Cloud-base vertical velocity statistics: a comparison between an atmospheric mesoscale model and remote sensing observations

The statistics of cloud-base vertical velocity simulated by the non-hydrostatic mesoscale model AROME are compared with Cloudnet remote sensing observations at two locations: the ARM SGP site in Central Oklahoma, and the DWD observatory at Lindenberg, Germany. The results show that, as expected, AROME significantly underestimates the variability of vertical velocity at cloud-base compared to observations at their nominal resolution; the standard deviation of vertical velocity in the model is typically 4-6 times smaller than observed, and even more during the winter at Lindenberg. Averaging the observations to the horizontal scale corresponding to the physical grid spacing of AROME (2.5 km) explains 70-80% of the underestimation by the model. Further averaging of the observations in the horizontal is required to match the model values for the standard deviation in vertical velocity. This indicates an effective horizontal resolution for the AROME model of at least 4 times the physically-defined grid spacing. The results illustrate the need for special treatment of sub-grid scale variability of vertical velocities in kilometer-scale atmospheric models, if processes such as aerosol-cloud interactions are to be included in the future.

Cyclic extrusion of a lava dome based on a stick-slip mechanism

Lava dome eruptions are sometimes characterised by large periodic fluctuations in extrusion rate over periods of hours that may be accompanied by Vulcanian explosions and pyroclastic flows. We consider a simple system of nonlinear equations describing a 1D flow of lava extrusion through a deep elastic dyke feeding a shallower cylindrical conduit in order to simulate this short-period cyclicity. Stick-slip conditions depending on a critical shear stress are assumed at the wall boundary of the cylindrical conduit. By analogy with the behaviour of industrial polymers in a plastic extruder, the elastic dyke acts like a barrel and the shallower cylindrical portion of the conduit as a die for the flow of magma acting as a polymer. When we applied the model to the Soufrière Hills Volcano, Montserrat, for which the key parameters have been evaluated from previous studies, cyclic extrusions with periods from 3 to 30 h were readily simulated, matching observations. The model also reproduces the reduced period of cycles observed when a major unloading event occurs due to lava dome collapse.

Estimation of the friction velocity in stably stratified boundary-layer flows over hills

A method is suggested for the calculation of the friction velocity for stable turbulent boundary-layer flow over hills. The method is tested using a continuous upstream mean velocity profile compatible with the propagation of gravity waves, and is incorporated into the linear model of Hunt, Leibovich and Richards with the modification proposed by Hunt, Richards and Brighton to include the effects of stability, and the reformulated solution of Weng for the near-surface region. Those theoretical results are compared with results from simulations using a non-hydrostatic microscale-mesoscale two-dimensional numerical model, and with field observations for different values of stability. These comparisons show a considerable improvement in the behaviour of the theoretical model when the friction velocity is calculated using the method proposed here, leading to a consistent variation of the boundary-layer structure with stability, and better agreement with observational and numerical data.

Dissipation of shear-free turbulence near boundaries

The rapid-distortion model of Hunt & Graham (1978) for the initial distortion of turbulence by a flat boundary is extended to account fully for viscous processes. Two types of boundary are considered: a solid wall and a free surface. The model is shown to be formally valid provided two conditions are satisfied. The first condition is that time is short compared with the decorrelation time of the energy-containing eddies, so that nonlinear processes can be neglected. The second condition is that the viscous layer near the boundary, where tangential motions adjust to the boundary condition, is thin compared with the scales of the smallest eddies. The viscous layer can then be treated using thin-boundary-layer methods. Given these conditions, the distorted turbulence near the boundary is related to the undistorted turbulence, and thence profiles of turbulence dissipation rate near the two types of boundary are calculated and shown to agree extremely well with profiles obtained by Perot & Moin (1993) by direct numerical simulation. The dissipation rates are higher near a solid wall than in the bulk of the flow because the no-slip boundary condition leads to large velocity gradients across the viscous layer. In contrast, the weaker constraint of no stress at a free surface leads to the dissipation rate close to a free surface actually being smaller than in the bulk of the flow. This explains why tangential velocity fluctuations parallel to a free surface are so large. In addition we show that it is the adjustment of the large energy-containing eddies across the viscous layer that controls the dissipation rate, which explains why rapid-distortion theory can give quantitatively accurate values for the dissipation rate. We also find that the dissipation rate obtained from the model evaluated at the time when the model is expected to fail actually yields useful estimates of the dissipation obtained from the direct numerical simulation at times when the nonlinear processes are significant. We conclude that the main role of nonlinear processes is to arrest growth by linear processes of the viscous layer after about one large-eddy turnover time.

Kinematical analysis of redundant drive wire mechanisms with velocity constraint

In this paper, we propose a new velocity constraint type for Redundant Drive Wire Mechanisms. The purpose of this paper is to demonstrate that the proposed velocity constraint module can fix the orientation of the movable part and to use the kinematical analysis method to obtain the moving direction of the movable part. First, we discuss the necessity of using this velocity constraint type and the possible applications of the proposed mechanism. Second, we derive the basic equations of a wire mechanism with this constraint type. Next, we present a method of motion analysis on active and passive constraint spaces, which is used to find the moving direction of a movable part. Finally, we apply the above analysis method on a wire mechanism with a velocity constraint module and on a wire mechanism with four double actuator modules. By evaluating the results, we prove the validity of the proposed constraint type.

Axonal velocity distributions in neural feld equations

By modelling the average activity of large neuronal populations, continuum mean field models (MFMs) have become an increasingly important theoretical tool for understanding the emergent activity of cortical tissue. In order to be computationally tractable, long-range propagation of activity in MFMs is often approximated with partial differential equations (PDEs). However, PDE approximations in current use correspond to underlying axonal velocity distributions incompatible with experimental measurements. In order to rectify this deficiency, we here introduce novel propagation PDEs that give rise to smooth unimodal distributions of axonal conduction velocities. We also argue that velocities estimated from fibre diameters in slice and from latency measurements, respectively, relate quite differently to such distributions, a significant point for any phenomenological description. Our PDEs are then successfully fit to fibre diameter data from human corpus callosum and rat subcortical white matter. This allows for the first time to simulate long-range conduction in the mammalian brain with realistic, convenient PDEs. Furthermore, the obtained results suggest that the propagation of activity in rat and human differs significantly beyond mere scaling. The dynamical consequences of our new formulation are investigated in the context of a well known neural field model. On the basis of Turing instability analyses, we conclude that pattern formation is more easily initiated using our more realistic propagator. By increasing characteristic conduction velocities, a smooth transition can occur from self-sustaining bulk oscillations to travelling waves of various wavelengths, which may influence axonal growth during development. Our analytic results are also corroborated numerically using simulations on a large spatial grid. Thus we provide here a comprehensive analysis of empirically constrained activity propagation in the context of MFMs, which will allow more realistic studies of mammalian brain activity in the future.

On the group-velocity property for wave-activity conservation laws

The density and the flux of wave-activity conservation laws are generally required to satisfy the group-velocity property: under the WKB approximation (i.e., for nearly monochromatic small-amplitude waves in a slowly varying medium), the flux divided by the density equals the group velocity. It is shown that this property is automatically satisfied if, under the WKB approximation, the only source of rapid variations in the density and the flux lies in the wave phase. A particular form of the density, based on a self-adjoint operator, is proposed as a systematic choice for a density verifying this condition.

On the generalized eigenvalue problem for the Rossby wave vertical velocity in the presence of mean flow and topography

In a series of papers, Killworth and Blundell have proposed to study the effects of a background mean flow and topography on Rossby wave propagation by means of a generalized eigenvalue problem formulated in terms of the vertical velocity, obtained from a linearization of the primitive equations of motion. However, it has been known for a number of years that this eigenvalue problem contains an error, which Killworth was prevented from correcting himself by his unfortunate passing and whose correction is therefore taken up in this note. Here, the author shows in the context of quasigeostrophic (QG) theory that the error can ulti- mately be traced to the fact that the eigenvalue problem for the vertical velocity is fundamentally a non- linear one (the eigenvalue appears both in the numerator and denominator), unlike that for the pressure. The reason that this nonlinear term is lacking in the Killworth and Blundell theory comes from neglecting the depth dependence of a depth-dependent term. This nonlinear term is shown on idealized examples to alter significantly the Rossby wave dispersion relation in the high-wavenumber regime but is otherwise irrelevant in the long-wave limit, in which case the eigenvalue problems for the vertical velocity and pressure are both linear. In the general dispersive case, however, one should first solve the generalized eigenvalue problem for the pressure vertical structure and, if needed, diagnose the vertical velocity vertical structure from the latter.

Critical slip and time dependence in sea ice friction

Recent research into sea ice friction has focussed on ways to provide a model which maintains much of the clarity and simplicity of Amonton's law, yet also accounts for memory effects. One promising avenue of research has been to adapt the rate- and state- dependent models which are prevalent in rock friction. In such models it is assumed that there is some fixed critical slip displacement, which is effectively a measure of the displacement over which memory effects might be considered important. Here we show experimentally that a fixed critical slip displacement is not a valid assumption in ice friction, whereas a constant critical slip time appears to hold across a range of parameters and scales. As a simple rule of thumb, memory effects persist to a significant level for 10 s. We then discuss the implications of this finding for modelling sea ice friction and for our understanding of friction in general.

Optimization of a sea ice model using basinwide observations of Arctic sea ice thickness, extent, and velocity

A stand-alone sea ice model is tuned and validated using satellite-derived, basinwide observations of sea ice thickness, extent, and velocity from the years 1993 to 2001. This is the first time that basin-scale measurements of sea ice thickness have been used for this purpose. The model is based on the CICE sea ice model code developed at the Los Alamos National Laboratory, with some minor modifications, and forcing consists of 40-yr ECMWF Re-Analysis (ERA-40) and Polar Exchange at the Sea Surface (POLES) data. Three parameters are varied in the tuning process: Ca, the air–ice drag coefficient; P*, the ice strength parameter; and α, the broadband albedo of cold bare ice, with the aim being to determine the subset of this three-dimensional parameter space that gives the best simultaneous agreement with observations with this forcing set. It is found that observations of sea ice extent and velocity alone are not sufficient to unambiguously tune the model, and that sea ice thickness measurements are necessary to locate a unique subset of parameter space in which simultaneous agreement is achieved with all three observational datasets.

Power transfer in velocity-vortex acceleration

A theoretical model is presented of an electron acceleration-as-oscillator method derived from the work of Joseph Larmor unified with J. Clerk Maxwell’s theory of vorticity for the displacement of radiation into free-space at an antenna interface.

Studying the contact point and interface moving in a sinusoidal tube with lattice Boltzmann method

The multicomponent nonideal gas lattice Boltzmann model by Shan and Chen (S-C) is used to study the immiscible displacement in a sinusoidal tube. The movement of interface and the contact point (contact line in three-dimension) is studied. Due to the roughness of the boundary, the contact point shows "stick-slip" mechanics. The "stick-slip" effect decreases as the speed of the interface increases. For fluids that are nonwetting, the interface is almost perpendicular to the boundaries at most time, although its shapes at different position of the tube are rather different. When the tube becomes narrow, the interface turns a complex curves rather than remains simple menisci. The velocity is found to vary considerably between the neighbor nodes close to the contact point, consistent with the experimental observation that the velocity is multi-values on the contact line. Finally, the effect of three boundary conditions is discussed. The average speed is found different for different boundary conditions. The simple bounce-back rule makes the contact point move fastest. Both the simple bounce-back and the no-slip bounce-back rules are more sensitive to the roughness of the boundary in comparison with the half-way bounce-back rule. The simulation results suggest that the S-C model may be a promising tool in simulating the displacement behaviour of two immiscible fluids in complex geometry.

The importance of vertical velocity variability for estimates of the indirect aerosol effects

The activation of aerosols to form cloud droplets is dependent upon vertical velocities whose local variability is not typically resolved at the GCM grid scale. Consequently, it is necessary to represent the subgrid-scale variability of vertical velocity in the calculation of cloud droplet number concentration. This study uses the UK Chemistry and Aerosols community model (UKCA) within the Hadley Centre Global Environmental Model (HadGEM3), coupled for the first time to an explicit aerosol activation parameterisation, and hence known as UKCA-Activate. We explore the range of uncertainty in estimates of the indirect aerosol effects attributable to the choice of parameterisation of the subgrid-scale variability of vertical velocity in HadGEM-UKCA. Results of simulations demonstrate that the use of a characteristic vertical velocity cannot replicate results derived with a distribution of vertical velocities, and is to be discouraged in GCMs. This study focuses on the effect of the variance (σw2) of a Gaussian pdf (probability density function) of vertical velocity. Fixed values of σw (spanning the range measured in situ by nine flight campaigns found in the literature) and a configuration in which σw depends on turbulent kinetic energy are tested. Results from the mid-range fixed σw and TKE-based configurations both compare well with observed vertical velocity distributions and cloud droplet number concentrations. The radiative flux perturbation due to the total effects of anthropogenic aerosol is estimated at −1.9 W m−2 with σw = 0.1 m s−1, −2.1 W m−2 with σw derived from TKE, −2.25 W m−2 with σw = 0.4 m s−1, and −2.3 W m−2 with σw = 0.7 m s−1. The breadth of this range is 0.4 W m−2, which is comparable to a substantial fraction of the total diversity of current aerosol forcing estimates. Reducing the uncertainty in the parameterisation of σw would therefore be an important step towards reducing the uncertainty in estimates of the indirect aerosol effects. Detailed examination of regional radiative flux perturbations reveals that aerosol microphysics can be responsible for some climate-relevant radiative effects, highlighting the importance of including microphysical aerosol processes in GCMs.