Integral Time Scale Research Articles

Aligning free surface properties in time-varying hydraulic jumps

Hydraulic jumps occur commonly in natural channels and energy dissipation systems of hydraulic structures in the violent transition from supercritical to subcritical flows. They are characterised by large flow aeration, high turbulence and strong fluctuations of the free surface and the jump toe. For free surface measurements, fast-sampling, fixed-point instruments such as acoustic displacement meters (ADMs) and wire gauges (WGs) are commonly used, while LIDAR technology is a relatively new method for recording instantaneous free surface motions of aerated flows. While each of these instruments has been shown previously to provide reasonable results for basic and advanced free surface properties, differences between instruments and experiments remain unexplained. To systematically analyse these differences, simultaneous laboratory experiments of aerated hydraulic jumps were conducted. Good agreement between the three instruments was obtained for basic free surface properties including elevations, fluctuations, skewness, kurtosis, and frequencies, as well as advanced free surface properties such as integral time and length scales. These new results indicate that any of these instruments can be used for the recording of free surface properties albeit the free surface integral scales are sensitive to the spacing of instruments. A key finding of this research was that differences between repeated experiments as well as previous studies were observed when using the visual jump toe for alignment. However, this bias could be resolved by using the mean jump toe location recorded with the LIDAR. Therefore, future research of the fundamental flow processes should simultaneously measure the instantaneous jump toe to provide more consistent results across studies.

Dispersion of Buoyant and Sinking Particles in a Simulated Wind‐ and Wave‐Driven Turbulent Coastal Ocean

AbstractIn shallow coastal oceans, turbulent flows driven by surface winds and waves and constrained by a solid bottom disperse particles. This work examines the mechanisms driving horizontal and vertical dispersion of buoyant and sinking particles for times much greater than turbulent integral time scales. Turbulent fields are modeled using a wind‐stress driven large eddy simulation (LES), incorporating wave‐driven Langmuir turbulence, surface breaking wave turbulent kinetic energy inputs, and a solid bottom boundary. A Lagrangian stochastic model is paired to the LES to incorporate Lagrangian particle tracking. Within a subset of intermediate buoyant rise velocities, particles experience synergistic vertical mixing in which breaking waves (BW) inject particles into Langmuir downwelling velocities sufficient to drive deep mixing. Along‐wind dispersion is controlled by vertical shear in mean along‐wind velocities. Wind and bottom friction‐driven vertical shear enhances dispersion of buoyant and sinking particles, while energetic turbulent mixing, such as from BW, dampens shear dispersion. Strongly rising and sinking particles trapped at the ocean surface and bottom, respectively, experience no vertical shear, resulting in low rates of along‐wind dispersion. Crosswind dispersion is shaped by particle advection in wind‐aligned fields of counter‐rotating Langmuir and Couette roll cells. Langmuir cells enhance crosswind dispersion in neutrally to intermediately buoyant particles through enhanced cell hopping. Surface trapping restricts particles to Langmuir convergence regions, strongly inhibiting crosswind dispersion. In shallow coastal systems, particle dispersion depends heavily on particle buoyancy and wave‐dependent turbulent effects.

The effects of free-stream turbulence on the performance of a model wind turbine

Free-stream turbulence characteristics play an important role in the mechanisms of power harvesting for wind turbines. Acquisitions of power and thrust from a model wind turbine of diameter 0.18 m have been carried out in a wind tunnel for a wide range of turbulent base flows, with varying free-stream turbulence intensity in the range between 3% and 16% and integral timescale spanning from 0.1 to 10 times the turbine rotation period. The results demonstrate that power is significantly affected by both the inflow turbulence scales and its intensity, while thrust is scarcely affected by free-stream turbulence. Fluctuations in the generated torques are also measured, with their behavior dominated by the free-stream turbulence scale, and only moderately affected by turbulence intensity. The frequency response of thrust fluctuations has been measured for a selected subset of operating conditions, demonstrating that the turbine thrust is unaffected by high-frequency components in the inflow. Conclusions are drawn on the necessity to match both turbulence intensity and base flow frequency content in wind tunnel studies if realistic results are to be obtained from small-scale studies.

30 years of temporal variability of temperature and currents below the main thermocline between 1980–2009 in the subtropical Northeast Atlantic (Kiel 276, 33∘N, 22∘W)

Abstract Data from the deep-sea mooring Kiel 276 (33 ∘ N, 22 ∘ W), 5300 m water depth in the northeast Atlantic, was used to investigate the temporal variability of temperature and currents below the main thermocline (1000 m, 1600 m, 3000 m, 5000 m) in the 30-year period (between 1980 and 2009). Daily averages were the basis to assess the temperature and currents changes, as well as kinetic energy, from annual to decadal and long-term scales. Below the main thermocline, no seasonal signal was identified for both, temperature and currents, during the 30 years. The record-length linear temperature trends at 1000 m and 1600 m are 0.03 ± 0.01 °C year−1 and 0.02 ± 0.02 °C year−1, respectively. The mean currents also intensified within the decades in the entire water column, and as a consequence, the mean kinetic energy increased. The fluctuating kinetic energy increased on a decadal scale only at 1000 m, as a possible consequence of the increase in the strength of Mediterranean Water lenses (MEDDIES) that crossed the mooring site. During the period 2001–2009, six MEDDIES crossed the Kiel 276 site, in addition to the 10 MEDDIES identified earlier during the previous 20 years, between 1980 and 2000 (Siedler et al., 2005). The integral time scales are of the same order in all depths (between 30 to 40 days), indicating that events occur on similar time scales, with mesoscale signals dominating and being present within the entire water column.

Multiscale Legacy Responses of Soil Gas Concentrations to Soil Moisture and Temperature Fluctuations

AbstractThe sensitivity of soil carbon dynamics to climate change is a major uncertainty in carbon cycle models. Of particular interest is the response of soil biogeochemical cycles to variability in hydroclimatic states and the related quantification of soil memory. Toward this goal, the power spectra of soil hydrologic and biogeochemical states were analyzed using measurements of soil temperature, moisture, oxygen, and carbon dioxide at two sites. Power spectra indicated multiscale power law scaling across subhourly to annual timescales. Precipitation fluctuations were most strongly expressed in the soil biogeochemical signals at monthly to annual timescales. Soil moisture and temperature fluctuations were comparable in strength at one site, while temperature was dominant at the other. The effect of soil hydrologic, thermal, and biogeochemical processes on gas concentration variability was evidenced by low spectral entropy relative to the white noise character of precipitation. A full mass balance model was unable to capture high‐frequency soil temperature influence, indicating a gap in commonly used model assumptions. A linearized model was shown to capture the main features of the observed and modeled gas concentration spectra and demonstrated how the means and variances of soil moisture and temperature interact to produce the gas concentration spectra. Breakpoints in the spectra corresponded to the mean rate of gas efflux, providing a first‐order estimate of the soil biogeochemical integral timescale (∼1 min). These methods can be used to identify biogeochemical system dynamics to develop robust, process‐based soil biogeochemistry models that capture variability in addition to long‐term mean values.

Linkages between Rainfed Cereal Production and Agricultural Drought through Remote Sensing Indices and a Land Data Assimilation System: A Case Study in Morocco

In Morocco, cereal production shows high interannual variability due to uncertain rainfall and recurrent drought periods. Considering the socioeconomic importance of cereal for the country, there is a serious need to characterize the impact of drought on cereal yields. In this study, drought is assessed through (1) indices derived from remote sensing data (the vegetation condition index (VCI), temperature condition index (TCI), vegetation health ind ex (VHI), soil moisture condition index (SMCI) and soil water index for different soil layers (SWI)) and (2) key land surface variables (Land Area Index (LAI), soil moisture (SM) at different depths, soil evaporation and plant transpiration) from a Land Data Assimilation System (LDAS) over 2000–2017. A lagged correlation analysis was conducted to assess the relationships between the drought indices and cereal yield at monthly time scales. The VCI and LAI around the heading stage (March-April) are highly linked to yield for all provinces (R = 0.94 for the Khemisset province), while a high link for TCI occurs during the development stage in January-February (R = 0.83 for the Beni Mellal province). Interestingly, indices related to soil moisture in the superficial soil layer are correlated with yield earlier in the season around the emergence stage (December). The results demonstrate the clear added value of using an LDAS compared with using a remote sensing product alone, particularly concerning the soil moisture in the root-zone, considered a key variable for yield production, that is not directly observable from space. The time scale of integration is also discussed. By integrating the indices on the main phenological stages of wheat using a dynamic threshold approach instead of the monthly time scale, the correlation between indices and yield increased by up to 14%. In addition, the contributions of VCI and TCI to VHI were optimized by using yield anomalies as proxies for drought. This study opens perspectives for the development of drought early warning systems in Morocco and over North Africa, as well as for seasonal crop yield forecasting.

Characteristics and similarity relations of turbulence dispersion parameters under heavy haze conditions

The parameterizations of atmospheric turbulence dispersion in many commonly used numerical models are based on the similarity relations in highly flat and sparsely populated areas. Such parameterizations limit the applicability of the models for simulating heavy haze processes that frequently occur in densely populated urban areas with complex terrains. In this study, we examined the similarity relations of key turbulence dispersion parameters in the Lagrangian dispersion models, including the turbulent standard deviations, high-order moments (the third and fourth moments), and integral time scales for longitudinal, lateral, and vertical wind velocity components during heavy haze days in downtown Beijing, China. The similarity relations were analyzed in the framework of the local similarity theory, which is commonly used in studies of urban turbulence. It was found that in highly stable or unstable conditions, the normalized turbulent standard deviations and high-order moments (the normalized integral time scales) during heavy haze days generally increased (decreased) significantly slower than those during clean days. However, in nearly neutral conditions, the normalized values for heavy haze and clean days were approximately equal. The results indicate that the development of parameterizations of turbulence dispersion during heavy haze days, especially in highly stable or unstable conditions, warrants greater research focus.

Interpreting neural network models of residual scalar flux

Abstract

Estimates of net community production from multiple approaches surrounding the spring ice-edge bloom in Baffin Bay

Measurements of net community production (NCP) provide an upper constraint on the strength of the oceanic biological pump, the dominant mechanism for removing CO2 from the ocean surface and sequestering it at depth. In this investigation, our objectives were to describe the spatial and temporal variability of NCP associated with the spring ice-edge bloom in Baffin Bay and to identify the key environmental drivers controlling its variability. Using data collected between June 9 and July 10, 2016, we estimated NCP based on (1) underway measurements of surface water oxygen to argon ratios (O2:Ar), (2) underway measurements of the partial pressure of CO2, and (3) seasonal nitrate drawdown from discrete samples. These multiple approaches displayed high NCP (up to 5.7 mol C m–2) in eastern Baffin Bay, associated with modified Atlantic waters, and low NCP (<1 mol C m–2) in the presence of Arctic outflow waters in western Baffin Bay. Arctic outflow waters were characterized by low surface salinities and nitrate concentrations, suggesting that high freshwater content may have limited the nutrient availability of these waters. Different integration depths and timescales associated with each NCP approach were exploited to understand the temporal progression and succession of the bloom, revealing that the bloom was initiated under ice up to 15 days prior to ice retreat and that a large portion of NCP in eastern Baffin Bay (potentially up to 70%) was driven by primary production occurring below the surface-mixed layer.

Turbulent boundary layer flow over two side-by-side wall-mounted cylinders: Wake characteristics and aerodynamic loads

The distinctive wake characteristics and aerodynamic loads of two side-by-side wall-mounted cylinders were experimentally studied under turbulent boundary layer flows with various gaps. Time-resolved particle image velocimetry was used to analyze the mean and unsteady wake features, whereas a high-resolution load cell was applied to measure the characteristics of lift and drag forces. The results show that the decrease in gap between two cylinders can effectively delay the wake recovery and suppress both the downwash and upwash flows near the top and bottom ends. Overall, with smaller gaps, the turbulence intensity near the top end becomes higher due to the stronger local velocity shear. The distribution of integral time scales indicates that the velocity fluctuations in the near wake region along the middle cylinder span are highly influenced by the local recirculation flows, whereas those near the top end are dominated by the mixing of boundary layer flows. By accounting the equivalent incoming velocity along the cylinder span, both lift and drag coefficient present a similar trend compared to the “infinite length” cylinder cases from previous works. Interestingly, different from cylinders with “infinite length,” no clear intermittency of aerodynamic loads was observed in the current work. This can be attributed to the suppression of two-dimensional vortex shedding due to the three-dimensional flow effects and strong background turbulence. The joint distribution of the lift and drag forces reveals that the lift fluctuations increase significantly with the growth of cylinder gaps, whereas that of drag force remains nearly constant.

Prediction of long-range infrasound propagation from tornadoes based on new atmospheric boundary layer wind tunnel experiments

Tornadoes generate infrasonic noise that propagates over long distances. NOAA is developing tornado early warning systems via infrasound microphone arrays. Accurate detection must be coupled with a propagation algorithm that accounts for infrasound distortion due to the effects of atmospheric turbulence. Numerical solutions of the generalized Burgers' equation and the acoustic ray equations are used to predict changes to infrasonic tornado noise within the turbulent atmosphere. The effects of nonlinearity, refraction, attenuation, dispersion, and scattering are captured by the solver. We define a new parameter to model the alteration of infrasound that depends on atmospheric turbulence. Turbulent kinetic energy, integral length scale, integral time scale, and local speed of sound are arguments of the model and vary along each ray path. A series of tests are designed and conducted at the University of Florida Boundary Layer Wind Tunnel to calibrate and validate the model at scale. Predictions show satisfactory agreement with measurements with varying wind speed, turbulence intensity, humidity, and temperature. Finally, we present a parametric study for propagation of sinusoidal signals at 90 dB and 7 Hz in regions of the United States using realistic weather.

Extended Slip-Weakening Model and Inference of Rupture Velocity

The slip-weakening model developed by Ohnaka and Yamashita is extended over the breakdown zone by equating the scaling relationships for the breakdown zone and the whole rupture area. For the extension, the study uses the relationship between rupture velocity and radiation efficiency, which was derived in the theory of linear elastic fracture mechanics, and the definition of fmax given in the specific barrier model proposed by Papageorgiou and Aki. The results clearly show that the extended scaling relationship is governed by the ratio of rupture velocity to S wave velocity, and the velocity ratio can be determined by the ratio of characteristic frequencies of a Fourier amplitude spectrum, which are corner frequency, fc, and source-controlled cut-off frequency, fmax, or vice versa. The derived relationship is tested by using the characteristic frequencies extracted from previous studies of more than 130 shallow crustal events (focal depth less than 25 km, MW 3.0~7.5) that occurred in Japan. Under the assumption of a dynamic similarity, the rupture velocity estimated from fmax/fc and the modified integral timescale give quite similar scale-dependence of the rupture area to that given by Kanamori and Anderson. Also, the results for large earthquakes show good agreement to the values from a kinematic inversion in previous studies. The test results also indicate the unavailability of the spectral self-similarity proposed by Aki because of the scale-dependent rupture velocity and the rupture velocity-dependent fmax/fc; however, the results do support the local similarity asserted by Ohnaka. It is also remarkable that the relationship between the rupture velocity and fmax/fc is quite similar to Kolmogorov’s hypothesis on a similarity in the theory of isotropic turbulence.

Fast laser speckle suppression with an intracavity diffuser

AbstractFast speckle suppression is crucial for time-resolved full-field imaging with laser illumination. Here, we introduce a method to accelerate the spatial decoherence of laser emission, achieving speckle suppression in the nanosecond integration time scale. The method relies on the insertion of an intracavity phase diffuser into a degenerate cavity laser to break the frequency degeneracy of transverse modes and broaden the lasing spectrum. The ultrafast decoherence of laser emission results in the reduction of speckle contrast to 3% in less than 1 ns.

Sensitivity of LES predictions of wind loading on a high-rise building to the inflow boundary condition

Large eddy simulations (LES) can provide a powerful tool for cladding design, but their accuracy strongly depends on the correct representation of the incoming atmospheric boundary layer (ABL). The objective of this work is to validate LES of a wind tunnel experiment of wind loading on a high-rise building, focusing on accounting for sensitivity to the incoming ABL. We define three uncertain parameters, i.e. the roughness length of the terrain, the turbulence kinetic energy, and the integral time-scale, using the available experimental data. Subsequently we perform 27 LES using different combinations of these parameters. The results indicate that (1) accurately quantifying the turbulence statistics at the building location, rather than at the inflow, is essential when analyzing LES of wind loading, and (2) correctly accounting for inflow uncertainty when performing validation against experiments could drastically improve confidence in the predictions. By accounting for this uncertainty, we predict intervals that encompass the experimental data for the rms pressure coefficients. The magnitude of the local peak pressure coefficients is generally under-predicted by 12%; however, the predicted intervals for design pressure coefficients on cladding panels of different sizes located at the upper-windward corner of the building fully encompass the experimental result.

Stochastic models for capturing dispersion in particle-laden flows

Abstract

Modulation induced splitting of the magnetic resonance

The splitting of magnetic resonance induced by a frequency modulated linearly polarized light field is presented for Hanle experimental configuration. The experiment is carried out with thermal Rubidium atoms in an anti-relaxation coated glass cell. The observed splitting corresponds to steady-state behaviour of the system over an integrated time scale that is longer than the modulation frequency. The splitting is only observed for dark resonances, with left and right circularly polarized light simultaneously coupled to the atomic system. The split components are separated by half of the modulation frequency with the central component lying at zero-magnetic field. The absence of odd split components at single photon resonance is consistent with the theoretical calculation. The different components of the split profile have distinct response to the direction of the transverse magnetic field. The response is captured by the theoretical calculation and the underlying physical mechanism is discussed. These studies will be useful in metrology and advancement of vector atomic magnetometer.

Near-Surface Transport Properties and Lagrangian Statistics during Two Contrasting Years in the Adriatic Sea

This paper describes the near-surface transport properties and Lagrangian statistics in the Adriatic semi-enclosed basin using synthetic drifters. Lagrangian transport models were used to simulate synthetic trajectories from the mean flow fields obtained by the Massachusetts Institute of Technology general circulation model (MITgcm), implemented in the Adriatic from October 2006 until December 2008. In particular, the surface circulation properties in two contrasting years (2007 had a mild winter and cold fall, while 2008 had a normal winter and hot summer) are compared here. In addition, the Lagrangian statistics for the entire Adriatic Basin after removing the Eulerian mean circulation for numerical particles were calculated. The results indicate that the numerical particles were slower in this simulation when compared with the real drifters. This is because of the reduced energetic flow field generated by the MIT general circulation model during the selected years. The numerical results showed that the balanced effects of the wind-driven recirculation in the northernmost area(which would be a sea response to the Bora wind field) and the Po River discharge cause the residence times to be similar during the two selected years (182 and 185 days in 2007 and 2008, respectively). Furthermore, the mean angular momentum, diffusivity, and Lagrangian velocity covariance values are smaller than in the real drifter observations, while the maximum Lagrangian integral time scale is the same.

Statistical analysis of deformation of a shock wave propagating in a local turbulent region

Direct numerical simulation is performed for analyzing the interaction between a normal shock wave and turbulence. The shock wave is initially located in a quiescent fluid and propagates into a local turbulent region. This flow setup allows investigation of the initial transition and statistically steady stages of the interaction. Shock deformation is quantified using the local shock wave position. The root-mean-square (rms) fluctuation in the shock wave position increases during the initial stage of the interaction, for which the time interval divided by the integral time scale increases with Mt2/(Ms2−1), where Mt is a turbulent Mach number and Ms is a shock Mach number. In late time, the rms fluctuation in the shock wave position hardly depends on the propagation time and follows a power law, [Mt2/(Ms2−1)]0.46, whose exponent is similar to the power law exponent of the rms pressure-jump fluctuation reported in experimental studies. Fluctuations in the shock wave position have a Gaussian probability density function. The spectral analysis confirms that the length scale that characterizes shock wave deformation is the integral length scale of turbulence. The fluctuating shock wave position is correlated with dilatation of the shock wave, where the correlation coefficient increases with Mt/(Ms − 1). In addition, the shock wave that deforms backward tends to be stronger than average and vice versa. Mean pressure jumps across the shock wave are different between areas with forward and backward deformations. This difference increases with the rms fluctuation in the shock wave position and is well-represented as a function of Mt2/(Ms2−1).

Multiple timescales of neural dynamics and integration of task-relevant signals across cortex

A long-lasting challenge in neuroscience has been to find a set of principles that could be used to organize the brain into distinct areas with specific functions. Recent studies have proposed the orderly progression in the time constants of neural dynamics as an organizational principle of cortical computations. However, relationships between these timescales and their dependence on response properties of individual neurons are unknown, making it impossible to determine how mechanisms underlying such a computational principle are related to other aspects of neural processing. Here, we developed a comprehensive method to simultaneously estimate multiple timescales in neuronal dynamics and integration of task-relevant signals along with selectivity to those signals. By applying our method to neural and behavioral data during a dynamic decision-making task, we found that most neurons exhibited multiple timescales in their response, which consistently increased from parietal to prefrontal and cingulate cortex. While predicting rates of behavioral adjustments, these timescales were not correlated across individual neurons in any cortical area, resulting in independent parallel hierarchies of timescales. Additionally, none of these timescales depended on selectivity to task-relevant signals. Our results not only suggest the existence of multiple canonical mechanisms for increasing timescales of neural dynamics across cortex but also point to additional mechanisms that allow decorrelation of these timescales to enable more flexibility.

Analysis of the spanwise extent and time persistence of uniform momentum zones in zero pressure gradient and adverse pressure gradient turbulent boundary layers

Time-resolved velocity fields from direct numerical simulations (DNS) are used to investigate the spanwise extent and the time persistence of uniform momentum zones (UMZs) in a zero pressure gradient turbulent boundary layer (ZPG-TBL) and a self-similar adverse pressure gradient turbulent boundary layer (APG-TBL) at the verge of separation. The instantaneous detection methodology introduced by Adrian et al. [1] is used to detect the UMZs and is extended to take into account the spanwise domain length and the temporal evolution of the UMZs. The Reynolds number based on friction velocity (Reτ) ranges from 1176 to 1277 for the ZPG-TBL and from 1652 to 1745 for the self-similar APG-TBL within the domain of interest. For both the TBL cases, probability density functions (PDFs) of the number of UMZs are computed as a function of the streamwise extent, spanwise extent and time extent. For the ZPG-TBL, when the streamwise length of the domain is greater than or equal to 3 boundary layer thickness, the probability of finding 4 UMZs becomes almost negligible. For the APG-TBL, even when the streamwise domain length is taken as large as 1.3 boundary layer thickness, the probability of finding 4 UMZs is still significant. The spanwise extent of the UMZs is found to be shorter than their streamwise extent regardless of the pressure gradient in the flow. In the ZPG-TBL flow, the majority of the UMZs have a spanwise extent of the order of one-tenth of a boundary layer thickness while for the APG-TBL, it is found to be on the order of one-hundredth of a boundary layer thickness. In the ZPG-TBL, the probability of finding 2 UMZs that persist over a time period of 2 integral time scale is around 50%. Similarly, for the APG-TBL, the probability of finding 2 UMZs with a time persistence of 0.4 integral time scale is over 50%. In the case of the ZPG-TBL, it is observed that some of the UMZs with higher persistence in time have higher streamwise momentum and are found to be closer to the free-stream in general. This result is consistent with the previous observations by Laskari et al. [2]. In contrast, for the APG-TBL, UMZs with longer time persistence are found closer to the wall with lower streamwise momentum.