Vertical Kinetic Energy Research Articles

Can a Descending Rain Curtain in a Supercell Instigate Tornadogenesis Barotropically?

Abstract This paper investigates whether the descending rain curtain associated with the hook echo of a supercell can instigate a tornado through a purely barotropic mechanism. A simple numerical model of a mesocyclone is constructed in order to rule out other tornadogenesis mechanisms in the simulations. The flow is axisymmetric and Boussinesq with constant eddy viscosity in a neutrally stratified environment. The domain is closed to avoid artificial decoupling of a vortex from the storm-scale circulation. In the principal simulation, the initial condition is a balanced, slowly decaying, Beltrami flow describing an updraft that is rotating cyclonically at midlevels around a low pressure center surrounded by a concentric downdraft that revolves cyclonically but has anticyclonic vorticity. The boundary conditions are no slip on the tangential wind and free slip on the radial or vertical wind to accommodate this initial condition and to allow strong interaction of a vortex with the ground. Precipitation is released through the top above the updraft and falls to the ground near the updraft–downdraft interface in an annular curtain. The downdraft enhancement induced by the precipitation drag upsets the balance of the Beltrami flow. The downdraft and its outflow toward the axis increase low-level convergence beneath the updraft and transport air with moderately high angular momentum downward and inward where it is entrained and stretched by the updraft. The resulting tornado has a corner region with an intense axial jet and low pressure capped by a vortex breakdown and a transition to a broader vortex aloft (a tornado cyclone). A clear slot of subsiding air with anticyclonic vorticity surrounds the vortex. The vertical kinetic energy of the entire circulation declines dramatically prior to tornado formation.

Long-term MST radar observations of vertical wave number spectra of gravity waves in the tropical troposphere over Gadanki (13.5° N, 79.2° E): comparison with model spectra

Abstract. The potential utility of Mesosphere-Stratosphere-Troposphere (MST) radar measurements of zonal, meridional and vertical winds for divulging the gravity wave vertical wave number spectra is discussed. The data collected during the years 1995–2004 are used to obtain the mean vertical wave number spectra of gravity wave kinetic energy in the tropical troposphere over Gadanki (13.5° N, 79.2° E). First, the climatology of 3-dimensional wind components is developed using ten years of radar observations, for the first time, over this latitude. This climatology brought out the salient features of background tropospheric winds over Gadanki. Further, using the second order polynomial fit as background, the day-to-day wind anomalies are estimated. These wind anomalies in the 4–14 km height regions are used to estimate the profiles of zonal, meridional and vertical kinetic energy per unit mass, which are then used to estimate the height profile of total kinetic energy. Finally, the height profiles of total kinetic energy are subjected to Fourier analysis to obtain the monthly mean vertical wave number spectra of gravity wave kinetic energy. The monthly mean vertical wave number spectra are then compared with a saturation spectrum predicted by gravity wave saturation theory. A slope of 5/3 is used for the model gravity wave spectrum estimation. In general, the agreement is good during all the months. However, it is noticed that the model spectrum overestimates the PSD at lower vertical wave numbers and underestimates it at higher vertical wave numbers, which is consistently observed during all the months. The observed discrepancies are attributed to the differences in the slopes of theoretical and observed gravity wave spectra. The slopes of the observed vertical wave number spectra are estimated and compared with the model spectrum slope, which are in good agreement. The estimated slopes of the observed monthly vertical wave number spectra are in the range of −2 to −2.8. The significance of the present study lies in using the ten years of data to estimate the monthly mean vertical wave number spectra of gravity waves, which will find their application in representing the realistic gravity wave characteristics in atmospheric models.

Sand detachment under rains with varying angle of incidence

In the case of wind-driven rain, as the angle of rain incidence increases, greater force components act parallel to the surface and lower force components act perpendicular to the surface. Therefore, raindrop impact angle could influence the detachment process in the existence of substantial lateral jet development. This could be particularly significant for a cohesionless sand surface that has a weaker resistance to the dislodgement by a raindrop impact than a soil surface. Experiments of simulated wind-driven rain were conducted to evaluate sand detachment rates under increased lateral jetting induced by wind velocities of 6.4, 10.0, and 12.0 m s− 1 at nozzle operating pressures of 75, 100, and 150 kPa and incident on windward and leeward slopes of 4 and 9°. With these set-ups, it was possible to have varying angles of incidence and to determine the effect of the compressive stress and shear stress, evaluated by the horizontal and vertical kinetic energy fluxes (Etx and Etz, respectively), on the detachment rates from the sand surface. At the same vectorwise sum of Etz and Etx, the results showed that there was, for similar values of Etz and Etx in windward slopes, more sand detachment rate; however, for dissimilar values of Etz and Etx in leeward slopes where Etx was significantly higher than Etz, there was less sand detachment rate. Consequently, with certain values of the compressive stress and shear stress, the sand detachment rates under wind-driven rains peaked; and Etz was the limiting component since the rates significantly decreased as Etz particularly decreased in spite of very large values of Etx.

High-Frequency Internal Waves on the Oregon Continental Shelf

Abstract Measurements of vertical velocity by isopycnal-following, neutrally buoyant floats deployed on the Oregon shelf during the summers of 2000 and 2001 were used to characterize internal gravity waves on the shelf using measurements of vertical velocity. The average spectrum of Wentzel–Kramers–Brillouin (WKB)-scaled vertical kinetic energy has the level predicted by the Garrett–Munk model (GM79), plus a narrow M2 tidal peak and a broad high-frequency peak extending from about 0.1N to N and rising a decade above GM79. The high-frequency peak varies in energy coherently with time across its entire bandwidth. Its energy is independent of the tidal energy. The energy in the “continuum” region between the peaks is weakly correlated with the level of the high-frequency peak energy and is independent of the tidal peak energy. The vertical velocity is not Gaussian but is highly intermittent, with a calculated kurtosis of 19. The vertical kinetic energy varies geographically. Low energy is found offshore and nearshore. The highest energy is found near a small seamount. High energy is found over the rough topography of Heceta Bank and near the shelf break. The highest energy occurs as packets of high-frequency waves, often occurring on the sharp downward phase of the M2 internal tide and called “tidal solibores.” A few isolated waves with high energy are also found. Of the 1-h periods with the highest vertical kinetic energy, 31% are tidal solibores, 8% are isolated waves, and the remainder of the periods appear unorganized. The two most energetic tidal solibores were examined in detail. As compared with the steady, propagating, two-dimensional, inviscid, internal-wave solutions to the equations of motion with no background shear [i.e., the Dubreil–Jacotin–Long (DJL) equation], all but the most energetic observed waveforms are too narrow for their height to be solitary waves. Despite the large near-N peak in vertical kinetic energy, the M2 internal tide contributes over 80% of the energy, ignoring near-inertial waves. The tidal solibores make a very small contribution, 0.5%, to the overall internal-wave energy.

Turbulent transport in the outer region of rough-wall open-channel flows: the contribution of large coherent shear stress structures (LC3S)

Acoustic Doppler velocity profiler (ADVP) measurements of instantaneous three-dimensional velocity profiles over the entire turbulent boundary layer height, δ, of rough-bed open-channel flows at moderate Reynolds numbers show the presence of large scale coherent shear stress structures (called LC3S herein) in the zones of uniformly retarded streamwise momentum. LC3S events over streamwise distances of several boundary layer thicknesses dominate the mean shear dynamics. Polymodal histograms of short streamwise velocity samples confirm the subdivision of uniform streamwise momentum into three zones also observed by Adrian et al. (J. Fluid Mech., vol. 422, 2000, p. 1). The mean streamwise dimension of the zones varies between 1δ and 2.5δ. In the intermediate region (0.2<z/δ<0.75), the contribution of conditionally sampled u'w' events to the mean vertical turbulent kinetic energy (TKE) flux as a function of threshold level H is found to be generated by LC3S events above a critical threshold level Hmax for which the ascendant net momentum flux between LC3S of ejection and sweep types is maximal. The vertical profile of Hmax is nearly constant over the intermediate region, with a value of 5 independent of the flow conditions. Very good agreement is found for all flow conditions including the free-stream shear flows studied in Adrian et al. (2000). If normalized by the squared bed friction velocity, the ascendant net momentum flux containing 90% of the mean TKE flux is equal to 20% of the shear stress due to bed friction. In the intermediate region this value is nearly constant for all flow conditions investigated herein. It can be deduced that free-surface turbulence in open-channel flows originates from processes driven by LC3S, associated with the zonal organization of streamwise momentum. The good agreement with mean quadrant distribution results in the literature implies that LC3S identified in this study are common features in the outer region of shear flows.

A numerical investigation of the Stokes boundary layer in the turbulent regime

The Stokes boundary layer in the turbulent regime is investigated by using large-eddy simulations (LES). The Reynolds number, based on the thickness of the Stokes boundary layer, is set equal to Reδ = 1790, which corresponds to test 8 of the experimental study of Jensen et al. (J. Fluid Mech. vol. 206, 1989, p. 265).Our results corroborate and extend the findings of relevant experimental studies: the alternating phases of acceleration and deceleration are correctly reproduced, as is the sharp transition to turbulence, observable at a phase angle between 30° and 45°, and its maximum between 90° and 105°. Overall, a very good agreement was found between our LES first- and second-order turbulent statistics and those of Jensen et al. (1989). Some discrepancies were observed when comparing turbulent intensities in the phases of the cycle characterized by a low level of turbulent activity.In the central part of the cycle, namely from the mid acceleration to the late deceleration phases, fully developed equilibrium turbulence is present in the flow field, and the boundary layer resembles that of a canonical, steady, wall-bounded flow. In those phases characterized by low turbulent activity, two separate regions can be detected in the flow field: a near-wall one, where the vertical turbulent kinetic energy varies much more rapidly than the other two components, thus giving rise to the formation of horizontal, pancake-like turbulence; and an outer region where both vertical and spanwise velocity fluctuations vary much faster than the streamwise ones, hence producing cigar-like turbulence.As a side result, the range of application of the plane-averaged dynamic mixed model was assessed based on the qualitative behaviour over the cycle of a significant parameter representing the ratio between a turbulent time scale and a free-stream time scale associated with the oscillatory motion.

Relationship between vertical shear rate and kinetic energy dissipation rate in stably stratified flows

High resolution direct numerical simulations of strongly stratified turbulence are analyzed in order to investigate the relationship between vertical shearing of horizontal motions and the dissipation rate of kinetic energy. The relative magnitude of each component of the dissipation rate is examined as a function of the Reynolds number and of the buoyancy Reynolds number. From the simulation results, in conjunction with published laboratory results, it is concluded that (1) the simulation results are consistent with the laboratory data but span a much larger range of buoyancy Reynolds number, (2) the ratio of the square of the vertical shear rate to the dissipation rate is a strong function of buoyancy Reynolds number, and (3) the approximation that vertical shear rate is the dominant cause of energy dissipation rate is only good when the buoyancy Reynolds number is less than order one.

Running over rough terrain: guinea fowl maintain dynamic stability despite a large unexpected change in substrate height

In the natural world, animals must routinely negotiate varied and unpredictable terrain. Yet, we know little about the locomotor strategies used by animals to accomplish this while maintaining dynamic stability. In this paper, we perturb the running of guinea fowl with an unexpected drop in substrate height (DeltaH). The drop is camouflaged to remove any visual cue about the upcoming change in terrain that would allow an anticipatory response. To maintain stability upon a sudden drop in substrate height and prevent a fall, the bird must compensate by dissipating energy or converting it to another form. The aim of this paper is to investigate the control strategies used by birds in this task. In particular, we assess the extent to which guinea fowl maintain body weight support and conservative spring-like body dynamics in the perturbed step. This will yield insight into how animals integrate mechanics and control to maintain dynamic stability in the face of real-world perturbations. Our results show that, despite altered body dynamics and a great deal of variability in the response, guinea fowl are quite successful in maintaining dynamic stability, as they stumbled only once (without falling) in the 19 unexpected perturbations. In contrast, when the birds could see the upcoming drop in terrain, they stumbled in 4 of 20 trials (20%, falling twice), and came to a complete stop in an additional 6 cases (30%). The bird's response to the unexpected perturbation fell into three general categories: (1) conversion of vertical energy (EV=EP+EKv) to horizontal kinetic energy (EKh), (2) absorption of EV through negative muscular work (-DeltaEcom), or (3) converting EP to vertical kinetic energy (EKv), effectively continuing the ballistic path of the animal's center of mass (COM) from the prior aerial phase. However, the mechanics that distinguish these categories actually occur along a continuum with varying degrees of body weight support and actuation by the limb, related to the magnitude and direction of the ground reaction force (GRF) impulse, respectively. In most cases, the muscles of the limb either produced or absorbed energy during the response, as indicated by net changes in COM energy (Ecom). The limb likely begins stance in a more retracted, extended position due to the 26 ms delay in ground contact relative to that anticipated by the bird. This could explain the diminished decelerating force during the first half of stance and the exchange between EP and EK during stance as the body vaults over the limb. The varying degree of weight support and energy absorption in the perturbed step suggests that variation in the initial limb configuration leads to different intrinsic dynamics and reflex action. Future investigation into the limb and muscle mechanics underlying these responses could yield further insight into the control mechanisms that allow such robust dynamic stability of running in the face of large, unexpected perturbations.

Specific kinetic energy concept for regular waves

The global kinetic energy of regular waves is usually characterized through the characteristic parameters wave height and wave length without reference to its vertical distribution. In this paper a new methodology to evaluate the vertical energy distribution from the velocity components is presented. The methodology could also be an alternative for irregular wave fields, with several wave lengths, to which the traditional method in the evaluation of the energy per unit area or wave length is not applicable. The squared velocity components functions for each water level can be theoretical or determined from long enough measurements time series. The average of those functions at one specific depth level over the length of interest gives the mean horizontal and vertical specific kinetic energy at that level. The global kinetic energy corresponds to the total specific kinetic energy integration in depth.

Large-scale Vertical Momentum, Kinetic Energy and Moisture Fluxes in the Antarctic Sea-ice Region

There are very strong thermal gradients between the Antarctic continent and the sea-ice zone, and between that zone and the ocean to the north. As a result of these contrasts the sea-ice domain is one of strong cyclogenesis and high cyclone frequency. In this study we explore many aspects of that cyclonic behaviour and investigate the manner in which these systems influence, and are influenced by, the sea ice. Using the NCEP-DOE re-analyses (1979–2002) we have determined variables that are proportional to the mean of the wind stress and the mean rate at which mechanical energy is imparted to the surface. Using two decompositions of the wind field we have obtained estimates of how much of these fluxes are contributed to by the transient eddies. We find these to be significant over the sea ice and the ocean to the north, particularly when a new decomposition is used. The presence of frequent and vigorous cyclones is a central factor that determines the positive mean freshwater flux over the sea-ice zone in all seasons. This transfer to the ocean is smallest in summer (0.49 mm day−1) and assumes a maximum of 1.27 mm day−1 in winter.

The mechanics of jumpingversussteady hopping in yellow-footed rock wallabies

The goal of our study was to explore the mechanical power requirements associated with jumping in yellow-footed rock wallabies and to determine how these requirements are achieved relative to steady-speed hopping mechanics. Whole body power output and limb mechanics were measured in yellow-footed rock wallabies during steady-speed hopping and moving jumps up to a landing ledge 1.0 m high (approximately 3 times the animals' hip height). High-speed video recordings and ground reaction force measurements from a runway-mounted force platform were used to calculate whole body power output and to construct a limb stiffness model to determine whole limb mechanics. The combined mass of the hind limb extensor muscles was used to estimate muscle mass-specific power output. Previous work suggested that a musculoskeletal design that favors elastic energy recovery, like that found in tammar wallabies and kangaroos, may impose constraints on mechanical power generation. Yet rock wallabies regularly make large jumps while maneuvering through their environment. As jumping often requires high power, we hypothesized that yellow-footed rock wallabies would be able to generate substantial amounts of mechanical power. This was confirmed, as we found net extensor muscle power outputs averaged 155 W kg(-1) during steady hopping and 495 W kg(-1) during jumping. The highest net power measured reached nearly 640 W kg(-1). As these values exceed the maximum power-producing capability of vertebrate skeletal muscle, we suggest that back, trunk and tail musculature likely play a substantial role in contributing power during jumping. Inclusion of this musculature yields a maximum power output estimate of 452 W kg(-1) muscle. Similar to human high-jumpers, rock wallabies use a moderate approach speed and relatively shallow leg angle of attack (45-55 degrees) during jumps. Additionally, initial leg stiffness increases nearly twofold from steady hopping to jumping, facilitating the transfer of horizontal kinetic energy into vertical kinetic energy. Time of contact is maintained during jumping by a substantial extension of the leg, which keeps the foot in contact with the ground.

Wave Response during Hydrostatic and Geostrophic Adjustment. Part II: Potential Vorticity Conservation and Energy Partitioning

Abstract This second part of a two-part study of the hydrostatic and geostrophic adjustment examines the potential vorticity and energetics of the acoustic waves, buoyancy waves, Lamb waves, and steady state that are generated following the prescribed injection of heat into an isothermal atmosphere at rest. The potential vorticity is only nonzero for the steady class and depends only on the spatial and time-integrated properties of the injection. The waves contain zero net potential vorticity, but undergo a time-dependent vorticity exchange involving latent and relative vorticities. The energy associated with a given injection may be partitioned distinctly among the various wave classes. The characteristics of this partitioning depend on the spatiotemporal detail of the injection, as well as whether the imbalance is generated by injection of heat, mass, or momentum. Spatially, waves of a scale similar to that of the injection are preferentially excited. Temporally, an extended duration injection preferentially filters high-frequency waves. An instantaneous injection, that is, the temporal Green’s function, contains the largest proportions of the high-frequency waves. The proportions of kinetic, available elastic, and available potential energies that are carried by the various waves are functions of the homogeneous system. For example, deep buoyancy waves of small horizontal scale primarily contain equal portions of available potential and vertical kinetic energy. The steady state contains more available potential energy than kinetic energy at small horizontal scale, and vice versa. These qualities of the wave energetics illustrate the mechanisms that characterize the physics of each wave class. The evolution and spectral partitioning of the energetics following localized warmings identical to those in Part I are presented in order to illustrate some of these basic properties of the energetics. For example, a heating lasting longer than a few minutes does not excite acoustic waves. However, Lamb waves of wide horizontal scale can be excited by a heating of several hours. The first buoyancy waves to be filtered by an extended duration heating are those of the deepest and narrowest structure that have a frequency approaching the buoyancy frequency. The energetics of the steady state depends only on the spatial and time-integrated properties of the warming. However, the energetics and transient evolution toward a given steady state depend on the temporal properties of the warming and may differ widely.

Observations of Transient Linear Organization and Nonlinear Scale Interactions in Lake-Effect Clouds. Part II: Nonlinear Scale Interactions

Abstract Linearly organized convection and associated horizontal roll vortices occasionally occur in atmospheric conditions in which theory predicts only cellular organization. One possible contributor to the occurrence of rolls in such conditions is nonlinear interactions between different scales of motion. In the winter of 1997/98, the Lake-Induced Convection Experiment (Lake-ICE) was conducted in part to investigate scale interactions in linearly organized convection. As discussed in Part I of this series, transient linear organization was observed during a wintertime lake-effect event during Lake-ICE. In Part II two-part nonlinear scale interactions and their possible role in the occurrence of linear organization in an unfavorable environment are investigated. Turbulence-scale vertical velocity variance peaks were consistently observed during roll strengthening and decay, suggesting a link between the scales. Composites of the nonlinear interaction terms in the roll-scale vertical turbulent kinetic energy (TKE) budget revealed that nonlinear interactions between the roll and turbulence scales were large compared to the observed change in roll-scale TKE, but do not coincide in time.

Adequacy of laboratory simulation of in-line skater falls

Currently most laboratory simulation of distal radius fractures and wrist injuries has been with axial limb loading or vertical drop technique. To better assess the contribution of horizontal velocity in momentum in the development of wrist injury and wrist fracture we have compared forces and fracture patterns for fall simulations involving strictly vertical impacts with those that incorporated horizontal momentum in fresh-frozen upper extremities. The premise for testing was based on a forward fall onto the palmar surface of an outstretched arm. A 45 degrees-incline impact device was used to model the horizontal and vertical velocity components of a skater fall at a representative speed. Sled mass was 26.2 kg. A 45.5-kg vertical impact system furnished contrasting data and represented prior state-of-the-art technology. Drop heights were adjusted to compensate for discrepancy in sled mass. Measurements from either impact system included vertical and horizontal forces and kinetic energy at impact. Fracture patterns were assessed radiographically. Nine trials were conducted with the incline device and 11 trials were conducted with the vertical impact system. The fracture rate was substantially higher for vertical impacts versus incline impacts (82% vs 33%). The rate of carpal fractures also was higher. Vertical and horizontal forces were similar statistically although slightly greater for vertical impacts. Kinetic energy, however, was 3 times greater for incline impacts than for vertical impacts. These kinetic parameters support the argument that the incline impacts should have resulted in far greater injury. The data suggest horizontal momentum changes limb loading. We submit that published methods for modeling skater falls have failed to provide a true simulation of the event in question.

The role of stability and moisture in the diurnal cycle of convection over land

AbstractThe diurnal cycle of convection over land is investigated by a cloud‐resolving model simulation. Three regimes of convection—dry, shallow, and deep—successively take place during daytime under the presence of substantial convective available potential energy. The convective inhibition (CIN) and the normalized saturation deficit (NSD) in the cloud‐base layer are identified as the major two variables that characterize the cycle of the convective regimes. The surface heating during daytime leads to the development of a quasi‐dry well‐mixed convective planetary boundary layer (PBL). This yields a decrease of CIN while NSD remains steady. Shallow convection is initiated as soon as the CIN becomes lower locally than the vertical kinetic energy in the PBL. This timing also marks the minimum of CIN, both in local and in domain‐mean senses. Then, detrainment of moisture from the cloud layer gradually moistens the low free troposphere, resulting in a NSD decrease. Finally, deep convection is triggered when sufficient moistening is realized, as measured by a NSD minimum. During deep convection, NSD rapidly increases and CIN increases. Once CIN has exceeded the vertical kinetic energy in the PBL, deep convection ceases. Copyright © 2004 Royal Meteorological Society

On the seemingly incompatible parcel and globally integrated views of the energetics of triggered atmospheric deep convection over land

AbstractThe energetics of the diurnal cycle of atmospheric deep convection over land remain difficult to understand and simulate accurately with current cumulus parametrizations. Furthermore, a proper formulation has remained elusive owing to seeming incompatibilities between, on the one hand, the parcel view of energetics which relies on such concepts as Convective Available Potential Energy (CAPE) and Convective Inhibition (CIN), and, on the other hand, the globally integrated view, which relies on such concepts as Moist Available Energy (MAE), reference states, and energy conversion terms. While the MAE is intuitively the global counterpart of the parcel‐defined CAPE, there seems to be no global analogue to the parcel‐defined concept of energy barrier attached to CIN. To gain insights into this issue, a new cost function PE is introduced to quantify the amount of positive or negative energy required for a given sounding to undergo an arbitrary adiabatic rearrangement of mass, and which encompasses both the parcel‐defined and global energy concepts as particular cases. The function PE offers a complementary view of the stability and energy characteristics of atmospheric soundings, whose local minima are naturally associated with the reference states of the system.It is established that:(a) MAE is essentially equivalent to CAPE multiplied by a mass conversion factor Mb which scales as the amount of convectively unstable boundary‐layer air. Using the available summer 1997 IOP data from the ARM–SGP site, Mb is found to correlate with CAPE, which suggests the existence of a functional relationship between CAPE and MAE; if further confirmed, this result would considerably simplify the computation of MAE.(b) A global counterpart to the parcel‐defined concept of energy barrier can only be defined if the system considered admits several reference states, and not one as is classically assumed. In that case, energy barriers naturally arise as the amount of energy required to switch from one reference state to another. In the context of triggered deep convection, there must be at least two reference states: a shallow one, which is the actual state (or a slightly modified one if there is boundary layer CAPE), and a deep one associated with the release of MAE/CAPE; the energy barrier separating these two reference states naturally defines a generalized CIN.In the limited context of the above‐mentioned IOP ARM data, it is further shown that:(c) Spatially averaged conditions exhibiting potential instability to deep convection may be associated with individual soundings having widely different stability characteristics, including absolute stability, potential instability, and absolute instability; this suggests that triggered deep convection may not necessarily be the result of a parcel's vertical kinetic energy exceeding its negative buoyancy, but rather from the destruction of convective inhibition (i.e. production of absolute instability) in a local region.(d) A few local soundings exhibit multiple reference states, corresponding roughly to multiple levels of neutral buoyancy. These may allow for convective clouds with cloud‐top heights significantly lower than those classically predicted by the undiluted ascent of a boundary‐layer air parcel up to its highest level of neutral buoyancy, even in the absence of complex entrainment scenarios. Copyright © 2004 Royal Meteorological Society

Measurements of Turbulent Vertical Kinetic Energy in the Ocean Mixed Layer from Lagrangian Floats

D’Asaro, in previous work using nearly neutrally buoyant Lagrangian floats in a wind forced mixed layer, found ^w2 &5 , where ^w2& is the mean square vertical velocity and u * is the friction velocity estimated 2 Au * from shipboard meteorological measurements using bulk formulas. Depth profiles of A(z) 5^ w 2 &(z)/ within 2 u * the mixed layer showed a maximum value of A(z) of about 2, which is 1.75‐2 times that measured in solidwall turbulent boundary layers driven by a wall stress alone. This result implied that the ocean mixed layer was more energetic than shear-driven turbulent boundary layers driven by the same stress. Here these results are verified using observations of vertical velocity in the mixed layer from 72 float days of data from two Lagrangian floats in the North Pacific Ocean in the autumn of 2000. These floats were more neutrally buoyant than those used previously by D’Asaro, thus reducing possible biases. Wind stress was estimated from Quick Scatterometer satellite measurements and is thus subject to errors and biases different from those in D’Asaro’s previous work. Despite these instrumental differences, the new results are very similar to those of the previous work, except that no corrections for internal wave velocities are needed. The values of ^w 2

Structure of unsteady stably stratified turbulence with mean shear

The statistics of unsteady turbulence with uniform stratification N (Brunt–Vaisala frequency) and shear α(=dU1/dx3) are analysed over the entire time range (0 0 and \it Ri>0.25 respectively, oscillatory momentum and positive and negative density fluxes develop. Above a critical value of \it Ri\scriptsize\it crit(∼0.3), their average values are persistently countergradient. This structural change in the turbulence is the primary mechanism whereby stable stratification reduces the fluxes and the production of variances. It is quite universal and differs from the energy and stability mechanisms of Richardson (1926) and Taylor (1931). The long-time asymptotics of the energy ratio ER(=\it PE/VKE) of the potential energy to the vertical kinetic energy generally decreases with \it Ri(≥0.25), reaching the smallest value of 3/2 when there is no shear (\it Ri→∞). For strong mean shear (\it Ri<0.25), RDT significantly overestimates ER since (as in unstratified shear flow) it underestimates the vertical kinetic energy VKE. The RDT results show that the asymptotic values of the energy ratio ER and the normalized vertical density flux are independent of the initial value of ER, in agreement with DNS. This independence of the initial condition occurs because the ratios of the contributions from the initial values PE0 and KE0 are the same for PE and VKE and can be explained by the linear processes. Stable stratification generates buoyancy oscillations in the direction of the energy propagation of the internal gravity wave and suppresses the generation of turbulence by mean shear. Because the shear distorts the wavenumber fluctuations, the low-wavenumber spectrum of the vertical kinetic energy has the general form E33(k)∝(αtk)−1, where (LXαt)−1≪k≪L−1X (LX: integral scale). The viscous decay is controlled by the shear, so that the components of larger streamwise wavenumber k1 decay faster. Then, combined with the spectrum distortion by the shear, the energy and the flux are increasingly dominated by the small-k1 components as time elapses. They oscillate at the buoyancy period π/N because even in a shear flow the components as k1→0 are weakly affected by the shear. The effects of stratification N and shear α at small scales are to reduce both VKE and PE. Even for the same \it Ri, larger N and α reduce the high-wavenumber components of VKE and PE. This supports the applicability of the linear assumption for large N and α. At large scales, the stratification and shear effects oppose each other, i.e. both VKE and PE decrease due to the stratification but they increase due to the shear. We conclude that certain of these unsteady results can be applied directly to estimate the properties of sheared turbulence in a statistically steady state, but others can only be applied qualitatively.

Dynamic Resources Used in Ambulation by Children With Spastic Hemiplegic Cerebral Palsy: Relationship to Kinematics, Energetics, and Asymmetries

The atypical walking pattern in children with spastic cerebral palsy is assumed to involve kinematic and morphological adaptations that allow them to move. The purpose of this study was to explore how the requirements of the task and the energy-generating and energy-conserving capabilities of children with cerebral palsy relate to kinematic and mechanical energy patterns of walking. Six children with hemiplegic cerebral palsy and a matched group of typically developing children participated in the study. Kinematic data were collected at 5 different walking speeds. Vertical stiffness, mechanical energy parameters, and landing angle were measured during the stance phase. The affected side of the children with cerebral palsy showed greater vertical stiffness, a greater ratio of kinetic forward energy to potential energy, and a smaller landing angle when compared with those of the nonaffected lower extremity and with those of typically developing children. Previous research has shown that children with cerebral palsy assumed a gait similar to an inverted pendulum on the nonaffected limb and a pogo stick on the affected limb. Our results indicate that asymmetries between lower extremities and differences from typically developing children in the landing angle of the lower extremity, vertical lower-extremity stiffness, and kinetic and potential energy profiles support the claim that walking patterns in children with spastic hemiplegic cerebral palsy emerge as a function of the resources available to them.

Linear processes in stably and unstably stratified rotating turbulence

Unsteady turbulence in stably and unstably stratified flow with system rotation around the vertical axis is analysed using the rapid distortion theory (RDT). Complete linear solutions for the spectra, variances and covariances are obtained analytically, and their characteristics, including the short- and long-time asymptotics and the effect of initial conditions, are examined in detail. It has been found that the rotation modifies the energy partition among the three kinetic energy components and the potential energy, and the ratio of the Coriolis parameter f to the Brunt–Väisälä frequency N, i.e. f/N, determines the final steady values of these components. The ratio also determines the phase of the energy/flux oscillation. Depending on whether f/N &gt; 1 or f/N &lt; 1, there is a phase shift of ±π/4. However, unsteady aspects are largely dominated by stratification. This occurs because the effects of the Coriolis parameter f appear only in the form of fk3, which vanishes for the horizontal wavenumber components (k3 = 0), which contribute most to the energies and the fluxes. For example, the oscillation frequency of the energies and the fluxes asymptotes to 2N over a long time, in agreement with the stratified non-rotating turbulence. The initial time development is also dominanted by the stratification, and the short-time asymptotics (Nt, ft [Lt ] 1) agree with those for non-rotating stratified fluids in the lowest-order approximation. In the special case of f = N, all the wavenumber components oscillate in phase, leading to no inviscid decay of oscillation. This is in contrast to the general case of f ≠ N, in which inviscid decay has been observed. For pure rotation (f ≠ 0, N = 0), analytical solutions showed that any turbulence that is initially axisymmetric around the rotation axis recovers exact three-dimensional isotropy in the kinetic energy components. Comparison with previous DNS and experiments shows that many of the unsteady aspects of the kinetic and potential energies and the vertical density flux can be explained by the linear processes described by RDT. Even the time development of the vertical vorticity, which would represent the small-scale characteristics of turbulence, agrees well with DNS. For unstably stratified turbulence, the initial processes observed in DNS and experiments, such as the initial decay of the kinetic energy due to viscosity and the subsequent rapid growth of the vertical kinetic energy compared to the horizontal kinetic energy, could be explained by RDT.