Dominant Length Scale Research Articles

The Unique Behavior of Vertical Velocity in Developing Deep Convection

AbstractWhen daytime tropical convection develops away from mesoscale disturbances, it typically transitions gradually from dry to shallow to deep convection on hourly timescales. The transition is commonly associated with the formation of larger horizontal boundary‐layer structures and an increasing level of cloud organization aloft. This study demonstrates that a spectral analysis of the resolved high‐resolution sub‐cloud flow features allows for a robust identification of dominant length scales and the quantification of their growth rates during the transition. Furthermore, it is shown that temperature, moisture, and horizontal winds develop multiple length scales with the largest ones growing up to several kilometers in magnitude. However, the vertical velocity behaves in a distinct manner developing significantly smaller values, comparable over land and ocean. This indicates stronger inherent limits of vertical velocity to self‐organize by size.

Quantification and assessment of the atmospheric boundary layer height measured during the AWAKEN experiment by a scanning LiDAR

The atmospheric boundary layer (ABL) height plays a key role in many atmospheric processes as one of the dominant flow length scales. However, a systematic quantification of the ABL height over the entire range of scales (i.e., with periods ranging from one minute to one year) is still lacking in literature. In this work, the ABL height is quantified based on high-resolution measurements collected by a scanning pulsed Doppler LiDAR during the recent American WAKE experimeNt (AWAKEN) campaign. The high availability of ABL height estimates (≈2200 collected over one year and each of them based on 10-min averaged statistics) allows to robustly assess five different ABL height models, i.e., one for convective thermal conditions and four for stable conditions. Thermal condition is quantified by a stability parameter spanning three orders of magnitude and probed by near-ground 3D sonic anemometry. The free-atmosphere stability, quantified by the Brunt–Väisälä frequency, is both calculated from simultaneous radiosonde measurements and obtained from the best fit of two of the chosen ABL height models. Good agreement is found between the data and three of the chosen models, quantified by mean absolute errors on the ABL height between 281 and 585 m. Furthermore, the seasonal variability of the convective ABL height model parameters (−15% to +23% with respect to the year baseline) agrees with the variability of buoyancy-generated turbulence caused by the variation in solar radiation throughout the year.

Asymptotic scaling relations for rotating spherical convection with strong zonal flows

We analyse the results of direct numerical simulations of rotating convection in spherical shell geometries with stress-free boundary conditions, which develop strong zonal flows. Both the Ekman number and the Rayleigh number are varied. We find that the asymptotic theory for rapidly rotating convection can be used to predict the Ekman number dependence of each term in the governing equations, along with the convective flow speeds and the dominant length scales. Using a balance between the Reynolds stress and the viscous stress, together with the asymptotic scaling for the convective velocity, we derive an asymptotic prediction for the scaling behaviour of the zonal flow with respect to the Ekman number, which is supported by the numerical simulations. We do not find evidence of distinct asymptotic scalings for the buoyancy and viscous forces and, in agreement with previous results from asymptotic plane layer models, we find that the ratio of the viscous force to the buoyancy force increases with Rayleigh number. Thus, viscosity remains non-negligible and we do not observe a trend towards a diffusion-free scaling behaviour within the rapidly rotating regime.

Elastic softening and hardening at intersections between twin walls and surfaces in ferroelastic materials

Surfaces play a key role during ferroelastic switching and define the interactions of materials with ionic species and biological systems. Here, we perform molecular dynamics simulations and identify ridges and valleys with rounded singularities around the intersections between twin walls and surfaces. Two dominant length scales stem from the elastic bending of the surface layer (>30 lattice units) and local atomic reshuffles (some five lattice units). For static twin walls, which do not shift laterally under external stress, the intrinsic change in Young’s modulus involves softening near valleys and hardening near ridges. The boundary-induced changes in the surface Young’s modulus are of the order of 0.7%.

Turbulence structures and entrainment length scales in large offshore wind farms

Abstract. The flow inside and around large offshore wind farms can range from smaller structures associated with the mechanical turbulence generated by wind turbines to larger structures indicative of the mesoscale flow. In this study, we explore the variation in turbulence structures and dominant scales of vertical entrainment above large offshore wind farms located in the North Sea, using data obtained from a research aircraft. The aircraft was flown upstream, downstream, and above wind farm clusters. Under neutrally stratified conditions, there is high ambient turbulence in the atmosphere and an elevated energy dissipation rate compared to stable conditions. The intensity of small-scale turbulence structures is increased above and downstream of the wind farm, and it prevails over mesoscale fluctuations. But in stable stratification, mesoscale flow structures are not only dominant upstream of the wind farm but also downstream. We observed that the vertical flux of horizontal momentum is the main source of energy recovery in large offshore wind farms, and it strongly depends on the magnitude of the length scales of the vertical wind velocity component. The dominant length scales of entrainment range from 20 to ∼60 m above the wind farm in all stratification strengths, and in the wake flow these scales range from 10 to ∼100 m only under near-neutral stratification. For strongly stable conditions, negligible vertical entrainment of momentum was observed even just 2 km downstream of large wind farms. We also observed that there is a significant lateral momentum flux above the offshore wind farms, especially under strongly stable conditions, which suggests that these wind farms do not satisfy the conditions of an “infinite wind farm”.

Turbulence Signatures in High‐Latitude Ionospheric Scintillation

AbstractGround‐based amplitude measurements of Global Navigation Satellite System signal during ionospheric scintillation are analyzed using prevalent data analysis tools developed in the fields of fluid and plasma turbulence. One such tool is the structure function of order q, with q = 1 to q = 6, which reduces to the computation of the second‐order difference in the GPS signal amplitude at various time lags, and allows for the exploration of dominant length scales in the propagation medium. We report the existence of a range where the structure function is linear with respect to time lag. This linear time segment could be considered as an analog to the inertial range in the context of neutral and plasma turbulence theory. Quantitatively, the slope of the structure function in the linear range is in good agreement with the scaling exponent determined from in situ measurements of the electrostatic potential at low altitude (E‐region) and the electron density at the topside ionosphere (F‐region). This in turn suggests the conjecture that scintillation could be considered a proxy for ionospheric turbulence. Furthermore, we have found that the probability distribution function of the second‐order difference in the signal amplitude has non‐Gaussian features at large time lags; a result that seems inconsistent with equilibrium statistical physics which suggests a Gaussian distribution for the conventional random‐walk processes. This could indicate that intermittency may occur at large time lags.

Urban neighbourhood classification and multi-scale heterogeneity analysis of Greater London

We study the compositional and configurational heterogeneity of Greater London at the city- and neighbourhood-scale using Geographic Information System (GIS) data. Urban morphometric indicators are calculated including plan-area indices and fractal dimensions of land cover, frontal area index of buildings, evenness, and contagion. To distinguish between city-scale heterogeneity and neighbourhood-scale heterogeneity, the study area of 720 km2 is divided into 1 [Formula: see text] 1 km2 neighbourhoods. City-scale heterogeneity is represented by categorisation of the neighbourhoods using a k-means clustering algorithm based on the morphometric indicators. This results in six neighbourhood types ranging from “greenspace” to “central business district”. Neighbourhood-scale heterogeneity is quantified using a hierarchical multi-scale analysis for each neighbourhood type. The analysis reveals the dominant length scales for land-cover and neighbourhood types and the resolutions with the most information gain. We analyse multi-scale anisotropy and show that small-scale features are homogeneous, and that anisotropy is present at larger length scales.

Modeling the Shallow Cumulus-Topped Boundary Layer at Gray Zone Resolutions

Abstract This study investigates simulated fair-weather shallow cumulus-topped boundary layer (SCTBL) on kilometer- and subkilometer-scale horizontal resolutions, also known as the numerical gray zone of boundary layer turbulence. Based on a priori analysis of a simulated classic SCTBL with large-eddy simulation, its gray zone scale is determined. The dominant length scale of the cloud layer (CL) is found to be the effective cloud diameter, while that of the underlying mixed layer (ML) is the size of organized convection. The two scales are linked by a simple geometric argument based on vertically coherent updrafts, and are quantified through spectral analysis. Comparison to a simulated dry convective boundary layer (CBL) further reveals that the ML gray zone scale does not differentiate between clear and cloudy conditions with the same bulk stability. A posteriori simulations are then performed over a range of resolutions to evaluate the performance of a recently developed scale-adaptive planetary boundary layer (PBL) scheme. Simulation results suggest indifferences to the scale-adaptive capability. Detailed analyses of flux partition reveal that, in the absence of a shallow cumulus scheme, overly energetic resolved fluxes develop in the CL at gray zone and coarse resolutions, and are responsible for overpredicted resolved convection in the ML. These results suggest that modifications are needed for scale-adaptive PBL schemes under shallow cumulus-topped conditions. Significance Statement Shallow cumulus (ShCu) clouds play an important role in the dynamical and radiative processes of the atmospheric boundary layer. As the grid resolution of modern numerical weather prediction models approach kilometer and subkilometer scales, also known as the gray zone, accurate modeling of ShCu clouds becomes challenging due to difficulties in their parameterization. This study identifies the spatial scale that sets the gray zone of ShCu clouds, providing the key to building better parameterizations. Performance of existing parameterizations developed for clear-sky conditions is evaluated for cloudy conditions, exposing deficiencies and motivating further development.

Formation of accretion disk by hydrodynamic subcritical transition

This work employs input-output analysis that is computationally efficient to provide insight into the dominant length scale the transition mechanism in rotating plane Couette flow that is relevant to the accretion disk. We also incorporate componentwise analysis to isolate the effect of different input body forces and different output velocity responses. We compared results associated with three different Reynolds numbers and rotation numbers considering both the overall effect and the effect under isolated input and output directions. We observe different patterns in which the maximum energy amplification strength changes as Reynolds number and rotation number change. We also derive the scaling law of the largest input-output gain over Reynolds number and rotation number, which suggests a higher rotation rate is playing a stabilizing role. We observe that the maximum amplification at rotation number equal to one shows symmetry against the lift-up mechanism in non-rotating plane Couette flow. As the stabilizing effect of rotation is further increased, we observe the most amplified flow structures are more elongated in the spanwise direction reminiscent of the Taylor-Proudman effect.

Aerodynamics of a wing in turbulent bluff body wakes

The aerodynamics of a stationary wing in a turbulent wake are investigated. Force and velocity measurements are used to describe the unsteady flow. Various wakes are studied with different dominant frequencies and length scales. In contrast to the pre-stall angles of attack, the time-averaged lift increases substantially at post-stall angles of attack as the wing interacts with the von Kármán vortex street and experiences temporal variations of the effective angle of attack. At an optimal offset distance from the wake centreline, the time-averaged lift becomes maximum despite of small amplitude oscillations in the effective angle of attack. The stall angle of attack can reach 20° and the maximum lift coefficient can reach 64 % higher than that in the freestream. Whereas large velocity fluctuations at the wake centreline cause excursions into the fully attached and separated flows during the cycle, small-amplitude oscillations at the optimal location result in periodic shedding of leading edge vortices. These vortices may produce large separation bubbles with reattachment near the trailing-edge. Vorticity roll-up, strength and size of the vortices increase with increasing wavelength and period of the von Kármán vortex street, which also coincides with an increase in the spanwise length scale of the incident wake, and all contribute to the remarkable increase in lift.

The Implications of TeV-detected GRB Afterglows for Acceleration at Relativistic Shocks

Abstract Motivated by the detection of very-high-energy (VHE) gamma rays deep in the afterglow emission of a gamma-ray burst (GRB), we revisit predictions of the maximum energy to which electrons can be accelerated at a relativistic blast wave. Acceleration at the weakly magnetized forward shock of a blast wave can be limited by either the rapid damping of turbulence generated behind the shock, the effect of a large-scale ambient magnetic field, or radiation losses. Within the confines of a standard, single-zone, synchrotron self-Compton (SSC) model, we show that observations of GRB 190829A rule out a rapid damping of the downstream turbulence. Furthermore, simultaneous fits to the X-ray and TeV gamma-ray emission of this object are not possible unless the limit on acceleration imposed by the ambient magnetic field is comparable to or weaker than that imposed by radiation losses. This requires the dominant length scale of the turbulence behind the shock to be larger than that implied by particle-in-cell simulations. However, even then, Klein–Nishina effects prevent production of the hard VHE gamma-ray spectrum suggested by observations. Thus, TeV observations of GRB afterglows, though still very sparse, are already in tension with the SSC emission scenario.

Stable channel flow with spanwise heterogeneous surface temperature

Recent studies have demonstrated that large secondary motions are excited by surface roughness with dominant spanwise length scales of the order of the flow's outer length scale. Inspired by this, we explore the effect of spanwise heterogeneous surface temperature in weakly to strongly stratified closed channel flow (at$Ri_\tau =120$, 960;$Re_\tau = 180$, 550) with direct numerical simulations. The configuration consists of equally sized strips of high and low temperature at the lower and upper boundaries, while an overall stable stratification is induced by imposing an average temperature difference between the top and bottom. We consider the influence of the width of the strips (${\rm \pi} /8 \leq \lambda /h \leq 4{\rm \pi} $), Reynolds number, stability and upper boundary condition on the mean flow structure, skin friction and heat transfer. Results indicate that secondary flows are excited, with alternating high- and low-momentum pathways and vortices, similar to the patterns induced by spanwise heterogeneous surface roughness. We find that the impact of the surface heterogeneity on the outer layer depends strongly on the spanwise heterogeneity length scale of the surface temperature. Comparison to stable channel flow with uniform temperature reveals that the heterogeneous surface temperature increases the global friction coefficient and reduces the global Nusselt number in most cases. However, for the high-Reynolds cases with$\lambda /h \geq {\rm \pi} /2$, we find a reduction of the friction coefficient. At stronger stability, the vertical extent of the vortices is reduced and the impact of the heterogeneous temperature on momentum and heat transfer is smaller.

Big or small, patchy all: Resolution of marine plankton patch structure at micro- to submesoscales for 36 taxa.

Despite the ecological importance of microscale (0.01–1 meter) and fine-scale (1 to hundreds of meters) plankton patchiness, the dimensions and taxonomic identity of patches in the ocean are nearly unknown. We used underwater imaging to identify the position, horizontal length scale, and density of taxa-specific patches of 32 million organisms representing 36 taxa (200 micrometers to 20 centimeters) in the continental and oceanic environments of a subtropical, western boundary current. Patches were the most frequent in shallow, continental waters. For multiple taxa, patch count varied parabolically with background density. Taxa-specific patch length and organism size exhibited negative size scaling relationships. Organism size explained 21 to 30% of the variance in patch length. The dominant length scale was phylogenetically random and <100 meters for 64% of taxa. The predominance of micro- and fine-scale patches among a diverse suite of plankton suggests social and coactive processes may contribute to patch formation.

Urban Boundary Layers Over Dense and Tall Canopies

Wind-tunnel experiments were carried out on four urban morphologies: two tall canopies with uniform height and two super-tall canopies with a large variation in element heights (where the maximum element height is more than double the average canopy height, h_{max}=2.5h_{avg}). The average canopy height and packing density are fixed across the surfaces to h_{avg} = 80~hbox {mm}, and lambda _{p} = 0.44, respectively. A combination of laser Doppler anemometry and direct-drag measurements are used to calculate and scale the mean velocity profiles with the boundary-layer depth delta . In the uniform-height experiment, the high packing density results in a ‘skimming flow’ regime with very little flow penetration into the canopy. This leads to a surprisingly shallow roughness sublayer (depth approx 1.15h_{avg}), and a well-defined inertial sublayer above it. In the heterogeneous-height canopies, despite the same packing density and average height, the flow features are significantly different. The height heterogeneity enhances mixing, thus encouraging deep flow penetration into the canopy. A deeper roughness sublayer is found to exist extending up to just above the tallest element height (corresponding to z/h_{avg} = 2.85), which is found to be the dominant length scale controlling the flow behaviour. Results point toward the existence of a constant-stress layer for all surfaces considered herein despite the severity of the surface roughness (delta /h_{avg} = 3 - 6.25). This contrasts with the previous literature.

Complex conductivity signatures of compressive deformation and shear failure in soils

The mechanical properties of soils play a crucial role in site assessment for construction and infrastructure. Soils with low shear strength can become unstable as a result of natural and/or anthropogenic induced forces. Standard geotechnical methods, such as compressive strength tests, quantify the mechanical properties of soils, but these methods have low spatiotemporal resolution and may involve disruption of existing infrastructure. In contrast, the complex conductivity geophysical method can provide information on spatiotemporal changes in the subsurface in a minimally invasive manner. We investigated complex conductivity signatures resulting from soil deformation and failure during an unconfined compression test. A synthetic soil composed of silica sand (98%) and kaolin powder (2%) was saturated below its liquid limit and packed inside a flexible sample holder custom-equipped with four electrodes under zero confining stress to simulate an unconfined condition. This soil sample underwent a constant and slow rate of compression. Soil stress, strain, effluent volume, along with the frequency dependent real and imaginary parts of the complex conductivity were recorded over distinct time intervals. The first experiment focused on the sensitivity of complex conductivity to soil failure. Imaginary conductivity (equivalent to surface conductivity) abruptly decreased at the failure point (similar to the decrease in stress) compared to the real conductivity signal. The square of the dominant geophysical length scale L determined from the complex conductivity spectra (related to pore size) exhibits an inverse linear dependence on compression. The second experiment focused on the complex conductivity during shearing (beyond failure). In this case, the imaginary (or surface) conductivity closely tracked changes in the sample stress. In both experiments, imaginary (or surface) conductivity is highly sensitive to changes caused by rearrangement of soil structure under stress (i.e., deformation and failure). In contrast, the real conductivity is minimally sensitive, and the electrolytic conductivity is insensitive to these changes. Our findings indicate that complex conductivity is capable of tracking mechanical changes of soils under stress and during failure foremost through the surface conductivity.

Nanoscale dynamics during self-organized ion beam patterning of Si. I. Ar+ bombardment

Coherent grazing-incidence small-angle X-ray scattering is used to investigate the average kinetics and the fluctuation dynamics during self-organized nanopatterning of silicon by Ar$^+$ bombardment at 65$^{\circ}$ polar angle. At early times, the surface behavior can be understood within the framework of linear theory. The transition away from the linear theory behavior is observed in the dynamics through the intensity correlation function. It quickly evolves to exhibit stretched exponential decay on short length scales and compressed exponential decay on length scales corresponding the dominant structural length scale - the ripple wavelength. The correlation times also peak strongly at the ripple length scale. This behavior has notable similarities but also significant differences with the phenomenon of de Gennes narrowing. Overall, this dynamics behavior is found to be consistent with simulations of a nonlinear growth model.

A Scale-Adaptive Turbulence Model for the Dry Convective Boundary Layer

AbstractA scale-adaptive model is developed for the representation of dry convective boundary layer (CBL) turbulence in numerical models operating at O(100) m to O(1) km horizontal resolution, also known as the model gray zone of the CBL. The new model is constructed based on a planetary boundary layer (PBL) scheme and a large-eddy simulation (LES) closure that are both turbulence kinetic energy–based parameterizations. Scale adaptivity is achieved by “blending” the PBL scheme with the LES closure through an inverse averaging procedure that naturally accounts for vertical variations of the dominant turbulent length scales, hence the gray zone range. High-resolution wide-domain LES benchmark cases covering a broad range of CBL bulk stability are filtered to gray zone resolutions, and analyzed to determine the averaging coefficients. Stability dependence of the dominant length scales is revealed by the analysis and accounted for in the new model. The turbulence model is implemented into a community atmospheric model, and tested for idealized cases. Compared to two established gray zone models, the new model performs equally well under strongly convective conditions, and is more advantageous for the weakly unstable and near neutral CBL.

Geomagnetic semblance and dipolar–multipolar transition in top-heavy double-diffusive geodynamo models

SUMMARY Convection in the liquid outer core of the Earth is driven by thermal and chemical perturbations. The main purpose of this study is to examine the impact of double-diffusive convection on magnetic field generation by means of 3-D global geodynamo models, in the so-called ‘top-heavy’ regime of double-diffusive convection, when both thermal and compositional background gradients are destabilizing. Using a linear eigensolver, we begin by confirming that, compared to the standard single-diffusive configuration, the onset of convection is facilitated by the addition of a second buoyancy source. We next carry out a systematic parameter survey by performing 79 numerical dynamo simulations. We show that a good agreement between simulated magnetic fields and the geomagnetic field can be attained for any partitioning of the convective input power between its thermal and chemical components. On the contrary, the transition between dipole-dominated and multipolar dynamos is found to strongly depend on the nature of the buoyancy forcing. Classical parameters expected to govern this transition, such as the local Rossby number—a proxy of the ratio of inertial to Coriolis forces—or the degree of equatorial symmetry of the flow, fail to capture the dipole breakdown. A scale-dependent analysis of the force balance instead reveals that the transition occurs when the ratio of inertial to Lorentz forces at the dominant length scale reaches 0.5, regardless of the partitioning of the buoyancy power. The ratio of integrated kinetic to magnetic energy Ek/Em provides a reasonable proxy of this force ratio. Given that Ek/Em ≈ 10−4 − 10−3 in the Earth’s core, the geodynamo is expected to operate far from the dipole–multipole transition. It hence appears that the occurrence of geomagnetic reversals is unlikely related to dramatic and punctual changes of the amplitude of inertial forces in the Earth’s core, and that another mechanism must be sought.

Effect of Scale-Aware Planetary Boundary Layer Schemes on Tropical Cyclone Intensification and Structural Changes in the Gray Zone

AbstractHorizontal grid spacings of numerical weather prediction models are rapidly approaching O (1 km) and have become comparable with the dominant length scales of flows in the boundary layer; within such “gray-zone”, conventional planetary boundary layer (PBL) parameterization schemes start to violate basic design assumptions. Scale-aware PBL schemes have been developed recently to address the gray-zone issue. By performing WRF simulations of Hurricane Earl (2010) at sub-kilometer grid spacings, this study investigates the effect of the scale-aware Shin-Hong (SH) scheme on the tropical cyclone (TC) intensification and structural changes in comparison to the non-scale-aware YSU scheme it is built upon. Results indicate that SH tends to produce a stronger TC with a more compact inner core than YSU. At early stages, the scale-aware coefficients in SH gradually decrease as the diagnosed boundary layer height exceeds the horizontal grid spacing. This scale-aware effect is most prominent for the nonlocal subgrid-scale vertical turbulent fluxes, in the non-precipitation regions radially outside of the convective rainband, and from the early stage through the middle of rapid intensification (RI) phase. Both the scale awareness and different parameterization of the nonlocal turbulent heat flux in SH reduce the parameterized vertical turbulent mixing, which further induces stronger radial inflows and helps retain more water vapor in the boundary layer. The resulting stronger moisture convergence and diabatic heating near the TC center account for the faster inner-core contraction before RI onset and the higher intensification rate during the RI period. Potential issues of applying these two PBL schemes in TC simulations and suggestions for improvements are discussed.

Instability of ultrathin viscoelastic freestanding films

The linear stability of freestanding thin films under the influence of attractive van der Waals forces is investigated for three rheological models, viz., Newtonian viscous films, viscoelastic solid films, and Jeffreys viscoelastic liquid films, with the aim of studying the role of rheology on the instability. Thin freestanding viscous films are unconditionally unstable, whereas the shear modulus in thin freestanding solid viscoelastic films governs the onset of instability. Interestingly, elasticity plays a dual role with regard to the stability of freestanding solid and liquid films: while it has a stabilizing influence on the former, it is destabilizing in the latter. Linear stability results of Jeffreys viscoelastic freestanding films are compared with those from supported films in the inertialess limit. The instability of Jeffreys viscoelastic freestanding film is unaffected by the relaxation time, but is enhanced with decrease in the viscosity ratio (μr, the ratio of solvent viscosity to total viscosity). The dominant length scale of instability in Jeffreys viscoelastic freestanding film shifts toward shorter wavelengths with decrease in μr. For μr→0, the maximum growth rate remains bounded in a freestanding viscoelastic film in the presence of inertia, but diverges in its absence, similar to supported viscoelastic films. In general, our results show that freestanding thin films exhibit faster dynamics than supported thin films. The mode of deformation of the freestanding film (viz., bending or squeezing) is not imposed a priori in our analysis and is found to be a squeezing (symmetric) mode with equal amplitudes at the interfaces.