Vertical Velocity Gradient Research Articles

Waves, circulation and vertical dependence

Longuet-Higgins and Stewart (J Fluid Mech 13:481–504, 1962; Deep-Sea Res 11:529–562, 1964) and later Phillips (1977) introduced the problem of waves incident on a beach, from deep to shallow water. From the wave energy equation and the vertically integrated continuity equation, they inferred velocities to be Stokes drift plus a return current so that the vertical integral of the combined velocities was nil. As a consequence, it can be shown that velocities of the order of Stokes drift rendered the advective term in the momentum equation negligible resulting in a simple balance between the horizontal gradients of the vertically integrated elevation and wave radiation stress terms; the latter was first derived by Longuet-Higgins and Stewart. Mellor (J Phys Oceanogr 33:1978–1989, 2003a), noting that vertically integrated continuity and momentum equations were not able to deal with three-dimensional numerical or analytical ocean models, derived a vertically dependent theory of wave–circulation interaction. It has since been partially revised and the revisions are reviewed here. The theory is comprised of the conventional, three-dimensional, continuity and momentum equations plus a vertically distributed, wave radiation stress term. When applied to the problem of waves incident on a beach with essentially zero turbulence momentum mixing, velocities are very large and the simple balance between elevation and radiation stress gradients no longer prevails. However, when turbulence mixing is reinstated, the vertically dependent radiation stresses produce vertical velocity gradients which then produce turbulent mixing; as a consequence, velocities are reduced, but are still larger by an order of magnitude compared to Stokes drift. Nevertheless, the velocity reduction is sufficient so that elevation set-down obtained from a balance between elevation gradient and radiation stress gradients is nearly coincident with that obtained by the aforementioned papers. This paper includes four appendices. The first appendix demonstrates the numerical process by which Stokes drift is excluded from the turbulence stress parameterization in the momentum equation. A second appendix determines a bottom slope criterion for the application of linear wave relations to the derivation of the wave radiation stress. The third appendix explores the possibility of generalizing results by non-dimensionalization. The final appendix applies the basic theory to a problem introduced by Bennis and Ardhuin (J Phys Oceanogr 41:2008–2012, 2011).

Kinematic imprint of clumpy disk formation on halo objects

Context: Clumpy disk galaxies in the distant universe, at redshift of z>1, have been observed to host several giant clumps in their disks. They are thought to correspond to early formative stages of disk galaxies. On the other hand, halo objects, such as old globular clusters and halo stars, are likely to consist of the oldest stars in a galaxy (age>10 Gyr), therefore the clumpy disk formation can be presumed to take place in a pre-existing halo system. Aims: Giant clumps are orbiting in the same direction in a premature disk and so massive that they may be expected to interact gravitationally with halo objects and exercise influence on kinematic state of the halo. Accordingly, I scrutinize the possibility that the clumps leave a kinematic imprint of the clumpy disk formation on a halo system. Methods: I perform a restricted N-body calculation with a toy-model to study the kinematic influence on a halo by orbital motions of clumps, examine dependence of the results on masses (mass-loss), number and orbital radii of the clumps. Results: I will show that halo objects can catch clump motions and acquire disky rotation in a dynamical friction time-scale of the clumps, ~0.5 Gyr. The influence of clumps is limited within a region around the disk, the halo system shows vertical gradients of net rotation velocity and orbital eccentricity. The significance of the kinematic influence strongly depends on the clump masses, the lower limit of postulated clump mass would be 5x10^8 solar masses. The result depends also on whether the clumps are subjected to rapid mass-loss or not, which is an open question under debate in recent studies. The existence of such massive clumps is not unrealistic, I therefore suggest that there could remain the imprints of past clumpy disk formation in current galactic halos.

Disk Weather

Recent years have shown that accretion disks around young stars have extended regions, which are too low ionized to couple to magnetic fields and thus the nature of the underlying turbulence cannot be exclusively magnetic. We also found that disks have in general a baroclinic density and temperature structure which means that a typical disk is radially buoyant and has a vertical velocity gradient also known as thermal wind. Here we show that the expected entropy gradients in observed accretion disks around young stars are in fact steep enough and that the thermal relaxation times are sufficiently short to allow for efficient amplification of vortices.

Generating starting models for seismic refraction tomography with common offset stacks

Common offset refraction (COR) traveltime attributes are derived from multi-fold data with novel adaptations of the generalised reciprocal method (GRM). COR GRM stacks are generated from a refraction equivalent of common midpoint (CMP) gathers, which are computed at each CMP with the COR GRM algorithms. The COR GRM stacks, which generate detailed spatially varying attributes for each layer detected in the near surface region, provide useful starting models for automatic refraction tomography.The spatial resolution of the depth models of the wavepath eikonal traveltime (WET) refraction tomograms obtained with starting models derived with the COR GRM is similar to the WET tomogram obtained with the standard GRM, whereas the COR GRM seismic velocity model is a smoothed version of the standard GRM model. In all cases, the GRM-derived WET tomograms avoid the generation of undetectable artefacts with common implementations of automatic refraction tomography, which can occur with the use of default starting models consisting of smooth vertical velocity gradients and with the need to minimise misfit errors through over-processing.The COR GRM attributes demonstrate that the traveltime data are consistent with minimal penetration within the sub-weathering, representative of uniform seismic velocities, and that the spatial variations in the time model and seismic velocities are more significant than any variations caused by vertical velocity gradients in the sub-weathered zone. However, the occurrence of vertical velocity gradients in the sub-weathering largely remains unresolved because minimal penetration of the first arrivals can occur even with large vertical velocity gradients, such as the hyperbolic velocity function.The WET tomograms generated with the COR GRM time model and seismic velocity attributes are generally very similar visually to the starting models, even though the misfit errors may differ. It is concluded that COR GRM starting models can frequently be a useful alternative to refraction tomography.

Impacts of cloud flare-ups on hurricane intensity resulting from departures from balance laws

ABSTRACTCloud flare-ups along the inner eye wall of a hurricane lead to enhancement of cloud scale divergence, which in turn leads to a large local enhancement of the departure from balance laws and can lead to local supergradient winds. This scenario is tested using the results from a mesoscale microphysical model at horizontal resolution of 1.33 km for the simulation of hurricane Katrina. Rainwater mixing ratio tags growing cloud elements. The departure from balance laws includes terms such as the local, horizontal and vertical advections of divergence, divergence square and a term invoking the gradient of vertical velocity. It is noted that these terms collectively contribute to a substantial local enhancement of the departure from balance laws. Departures from balance laws are related to the radial gradient wind imbalances in a storm-centred coordinate. In this study, several examples, from the hurricane Katrina simulations, that display this scenario of rapid intensification are illustrated. Organisation of convection in the azimuthal direction seems important for the hurricane scale; cloud flare-ups away from such regions of azimuthal organisation fail to contribute to this scenario for the overall intensification of the hurricane.

Uncertainty in Near-Surface Refraction Inversion

Uncertainty in the tomographic inversion of near-surface seismic refraction data can be separated into aleatory variability, which describes the misfit errors and epistemic uncertainty, which describes the suite of acceptable models. Common implementations of refraction tomography usually focus on reducing aleatory variability and frequently disregard epistemic uncertainty. In this study, the tomograms generated with three models of the seismic velocities in both the weathering and in the sub-weathering, using the generalized reciprocal method (GRM), are consistent with the traveltime data. However, only one tomogram is consistent with the optimum XY value and the attributes derived from the head wave amplitudes and seismic velocities. This study demonstrates that epistemic uncertainty can be explicitly addressed with the GRM, because the most probable tomogram can be selected objectively from a number of acceptable alternatives. The GRM-based tomogram successfully detects, defines and differentiates narrow regions with low seismic velocities which represent shear zones and a massive sulphide ore body. None of these zones is detected with the tomogram generated with the default starting model using smooth vertical velocity gradients. It is concluded that minimizing epistemic uncertainty through the use of the most appropriate starting model is more important than minimizing aleatory variability.

Seismic ground motion amplification in a 3D sedimentary basin: the effect of the vertical velocity gradient

Ground motion amplification in sedimentary basins has been observed in some moderate or large earthquakes, such as the 1994 Northridge and 1999 Chi-Chi event. Many numerical studies with simplified 2D models have shown significant effects of the vertical velocity gradient of sediment on basin amplification. However, we need to consider a more realistic 3D model and solve wave equations with 3D numerical methods in order to improve our understanding of basin amplification. In this study, we extend a 2D pseudospectral and finite difference hybrid method to a 3D case and investigate the effects of the vertical velocity gradient for a 3D basin model. Numerical simulations were performed for four basin models with increasing vertical velocity gradients on a PC cluster using 64 processors for 67 108 864 discretized grids. The results show that the vertical velocity gradient enhances basin amplification through strong secondary surface waves and basin trapped waves. The 3D geometry of the basin causes a wave-front focusing effect that contributes significantly to a localized strong amplification with the maximum peak ground velocity in the basin. The results of this study suggest that it is important to consider the detailed properties of sedimentary basins in seismic ground motion studies.

Kinematics of stars in the northern and southern galactic hemispheres

We use vector spherical harmonics for a kinematic analysis of the proper motions of stars from the Hipparcos, Tycho-2, and UCAC3 catalogues in the northern and southern Galactic hemispheres. We have found that the statistically reliable values of the Ogorodnikov-Milne model parameters M32+ and M32− have different signs in different hemispheres. This is a consequence of the Galaxy’s rotational retardation with distance from the principal Galactic plane. Based on various samples of stars from the above catalogues, we have obtained the following estimate for the magnitude of the vertical gradient of Galactic rotation velocity in the solar neighborhoods: (20.1 ± 2.9) < |∂V⊙/∂z| < (49.2 ± 0.8) km s−1 kpc−1. Another result that is revealed by our analysis of the parameters M13− and M13+ in different Galactic hemispheres is that the vertical gradient of expansion velocity for the stellar system ∂VR/∂z is positive in the northern hemisphere and negative in the southern one. This suggests that the expansion velocity VR increases with distance fromthe Galactic plane. We show that both these gradients give rise to an apparent acceleration of the solar motion along the x and y axes of the rectangular Galactic coordinate system. Our analysis of the parameters M21− and M12+ shows no significant differences in both hemispheres and has allowed us to determine the Oort parameters, to estimate the Galactic rotation velocity and period in the solar neighborhood, and to calculate the ratio of the epicyclic frequency to the angular velocity of Galactic rotation in the solar neighborhood. The derived diagonal elements of the velocity field deformation tensor suggest that the orientation of the rectangular Galactic coordinate system in space must be determined by taking into account not only the geometrical factors but also the dynamical ones. All these results agree well with these quantities estimated over the entire sphere by various authors.

Profiles of the turbulent-exchange coefficient and suspension concentration in a system of stratified currents

The theoretical distribution of the turbulent-diffusion coefficient for a system of stratified currents is presented taking the specific features of exchange in boundary layers and in zones with a zero vertical-velocity gradient into account. The suspension-diffusion equation is solved using the obtained turbulent-viscosity distribution. The theoretical solution is tested against field measurements of the suspension-concentration distribution over the entire depth of a water body in four systems of currents.

An integrated geophysical study of Vestbakken Volcanic Province, western Barents Sea continental margin, and adjacent oceanic crust

This paper describes results from a geophysical study in the Vestbakken Volcanic Province, located on the central parts of the western Barents Sea continental margin, and adjacent oceanic crust in the Norwegian-Greenland Sea. The results are derived mainly from interpretation and modeling of multichannel seismic, ocean bottom seismometer and land station data along a regional seismic profile. The resulting model shows oceanic crust in the western parts of the profile. This crust is buried by a thick Cenozoic sedimentary package. Low velocities in the bottom of this package indicate overpressure. The igneous oceanic crust shows an average thickness of 7.2 km with the thinnest crust (5–6 km) in the southwest and the thickest crust (8–9 km) close to the continent-ocean boundary (COB). The thick oceanic crust is probably related to high mantle temperatures formed by brittle weakening and shear heating along a shear system prior to continental breakup. The COB is interpreted in the central parts of the profile where the velocity structure and Bouguer anomalies change significantly. East of the COB Moho depths increase while the vertical velocity gradient decreases. Below the assumed center for Early Eocene volcanic activity the model shows increased velocities in the crust. These increased crustal velocities are interpreted to represent Early Eocene mafic feeder dykes. East of the zone of volcanoes velocities in the crust decrease and sedimentary velocities are observed at depths of more than 10 km. The amount of crustal intrusions is much lower in this area than farther west. East of the Knolegga Fault crystalline basement velocities are brought close to the seabed. This fault marks the eastern limit of thick Cenozoic and Mesozoic packages on central parts of the western Barents Sea continental margin.

Vertical dispersion of model microorganisms in horizontal shear flow

AbstractMicroorganisms often swim upwards due to the cell’s phototaxis, chemotaxis or geotaxis, in flow fields with vertical velocity gradients. In this study, the vertical dispersion of model microorganisms was investigated under horizontal shear conditions. A microorganism was modelled as a spherical squirmer with or without bottom-heaviness. First, the three-dimensional movement of 100 identical squirmers in a homogeneous suspension was computed by the Stokesian dynamics method. The results show that the dispersion of squirmers is strongly affected by the swimming velocity and bottom-heaviness of the cells and the shear rate of the background flow. The vertical diffusion is considerably smaller than the horizontal diffusion. Interestingly, the vertical diffusion decreases as the volume fraction and the stresslet of squirmers decrease, which is opposite of the tendency in diffusion with no background flow. Next, a continuum model of a suspension of squirmers was developed using the diffusion tensor and the drift velocity to simulate the spatial distribution of squirmers in macroscopic flow fields. The results of the continuum model illustrate that the gyrotactic trapping found by Durham, Kessler &amp; Stocker (Science, vol. 323, 2009, pp. 1067–1070) also appears in the present model considering cell–cell hydrodynamic interactions. In the case of horizontal Poiseuille flow, the volume fraction of bottom-heavy cells in the channel becomes considerably larger than that at the inlet. These fundamental findings are helpful for understanding the distribution of microorganisms in various water regimes in nature and industry.

The role of large-scale magnetic fields in galaxy NGC 891: can magnetic fields help to reduce the local mass-to-light ratio in the galactic outskirts?

We address the problem of the influence of large-scale magnetic fields on galactic rotation for the example of the spiral galaxy NGC 891. Based on its rotation curve and the surface density of HI we determine, in the framework of the global disc model, the surface density of matter. Then, based on the surface brightness, we determine the corresponding profile of the local mass-to-light ratio. We also model the vertical gradient of azimuthal velocity in the quasi-circular-orbit approximation, and compare it with measurements. We discuss what factors may influence the rotation of matter in NGC 891 and how this can translate to changes in the profile of the local mass-to-light ratio. In particular, we discuss the possible effect of magnetic fields on the motion of ionized gas, and, consequently, on the determination of the profile of the local mass-to-light ratio. Finally, we put forward the hypothesis that the asymmetry in magnetic fields observed in NGC 891 might be responsible for the observed anomalous behaviour of the vertical gradient.

Assessing vertical soil moisture dynamics using multi-frequency GPR common-midpoint soundings

Soil moisture measurement techniques are of utmost importance to vadose zone hydrologists. Surface hydrogeophysical methods, such as ground-penetrating radar (GPR), have the capacity to provide field-scale soil moisture information across a range of depth scales. This paper presents an extensive field study using multi-frequency (i.e., 225 MHz, 450 MHz, 900 MHz) GPR common-midpoint (CMP) soundings to monitor a complete annual cycle of soil moisture conditions at three distinct sites. We examine the use of normal-moveout (NMO) velocity analysis applied to CMP data for monitoring highly dynamic vertical soil moisture conditions in a mid-latitude climate consisting of wetting/drying and freeze/thaw cycles with varying degrees of magnitude and vertical velocity gradient. NMO velocity analysis is used to construct interval-velocity-depth models at a fixed location collected every 1–4 weeks. These time-lapse models are combined to construct temporal interval-velocity fields, which are converted into soil moisture content using an appropriate petrophysical relationship. Using these moisture fields, we were able to characterize the vertical distribution and dynamics of soil moisture in the shallow vadose zone. Although the use of multiple antenna frequencies provided varying investigation depths and vertical resolving capabilities, optimal characterization of soil moisture conditions was obtained with high-frequency 900 MHz antennas. The integration of direct ground wave and NMO velocity data from a single CMP sounding allowed us to better refine the shallow soil moisture profile and underlying vadose zone conditions during seasonal wetting, drying and freezing cycles. This study demonstrates the capacity of GPR to characterize vertical moisture dynamics, and highlights the importance of collecting high-resolution data along the air–soil interface to resolve the water content profile from the surface down to the deeper vadose zone conditions.

Eddy Diffusivities for Momentum and Heat in the Upper Troposphere and Lower Stratosphere Measured by MU Radar and RASS, and a Comparison of Turbulence Model Predictions

Abstract Recently, middle- and upper-atmosphere Doppler radar (MU radar) has enabled the measurement of middle-atmosphere turbulence from radar backscatter Doppler spectra. In this work, eddy diffusivities for momentum Km in the upper troposphere and lower stratosphere during clear-air conditions were derived from direct measurements of the Reynolds stress and vertical gradient of mean wind velocity measured by MU radar. Eddy diffusivity for heat Kh below 8 km was determined from measurements of temperature fluctuations by the Radio Acoustic Sounding System (RASS) attached to the MU radar. The eddy diffusivity for momentum was on the order of 10 m2 s−1 in the upper troposphere and decreased gradually in the stratosphere by an order of magnitude or more. The eddy diffusivity for heat was almost of the same order of magnitude as Km. Estimates of eddy diffusivity from the radar echo power spectral width give fairly good values compared with the direct measurement of Km. Applicability of three turbulence models—the spectral width method, the k–ɛ model modified for stratified flows, and the algebraic stress model—were also examined, using radar observation values of turbulent kinetic energy k and turbulent energy dissipation rate ɛ together with atmospheric stability observations from rawinsonde data. It is concluded that the algebraic stress model shows the best fit with the direct measurement of Km, even in the free atmosphere above the atmospheric boundary layer once k and ɛ values are obtained from observations or a model.

Improving storm surge estimates: Increased downwards transfer of horizontal momentum by wind-driven waves

The numerical predictions of historical storm surges in which the low pressure meteorological system remains well offshore requires a factor three, or more, wind stress than that provided using the standard wind stress coefficients found in the literature. The literature values are from the ‘air side’, where wind stress coefficients are determined either from the measured vertical velocity gradient of the wind over the water or more commonly from wind Reynolds stresses. On the other hand, the wind stress required to match the observed storm surges is consistent with the momentum transfer observed during wind-wave growth experiments (i.e., the inferred wind stress coefficients from experiments measuring wave height growth due to wind). Both the wind-wave growth data and our storm surge modelling are consistent with field and laboratory measurements of Reynolds stresses of wind-driven waves. The possibility that there is more momentum being transferred downwards urges the development of a storm surge model capable of using the wind stress inferred from the wind-wave growth data. This requires a Reynolds stress model covering deep through to shallow water depths and at arbitrary levels (3D model implementation), which has been formulated herein. Application of this wind stress to Tropical Cyclone Roger using the steady shallow water equations qualitatively explains the observed storm surge. This new approach also raises the question of why storm surge estimates are generally acceptable for weather systems that cross the coastline despite the use of momentum transfer based on air side wind stress.

Understanding and modeling turbulent fluxes and entrainment in a gravity current

We present an experimental study of the mixing processes in a gravity current flowing on an inclined plane. The turbulent transport of momentum and density can be described in a very direct and compact form by a Prandtl mixing length model: the turbulent vertical fluxes of momentum and density are found to scale quadratically with the vertical mean gradients of velocity and density. The scaling coefficient, the square of the mixing length, is approximately constant over the mixing zone of the stratified shear layer. We show how, in different flow configurations, this length can be related to the shear length of the flow ( ε / ∂ z u 3 ) 1 / 2 . We also study the fluctuations of the momentum and density turbulent fluxes, showing how they relate to mixing and to the entrainment/detrainment balance. We suggest a quantitative measure of local entrainment and detrainment derived from observed conditional correlations of density flux and density or vertical velocity fluctuations.

Assessment of longitudinal dispersion coefficients using Acoustic Doppler Current Profilers in large river

The present paper provides algorithms to be used in calculating longitudinal dispersion coefficients using ADCP data driven by either vertical or transverse velocity gradients in large river, and describes software components capitalizing on these ADCP measurement capabilities to provide the longitudinal dispersion coefficients based on in-situ measurements. The paper couples in an innovative way the wealth of data provided by ADCPs with robust and theoretical algorithms to compute longitudinal dispersion coefficient relying only on actual velocity data, rather assuming horizontal or vertical velocity models due to traditional lack of field data. The paper clearly provides the promise of ADCP data and the associated analytical algorithms for estimating longitudinal dispersion coefficients. We also compared longitudinal dispersion coefficients obtained with the theoretical formula using ADCP with those from the other available alternative empirical formulas, and found that empirical formula overestimated the longitudinal dispersion coefficient in large river. Therefore, further use of the software and the embedded procedures can uniquely support in-situ measurement campaigns designed to document important aspects of the dispersion processes and formulation of reliable knowledge that circumvent the empirical approaches of the past.

Network velocity gradients in the photosphere

We present an extension of the Unno-Rachkovsky solution that provides the theoretical profiles coming out of a Milne-Eddington atmosphere imbedded in a magnetic field, and that then takes a vertical velocity gradient into account. Thus, the theoretical profiles may display asymmetries as do the observed profiles, which facilitates the inversion based on the Unno-Rachkovsky theory, and leads to the additional determination of the vertical velocity gradient. We present UNNOFIT inversion on synthetic data and spectropolarimetric observations performed on an active region of the Sun with the French-Italian telescope THEMIS operated by CNRS and CNR on the island of Tenerife.

Modification of the land surface energy balance relationship by introducing vertical sensible heat advection and soil heat storage over the Loess Plateau

Little is known about the surface energy balance problem for a complex underlying surface. Taking data from the Loess Plateau Land-surface Processes Experiment (LOPEX) and investigating the characteristics of the surface energy balance over a complex underlying surface, this paper calculates the soil heat storage and vertical sensible heat advection, analyzes their contributions to the surface energy imbalance, and discusses the mechanism by which the vertical velocity and temperature gradient in the surface layer affect the vertical sensible heat advection transfer. We found that the vertical velocity in the surface layer provides the necessary dynamic power for vertical sensible heat advection, and a relatively strong temperature gradient is the energy source generating vertical sensible heat advection. Under an ascending condition, the effect of vertical sensible heat advection on the surface energy budget is more obvious. It is also found that when the soil heat storage term and the vertical sensible heat advection term are added to the energy balance equation, the imbalance significantly improves. The peak of average diurnal residuals decreases from 125.1 to 41.5 W m−2, the daily average absolute value of residuals falls from 59.0 to 26.4 W m−2, and the surface energy balance closure increases from 78.4% to 94.0%.

Large-eddy simulation of turbulent transports in urban street canyons in different thermal stabilities

Five sets of large-eddy simulations (LES) were performed to examine the characteristics of flows and pollutant dispersion in two-dimensional (2D) urban street canyons of unity building-height-to-street-width ratio in neutral, unstable, and stable thermal stratifications. The characteristic flows fall into the skimming flow regime for all the cases tested. The mean wind speed is increased and decreased, respectively, in unstable and stable conditions. Turbulence is enhanced in unstable conditions. Whereas, in stable conditions, the low-level temperature inversion weakens the recirculating flows forming another layer of stagnant air in the vicinity of the ground level. Unexpectedly, an increase in turbulence is found in the street canyon core in the slightly stable condition (Richardson number Rb=0.18). The turbulence promotion could be caused by the unique geometry of 2D street canyon in which the stable stratification slows down the primary recirculation. The rather stagnant flows in turn sharpen the roof-level vertical velocity gradient and deter the entrainment penetrating down to the ground level, leading to a substantial pollutant accumulation. While the pollutant tends to be well mixed in the street canyons in neutral and unstable conditions, a mildly improved pollutant removal in unstable conditions is observed because of the enhanced roof-level buoyancy-driven turbulence.