troposphere is conversion of APE, while in the stratosphere it is the vertical flux. At mesoscales, the spectral transfers of RKE and DKE are both downscale, and conversion from RKE to DKE exists at sub-800-km scales in the upper troposphere, which is mainly attributed to the contribution from relative vorticity. At different heights, the intersection scales of RKE and DKE spectra are affected by the scales of positive peaks of the local spectral conversion from DKE to RKE around total wavenumber 10. Significance Statement The purpose of this study is to explore more physical insights on the dynamics underlying the atmospheric energy spectra from the perspective of rotational and divergent components of motion. We derive a new formulation of the spectral rotational and divergent kinetic energy budget in the pressure coordinate for the global atmosphere, with application to ERA5 global reanalysis. Our results reveal the differences of spectral energy budget between rotational and divergent motions at different heights and scales. This new formulation provides a good tool for revealing the multiscale cascade and interaction between atmospheric rotational and divergent motions. Future work should investigate these dynamical processes with higher-resolution simulations and datasets.

Simulation-based study of turbulent aquatic canopy flows with flexible stems

Large-eddy simulation (LES) is performed to investigate the dynamics of flow and canopy motions and the energy transfer in turbulent canopy flows. Different from the traditional approach that models the canopy as a continuous medium with a drag coefficient prescribed a priori, an immersed boundary method together with a beam model is employed to explicitly capture the dynamics of individual stems and resolve monami. The simulation cases cover a broad range of stem flexibilities from rigid stems to oscillatory stems to stems yielding to the flow. For highly flexible canopies, the stem fluctuation is small such that the canopy behaves like a rigid canopy, which is used to explain the similarities of the flow features between rigid and highly flexible canopies. Analyses of the turbulent kinetic energy (TKE) budget show that, in the flexible canopy cases, the waving term associated with the canopy drag–flow velocity correlation can be as large as one-half of the shear production term near the canopy top. Spectral TKE budget analyses further reveal dominant effects at two characteristic scales: the monami scale associated with the coherent structures in the mixing layer and the wake scale associated with the interval between adjacent stems. For the TKE in flexible canopies, the waving term is found to play an important role in the interscale and wall-normal transport terms. Our LES data show that the spectral shortcut mechanism proposed by previous studies is caused by the waving term.

Spectral Analysis on Transport Budgets of Turbulent Heat Fluxes in Plane Couette Turbulence

In recent years, scale-by-scale energy transport in wall turbulence has been intensively studied, and the complex spatial and interscale transfer of turbulent energy has been investigated. As the enhancement of heat transfer is one of the most important aspects of turbulence from an engineering perspective, it is also important to study how turbulent heat fluxes are transported in space and in scale by nonlinear multi-scale interactions in wall turbulence as well as turbulent energy. In the present study, the spectral transport budgets of turbulent heat fluxes are investigated based on direct numerical simulation data of a turbulent plane Couette flow with a passive scalar heat transfer. The transport budgets of spanwise spectra of temperature fluctuation and velocity-temperature correlations are investigated in detail in comparison to those of the corresponding Reynolds stress spectra. The similarity and difference between those scale-by-scale transports are discussed, with a particular focus on the roles of interscale transport and spatial turbulent diffusion. As a result, it is found that the spectral transport of the temperature-related statistics is quite similar to those of the Reynolds stresses, and in particular, the inverse interscale transfer is commonly observed throughout the channel in both transport of the Reynolds shear stress and wall-normal turbulent heat flux.

Spectral analysis on dissimilarity between turbulent momentum and heat transfers in plane Couette turbulence

Nonlinear interactions between different scales in turbulence result in both interscale and spatial transport of turbulent energy, and their role in the turbulent heat transfer mechanism is also of practical importance from an engineering viewpoint. In this study, we investigate a turbulent plane Couette flow with passive-scalar heat transfer at the Prandtl number of 0.71 to discuss the similarity/difference between scale interactions in velocity and temperature fields. The constant-temperature-difference boundary condition is used so that the mean velocity and temperature profiles are similar, and then, the roles of interscale and spatial transports are compared for the spectral transport budgets of turbulent energies and temperature-related statistics. We show that turbulent heat transfer occurs at relatively small streamwise length scales compared to momentum transfer, although molecular diffusion is more significant in the temperature field as the Prandtl number is less than 1. Detailed analysis on the transport budgets of temperature-related spectra shows that scale interactions in the temperature field supply more energy to small scales than those in the velocity field. This significant temperature cascade causes more energetic temperature fluctuation at small scales, resulting in the spectral dissimilarity between turbulent heat and momentum transfers.

Transport of Turbulence Across Permeable Interface in a Turbulent Channel Flow: Interface-Resolved Direct Numerical Simulation

Turbulence transportation across permeable interfaces is investigated using direct numerical simulation, and the connection between the turbulent surface flow and the pore flow is explored. The porous media domain is constructed with an in-line arranged circular cylinder array. The effects of Reynolds number and porosity are also investigated by comparing cases with two Reynolds numbers (Reapprox 3000,6000) and two porosities (varphi =0.5,0.8). It was found that the change of porosity leads to the variation of flow motions near the interface region, which further affect turbulence transportation below the interface. The turbulent kinetic energy (TKE) budget shows that turbulent diffusion and pressure transportation work as energy sink and source alternatively, which suggests a possible route for turbulence transferring into porous region. Further analysis on the spectral TKE budget reveals the role of modes of different wavelengths. A major finding is that mean convection not only affects the distribution of TKE in spatial space, but also in scale space. The permeability of the wall also have an major impact on the occurrence ratio between blow and suction events as well as their corresponding flow structures, which can be related to the change of the Kármán constant of the mean velocity profile.

Characteristics of Atmospheric Kinetic Energy Spectra during the Intensification of Typhoon Lekima (2019)

The intensification of Typhoon Lekima (2019) is simulated with the Weather Research and Forecasting model to study the atmospheric horizontal kinetic energy (HKE) spectra and corresponding spectral HKE budgets under the control of real tropical cyclone (TC). The results show that the TC has the ability to modify the canonical atmospheric energy spectrum during its evolution, which is dominated by its rotational mode. With the intensification of Lekima, the HKE spectrum in the troposphere swells over the central mesoscale and develops an arc-like shape. The stronger the TC, the more pronounced the arc-like shape is and the smaller scale it extends to. The roles various physical processes play at different heights and horizontal scales during the intensification of Lekima are investigated and the dependence of the effect of physical processes on scale and height is revealed. Meanwhile, the potential relationship between the intensification of TC, the activation of energy activity at smaller scales, and the downscale extension of the arc-like spectral shape is found.

Sensor placement and resource allocation for energy harvesting IoT networks

Optimal sensor selection for source parameter estimation in energy harvesting Internet of Things (IoT) networks is studied in this paper. Specifically, the focus is on the selection of the sensor locations which minimizes the estimation error at a fusion center, and to optimally allocate power and bandwidth for each selected sensor subject to a prescribed spectral and energy budget. To do so, measurement accuracy, communication link quality, and the amount of energy harvested are all taken into account. The sensor selection is studied under both analog and digital transmission schemes from the selected sensors to the fusion center. In the digital transmission case, an information theoretic approach is used to model the transmission rate, observation quantization, and encoding. We numerically prove that with a sufficient system bandwidth, the digital system outperforms the analog system with a possibly different sensor selection. The design problem of interest is a Boolean non convex optimization problem, which is solved by relaxing the Boolean constraints. To efficiently round the obtained relaxed solution, we propose a randomized rounding algorithm which generalizes the existing algorithm.

Enhancement of Spectral Efficiency and Power Budget in WDN-PON Employing LDPC-Coded Probabilistic Shaping PAM8

A $5\times60$ Gb/s low-density parity-check (LDPC) coded WDM-PON using 8-level pulse amplitude modulation (PAM8) signals with probabilistic shaping (PS) over 20-km standard single-mode fiber (SSMF) with direct detection is proposed and experimentally demonstrated. Each optical carrier at the optical line terminal (OLT) carries a 20-Gbaud probabilistically-shaped LDPC-coded PS-PAM8 signal from a conventional uniform PAM16 signal following a designed approximate Gaussian distribution (AGD). A LDPC-based bit-interleaved coded modulation scheme with iterative decoding (BICM-ID) is utilized to recover the inherently overlapped symbols due to the proposed PS mapping. Combining decision-directed least-mean-squares (DD-LMS) and constant modulus algorithm (CMA), a blind feedback pre-equalizer is adopted to reduce the frequency loss of the signal owing to imperfect electro-optical components in experiment. As for experimental verification and application, 1.48-dB superior receiver power sensitivity and 1.7-dB launch fiber power optimization are gained respectively by using LDPC-coded PS-PAM8 signals in WDM-PON, which can bring higher spectral efficiency and power loss budget for the optical distribution networks.

Investigation of Mesoscale Available Potential Energy Spectra in a Simulated Tropical Cyclone

We investigated the moist mesoscale available potential energy (APE) spectra and corresponding spectral budgets of an idealized tropical cyclone (TC). The APE is defined with respect to a dry air mass using a modified potential temperature. For wavelengths below 500 km, the mesoscale APE spectra show a consistent quasi-linear shape and a -5/3 spectral slope in the troposphere and lower stratosphere during the mature period of the TC. The spectral APE budget in the troposphere is dominated by diabatic and energy conversion processes. The mesoscale APE is forcefully injected by the diabatic effect and immediately partially converted to other forms of energy by the buoyancy effect. The diabatic effect contains a positive contribution from the heating effect and a negative contribution from the dehumidifying effect, which weakens the heating effect by about 16%. The energy conversion tends toward the horizontal kinetic energy at larger scales and toward the gravitational potential energy of the total moist species at smaller scales. In the lower stratosphere, the mesoscale APE is primarily deposited by the three-dimensional divergent effect and removed by nonlinear interactions; however, the effect of the energy conversion is noisy. The lower troposphere and lower stratosphere are governed by clear downscale and upscale APE cascades, respectively, whereas the mid- and upper tropospheric mesoscale APE spectra undergo more complex cascade processes.

The Influence of Gravity Waves on the Slope of the Kinetic Energy Spectrum in Simulations of Idealized Midlatitude Cyclones

Abstract The influence of gravity waves generated by surface stress and by topography on the atmospheric kinetic energy (KE) spectrum is examined using idealized simulations of a cyclone growing in baroclinically unstable shear flow. Even in the absence of topography, surface stress greatly enhances the generation of gravity waves in the vicinity of the cold front, and vertical energy fluxes associated with these waves produce a pronounced shallowing of the KE spectrum at mesoscale wavelengths relative to the corresponding free-slip case. The impact of a single isolated ridge is, however, much more pronounced than that of surface stress. When the mountain waves are well developed, they produce a wavenumber to the −5/3 spectrum in the lower stratosphere over a broad range of mesoscale wavelengths. In the midtroposphere, a smaller range of wavelengths also exhibits a −5/3 spectrum. When the mountain is 500 m high, the waves do not break, and their KE is entirely associated with the divergent component of the velocity field, which is almost constant with height. When the mountain is 2 km high, wave breaking creates potential vorticity, and the rotational component of the KE spectrum is also strongly energized by the waves. Analysis of the spectral KE budgets shows that the actual spectrum is the result of continually shifting balances of direct forcing from vertical energy flux divergence, conservative advective transport, and buoyancy flux. Nevertheless, there is one interesting example where the −5/3-sloped lower-stratospheric energy spectrum appears to be associated with a gravity-wave-induced upscale inertial cascade.

Mesoscale Horizontal Kinetic Energy Spectra of a Tropical Cyclone

A high-resolution cloud-permitting simulation with the Weather Research and Forecasting (WRF) Model is performed to investigate the mesoscale horizontal kinetic energy (HKE) spectra of a tropical cyclone (TC). The spectrum displays an arc-like shape in the troposphere and a quasi-linear shape in the lower stratosphere for wavelengths below 500 km during the mature period of the TC, while they both develop a quasi −5/3 slope. The total HKE spectrum is dominated by its rotational component in the troposphere but by its divergent component in the lower stratosphere. Further spectral HKE budget diagnosis reveals a generally downscale cascade of HKE, although a local upscale cascade gradually forms in the lower stratosphere. However, the mesoscale energy spectrum is not only governed by the energy cascade, but is evidently influenced also by other physical processes, among which the buoyancy effect converts available potential energy (APE) to HKE in the mid- and upper troposphere and converts HKE to APE in the lower stratosphere, the vertically propagating inertia–gravity waves transport the HKE from the upper troposphere to lower and higher layers, and the vertical transportation of convection always transports HKE upward.

A model-based approach to the spatial and spectral calibration of NIRSpec onboard JWST

Context: The NIRSpec instrument for the James Webb Space Telescope (JWST) can be operated in multiobject (MOS), long-slit, and integral field (IFU) mode with spectral resolutions from 100 to 2700. Its MOS mode uses about a quarter of a million individually addressable minislits for object selection, covering a field of view of $\sim$9 $\mathrm{arcmin}^2$. Aims: The pipeline used to extract wavelength-calibrated spectra from NIRSpec detector images relies heavily on a model of NIRSpec optical geometry. We demonstrate how dedicated calibration data from a small subset of NIRSpec modes and apertures can be used to optimize this parametric model to the necessary levels of fidelity. Methods: Following an iterative procedure, the initial fiducial values of the model parameters are manually adjusted and then automatically optimized, so that the model predicted location of the images and spectral lines from the fixed slits, the IFU, and a small subset of the MOS apertures matches their measured location in the main optical planes of the instrument. Results: The NIRSpec parametric model is able to reproduce the spatial and spectral position of the input spectra with high fidelity. The intrinsic accuracy (1-sigma, RMS) of the model, as measured from the extracted calibration spectra, is better than 1/10 of a pixel along the spatial direction and better than 1/20 of a resolution element in the spectral direction for all of the grating-based spectral modes. This is fully consistent with the corresponding allocation in the spatial and spectral calibration budgets of NIRSpec.

A Spectral Budget Model for the Longitudinal Turbulent Velocity in the Stable Atmospheric Surface Layer

Abstract A spectral budget model is developed to describe the scaling behavior of the longitudinal turbulent velocity variance with the stability parameter and the normalized height in an idealized stably stratified atmospheric surface layer (ASL), where z is the height from the surface, L is the Obukhov length, and δ is the boundary layer height. The proposed framework employs Kolmogorov’s hypothesis for describing the shape of the longitudinal velocity spectra in the inertial subrange, Heisenberg’s eddy viscosity as a closure for the pressure redistribution and turbulent transfer terms, and the Monin–Obukhov similarity theory (MOST) scaling for linking the mean longitudinal velocity and temperature profiles to ζ. At a given friction velocity , reduces with increasing ζ as expected. The model is consistent with the disputed z-less stratification when the stability correction function for momentum increases with increasing ζ linearly or as a power law with the exponent exceeding unity. For the Businger–Dyer stability correction function for momentum, which varies linearly with ζ, the limit of the z-less onset is . The proposed framework explains why does not follow MOST scaling even when the mean velocity and temperature profiles may follow MOST in the ASL. It also explains how δ ceases to be a scaling variable in more strongly stable (although well-developed turbulent) ranges.

Spectral enstrophy budget in a shear-less flow with turbulent/non-turbulent interface

A numerical analysis of the interaction between decaying shear free turbulence and quiescent fluid is performed by means of global statistical budgets of enstrophy, both, at the single-point and two point levels. The single-point enstrophy budget allows us to recognize three physically relevant layers: a bulk turbulent region, an inhomogeneous turbulent layer, and an interfacial layer. Within these layers, enstrophy is produced, transferred, and finally destroyed while leading to a propagation of the turbulent front. These processes do not only depend on the position in the flow field but are also strongly scale dependent. In order to tackle this multi-dimensional behaviour of enstrophy in the space of scales and in physical space, we analyse the spectral enstrophy budget equation. The picture consists of an inviscid spatial cascade of enstrophy from large to small scales parallel to the interface moving towards the interface. At the interface, this phenomenon breaks, leaving place to an anisotropic cascade where large scale structures exhibit only a cascade process normal to the interface thus reducing their thickness while retaining their lengths parallel to the interface. The observed behaviour could be relevant for both the theoretical and the modelling approaches to flow with interacting turbulent/nonturbulent regions. The scale properties of the turbulent propagation mechanisms highlight that the inviscid turbulent transport is a large-scale phenomenon. On the contrary, the viscous diffusion, commonly associated with small scale mechanisms, highlights a much richer physics involving small lengths, normal to the interface, but at the same time large scales, parallel to the interface.

Spectral energy balance in dry convective boundary layers

Three-dimensional large-eddy simulations (LES) of the convective boundary layer over a domain of approximately 6 km are performed with the UCLA LES model. Simulations are forced with a constant surface heat flux and prescribed subsidence, and are run to equilibrium. Sub-grid scale fluxes are parameterised with the Smagorinsky–Lilly scheme. A range of grid spacings from 40 down to 5 m are employed. Kinetic energy spectra and the various terms in the kinetic energy spectral budget – heat flux, nonlinear transfer, pressure, and dissipation – are computed using two-dimensional discrete Fourier transforms at every vertical level. Despite the fact that isotropic grid spacings of down to 5 m (grid sizes of 11522×400) were used, an inertial range with a −5/3 spectrum is not obtained. Rather, shallower energy spectral slopes that are closer to −4/3 are found. The shallower spectra are shown to possibly result from the injection of kinetic energy over a wide range of scales via a very broad heat flux spectrum. Only with the highest resolution (Δx = 5 m) does the total heat flux begin to converge and the possibility of local isotropy emerge at small scales. Dependence on surface heat flux and domain size is considered. Preliminary sub-grid scale sensitivity results are obtained through comparison with the turbulent kinetic energy sub-grid scale model.