Vertical Profile Of Horizontal Velocity Research Articles

An Analytical Solution to the Perturbation Analysis of the Interaction between Downburst Outflows and Atmospheric Boundary Layer Winds

Abstract Downbursts are negatively buoyant downdrafts that emerge from a storm and spread outward upon hitting the surface. The produced outflow, however, is not spreading through a calm environment, but rather through an atmosphere characterized by larger-scale atmospheric boundary layer (ABL) winds. This interaction between ABL winds and downbursts forms an outflow that is more complex than an outflow created by an isolated downdraft. Here, we propose an analytical solution of the interaction between the ABL winds and an isolated downburst outflow. The model is applicable when the ratio of centerline downdraft velocity to the horizontal ABL velocity at the cloud base is larger than the nondimensional group (H/D)(r/H)1.1, where H is the cloud-base height, D is the diameter of the downdraft, and r is the distance from the centerline of isolated downdraft. Also, the solution is derived for a specific direction in the outflow when the ABL winds and the isolated downburst outflow are aligned and the vertical profiles of radial velocity are self-similar. The model is based on the use of impinging-jet dynamics, their spreading rates, and a universal renormalization group that describes numerous laboratory measurements of velocity profiles of impinging jets issuing into both quiescent and crossflowing backgrounds. The model assumes a “known” base state corresponding to an isolated downburst, and then derives its interaction with ABL winds by way of perturbation analysis. The radial and vertical profiles of horizontal velocity from our analytical model are compared against field observations of actual downbursts and other analytical models and physical simulations of downburst-like outflows. Significance Statement Downbursts are intense downdrafts that emerge from a thunderstorm and spread outward upon hitting the surface. Near-surface wind gusts in a downburst can be similar to those observed in an EF3-rated tornado (∼75 m s−1). A downburst outflow is not spreading through a calm environment, but rather through an atmosphere characterized by larger-scale atmospheric boundary layer (ABL) winds. This interaction between ABL winds and downbursts forms an outflow that is more complex than an outflow created by an isolated downdraft. However, most of the current analytical models of downbursts do not account for this interaction. Using experimental measurements of downburst-like impinging jets and mathematical rigor, our study derives an equation that quantifies this interaction between downburst and ABL winds.

Assessment of Turbulent Mixing Associated With Eddy‐Wave Coupling Based on Autonomous Observations From the Arctic Canada Basin

AbstractInteraction between mesoscale eddies and near‐inertial internal waves can contribute to enhanced turbulence mixing but quantitative knowledge from in situ observations is still lacking. This study reveals how eddy/near‐inertial wave interactions (ENIs) can affect the variability of turbulent mixing in the ice‐covered Canada Basin of the Arctic Ocean. We use data from five Ice‐Tethered Profiler with Velocity (ITP‐V) systems that autonomously obtained vertical profiles of horizontal velocity as well as temperature and salinity, which enabled quantification of ENI‐caused turbulent mixing using a fine‐scale parameterization. From the ITP‐V observations in 2013–2015, 67 anticyclones were detected, of which 90% had a deep core at 150–250 m depth. The remaining eddies had a shallow core, typically embedded in the Pacific Summer Water (PSW). Just over one third of the eddies showed evidence of ENI with enhanced near‐inertial internal wave amplitude (NIW) near the eddy cores. For these ENI cases, the parameterized turbulence dissipation rate was O (10−10–10−8 W kg−1), the larger estimates being several orders of magnitude greater than the background level. For the deep eddies, the ENI process can largely be accounted for by the classical theory, NIWs are trapped inside the negative relative vorticity core of anticyclones. For one shallow eddy, the NIW signal was greatest below the core. We postulate that a vertically elongated system of NIWs cannot be constrained vertically within such small‐cored eddies. It is also interpreted that the wave enhancement below the core was supported by the isopycnal slope near the PSW through its geostrophic shear.

Wind in a Natural and Artificial Wildland Fire Fuel Bed

Fuel beds represent the layer of fuel that typically supports continuous combustion and wildland fire spread. We examine how wind propagates through and above loose and packed pine needle beds and artificial 3D-printed fuel beds in a wind tunnel. Vertical profiles of horizontal velocities are measured for three artificial fuel beds with prescribed porosities and two types of fuel beds made with long-leaf pine needles. The dependence of the mean velocity within the fuel bed with respect to the ambient velocity is linked to the porosity. Experimental results show significant structure to the vertical profile of mean flow within the bed, and suggest that small-scale sweeps and ejections play a role in this system redistributing momentum similar to larger-scale canopy flows.

Drag coefficient parameter estimation for aquaculture systems

The flow conditions in and around a suspended canopy, resembling those formed by aquaculture structures such as rafts cages and longlines, were modeled using an augmented version of the hydrodynamic model Environmental Fluid Dynamics Code. The model was calibrated using vertical profiles of horizontal velocities, Reynolds stresses, and turbulent kinetic energies obtained from prior laboratory flume experiments. The parameter estimation code, PEST, was used to optimize various model parameters including horizontal momentum diffusivity, vertical eddy viscosity, turbulence closure constants, and, most importantly, depth-dependent drag coefficients. An increasing average drag coefficient was observed with decreasing canopy blockage ratio, and an empirical relationship for the vertical variation of drag coefficient was developed that may be appropriate for use in full-scale models of aquaculture systems. Overall, the calibrated canopy-turbulence parameters and drag-coefficient empiricisms may yield improved predictions of alterations to hydrodynamic and nutrient-transport conditions due to various aquaculture structures. Such predictions will help develop methods to minimize environmental impacts and to increase production from aquaculture farms.

Horizontal Circulation Patterns in a Large Shallow Lake: Taihu Lake, China

Wind induced hydrodynamic circulations play significant roles in the transport and mixing process of pollutants and nutrients in large shallow lakes, but they have been usually overlooked, while environmental, biological, and ecological aspects of eutrophication problems get the most focus. Herein we use a three-dimensional model, driven by steady/unsteady wind, river discharge, rainfall, evaporation to investigate the spatially heterogeneous, large-scale hydrodynamic circulations and their role in transporting and mixing mechanisms in Taihu Lake. Wind direction and velocity determines the overall hydrodynamic circulation structure, i.e. direction, intensity, and position. A relative stable hydrodynamic circulation pattern has been formed shortly with steady wind (~2 days). Vertical profiles of horizontal velocities are linearly correlated to the relative shallowness of water depth. Volume exchange between subbasins, influenced by wind speed and initial water level, differs due to the complex topography and irregular shape. With unsteady wind, these findings are still valid to a high degree. Vertical variations in hydrodynamic circulation are important in explaining the surface accumulation of algae scums in Meiliang Bay in summers. Vorticity of velocity field, a key indicator of hydrodynamic circulation, is determined by wind direction, bathymetry gradient, and water depth. The maximum change of velocity vorticity happens when wind direction is perpendicular to bathymetry gradient. Furthermore, Lagrangian-based tracer transport is used to estimate emergency pollution leakage impacts, and also to evaluate operational management measurements, such as, the large-scale water transfer. The conclusion is that the large-scale water transfer does not affect the hydrodynamic circulation and volume exchanges between subbasins significantly, but succeeds to transport and then mix the fresh, clean Yangtze River water to a majority area of Taihu Lake.

An assessment of the roller approach for wave breaking in a hybrid finite-volume finite-difference Boussinesq-type model for the surf-zone

This paper investigates the application of the roller approach for breaking waves in a 1D hybrid finite-volume finite-difference weakly-nonlinear Boussinesq-type model. The vorticity transport equation is employed to model the movement of vorticity through the fluid. This allows vertical profiles of horizontal velocity and undertow to be computed. Previous implementations of this method caused numerical dissipation that influenced the physical behaviour of the breaking process. The use of a hybrid scheme overcomes this issue as the need to filter flow variables in the surf-zone is removed. Greater numerical stability increases the flexibility of the calibration parameters, allowing finer control over the breaking process and a more detailed investigation of the underlying physics. The mechanism used to dissipate energy during breaking is derived from physical principles and the Boussinesq equations are retained throughout the breaking procedure, providing a realistic description of the hydrodynamics throughout the surf-zone. The dissipative performance of the proposed model is discussed and compared with other state-of-the-art approaches, proving the feasibility and value of using a rotational roller model with a finite-volume finite-difference scheme to model surf-zone hydrodynamics with a Boussinesq-type model. Tests involving waves breaking on a sloping beach are performed to validate against results from physical experiments, demonstrating the model to be capable of accurately resolving profiles of the free surface, velocity and undertow. The resulting new model overcomes many of the issues encountered by previous Boussinesq solvers based on the same approach and provides significant improvements in the accuracy of predictions of breaking wave processes. The proposed approach is very flexible and can be used in any hybrid finite-volume finite-difference weakly-nonlinear Boussinesq-type model.

Observations of pockmark flow structure in Belfast Bay, Maine, Part 1: current-induced mixing

Field observations of current profiles and temperature, salinity, and density structure were used to examine vertical mixing within two pockmarks in Belfast Bay, Maine. The first is located in 21 m water depth (sea level to rim), nearly circular in shape with a 45 m rim diameter and 12 m rim-to-bottom relief. The second is located in 25 m water depth, more elongated in shape with an approximately 80 m (36 m) major (minor) axis length at the rim, and 17 m relief. Hourly averaged current profiles were acquired from bottom-mounted acoustic Doppler current profilers deployed on the rim and center of each pockmark over successive 42 h periods in July 2011. Conductivity–temperature–depth casts at the rim and center of each pockmark show warmer, fresher water in the upper water column, evidence of both active and fossil thermocline structure 5–8 m above the rim, and well-mixed water below the rim to the bottom. Vertical velocities show up- and down-welling events that extend into the depths of each pockmark. An observed temperature change at both the rim and center occurs coincident with an overturning event below the rim, and suggests active mixing of the water column into the depths of each pockmark. Vertical profiles of horizontal velocities show depth variation at both the center and rim consistent with turbulent logarithmic current boundary layers, and suggest that form drag may possibly be influencing the local flow regime. While resource limitations prevented observation of the current structure and water properties at a control site, the acquired data suggest that active mixing and overturning within the sampled pockmarks occur under typical benign conditions, and that current flows are influenced by upstream bathymetric irregularities induced by distant pockmarks.

Observations of pockmark flow structure in Belfast Bay, Maine, Part 2: evidence for cavity flow

Pockmark flow circulation patterns were investigated through current measurements along the rim and center of two pockmarks in Belfast Bay, Maine. Observed time-varying current profiles have a complex vertical and directional structure that rotates significantly with depth and is strongly dependent on the phase of the tide. Observations of the vertical profiles of horizontal velocities in relation to relative geometric parameters of the pockmark are consistent with circulation patterns described qualitatively by cavity flow models (Ashcroft and Zhang 2005). The time-mean behavior of the shear layer is typically used to characterize cavity flow, and was estimated using vorticity thickness to quantify the growth rate of the shear layer horizontally across the pockmark. Estimated positive vorticity thickness spreading rates are consistent with cavity flow predictions, and occur at largely different rates between the two pockmarks. Previously modeled flow (Brothers et al. 2011) and laboratory measurements (Pau et al. 2014) over pockmarks of similar geometry to those examined herein are also qualitatively consistent with cavity flow circulation, suggesting that cavity flow may be a good first-order flow model for pockmarks in general.

Experimental investigation of the impact of macroalgal mats on the wave and current dynamics

Macroalgal mats of Ulva intestinalis are becoming increasingly common in many coastal and estuarine intertidal habitats, thus it is important to determine whether they increase flow resistance, promote bed stability and therefore reduce the risk of erosion favoring tidal flooding or degradation of coastal lagoons. Venier et al. (2012) [6] studied the impact of macroalgal mats of Ulva intestinalis on flow dynamics and sediment stability for uniform flow. Here we extend their experimental work to the case of vegetation under the combined action of waves and currents. These hydrodynamic conditions are very common in many shallow coastal environments and lagoons. The experimental facility employed in the present study and the series of flow runs are the same as that used by Venier et al. (2012)[6]. However, waves have been superposed to uniform current flowing firstly over a mobile sediment bed covered with U. intestinalis, then over a bare sediment surface. For the depth, wave and current conditions considered in the experiments, the time-averaged vertical profile of horizontal velocity for the case of coexisting waves and current turns out to be very close to that observed for a pure current, both with and without vegetation. However, contrary to what was observed in the case of a unidirectional current, in the presence of waves the time averaged velocity profile is only weakly influenced by the vegetation, whose main effect is to attenuate velocity oscillations induced by waves and to slightly increase the overall bed roughness.

Evaluation of nonlocal and local planetary boundary layer schemes in the WRF model

A realistic reproduction of planetary boundary layer (PBL) structure and its evolution is critical to numerical simulation of regional meteorology and air quality. Conversely, insufficient realism in the simulated physical properties often leads to degraded meteorological and air quality prognostic skills. This study employed the Weather Research and Forecasting model (WRF) to evaluate model performance and to quantify meteorological prediction differences produced by four widely used PBL schemes. Evaluated were two nonlocal PBL schemes, YSU and ACM2, and two local PBL schemes, MYJ and Boulac. The model grid comprised four nested domains at horizontal resolutions of 27 km, 9 km, 3 km and 1 km respectively. Simulated surface variables 2 m temperature and 10 m wind at 1 km resolution were compared to measurements collected in Hong Kong. A detailed analysis of land‐atmosphere energy balance explicates heat flux and temperature variability among the PBL schemes. Differences in vertical profiles of horizontal velocity, potential temperature, bulk Richardson number and water vapor mixing ratio were examined. Diagnosed PBL heights, estimated by scheme specific formulations, exhibited the large intrascheme variance. To eliminate formulation dependence in PBL height estimation, lidar measurements and a unified diagnosis were jointly used to reanalyze PBL heights. The diagnosis showed that local PBL schemes produced shallower PBL heights than those of nonlocal PBL schemes. It is reasonable to infer that WRF, coupled with the ACM2 PBL physics option can be a viable producer of meteorological forcing to regional air quality modeling in the Pearl River Delta (PRD) Region.

Influence of sediment and secondary currents on velocity

This paper investigates the vertical profile of horizontal velocity in sediment-laden flows. In contrast to previous investigators who assume that the velocity follows the log-law, this study demonstrates that the velocity in sediment-laden flows follows the power law, rather than the log-law. The mechanism of this shift has been attributed to the presence of upwards wall-normal velocity v caused by density stratification. Starting from Reynolds equations, this paper clearly shows that the log-law can be obtained only when v = 0. For flows with v ≠ 0, the momentum flux (uv) causes the deviation of Reynolds shear stress (−u′v¯′) from the standard linear distribution, and subsequently the integration of Reynolds equation yields the power law. The notable experimental datasets in the literature support the theory that the velocity profile in sediment-laden flows follows the power law, rather than the log-law. The validity of the proposed model has been verified using experimental data, and good agreement between the predicted and observed profiles has been achieved.

Temporal Variability of High Vertical Wavenumber Shear over the Izu-Ogasawara Ridge

Recent numerical studies (Hibiya et al., 1996, 1998, 2002) showed that the energy cascade across the internal wave spectrum down to small dissipation scales was un- der strong control of parametric subharmonic instabilities (PSI) which transfer en- ergy from low vertical mode double-inertial frequency internal waves to high vertical mode near-inertial internal waves. To see whether or not the numerically-predicted energy cascade process is actually dominant in the real deep ocean, we examine the temporal variability of vertical profiles of horizontal velocity observed by deploying a number of expendable current profilers (XCPs) at one location near the Izu- Ogasawara Ridge. By calculating EOFs, we find the observed velocity profiles are dominated by low mode semidiurnal (~double-inertial frequency) internal tides and high mode near-inertial internal waves. Furthermore, we find that the WKB-stretched vertical scales of the near-inertial current shear are about 250 sm and 100 sm. The observed features are reasonably explained if the energy cascade down to small dissi- pation scales is dominated by PSI.

Radiating Instabilities of Internal Inertio-Gravity Waves

The vertical radiation of local convective and shear instabilities of internal inertio-gravity waves is examined within linear stability theory. A steady, plane-parallel Boussinesq flow with vertical profiles of horizontal velocity and static stability resembling an internal inertio-gravity wave packet without mean vertical shear is used as the dynamical framework. The influence of primary wave frequency and amplitude, as well as orientation and horizontal wavenumber of the instability on vertical radiation, is discussed. Considerable radiation occurs at small to intermediate instability wavenumbers for basic-state gravity waves with high to intermediate frequencies and moderately convectively supercritical amplitudes. Radiation is then strongest when the horizontal wave vector of the instability is aligned parallel to the horizontal wave vector of the basic-state gravity wave. These radiating modes are essentially formed by shear instability. Convective instabilities, that occur at large instability wavenumbers or strongly convectively supercritical amplitudes, as well as shear instabilities of low-frequency basic-state gravity waves, are nonradiating, trapped in the region of instability. The radiation of an instability is found to be related to the existence of critical levels, a radiating mode being characterized by the absence of critical levels outside the region of instability of the primary wave.

Hydrodynamic and sediment suspension modelling in estuarine systems: Part II: Application to the Western Scheldt and Gironde estuaries

Applications of the 3D-baroclinic numerical model described in Part I of this paper were performed in the Western Scheldt (The Netherlands) and Gironde (France) estuaries. Simulations provide an insight into cohesive sediment transport and its dependency on 3D flow features. In the Scheldt estuary, non-linear processes associated with the geometry of the estuary and the vertical profile of horizontal velocity generate effective upward and downward movements promoting vertical mixing. These movements are responsible for the small vertical gradient of density. The sediment distribution is characterised by two zones of high concentration associated with the different characteristics of bottom sediments. The maximum turbidity is not directly associated with the density currents but mainly with the variation in estuarine width and its effects on flow field. In the Gironde estuary, the vertical gradient of the residual velocity is small. Until pk70, the flow is seaward over the whole cross-section. Between pk70 and the estuarine mouth there is a large eddy with seaward flow in the northern channel. The inward velocity is stronger near the surface, suggesting that the residual flow is associated with the tidal movement and, to a less extent, with the density. The simulation of cohesive sediment transport accounting for the effects of the density current shows that the location of the turbidity maximum is strongly controlled by the fluvial discharges.

Mixing process in estuaries

A theoretical expression for vertical profile of horizontal velocity in tenns of its depth-average is derived based on oscillatory boundary layer theory and estuarine flow characteristics. The derived theoretical profile is then incorporated into a vertical quasi-two-dimensional model, which is proved advantageous in more physical implications and less CPU time demand. To validate the proposed model, the calculated results are compared to the field data in the Yangtze River Estuary, exhibiting good agreement with observations. The proposed quasi-two-dimensional vertical model is used to study mixing process, especially dependence of salinity distribution and salt front strength on runoff and tides in estuaries.

Enhancing Estuarine Retention of Planktonic Larvae by Tidal Currents

To complete their life history, planktonic larvae of many marine species must be retained in or return to estuarine nursery grounds despite net downstream flows. Interactions between tidal currents and behaviour (vertical migration) of larvae are assumed to play an important role in upstream transport or station-holding, but the effects of tidal currents alone have not received close examination. To elucidate their effects, passive particles were followed numerically in a model of idealized flow. The model basin was patterned after the Newport River Narrows, part of a small coastal-plain estuary with simple bathymetry and a well-studied example of larval retention (mud crabs,Rhithropanopeus harrisii). The flow field, governed by an analytical solution of the linearized equation of motion, was forced by oscillating tidal currents at the seaward end of the estuarine channel, and its energy was dissipated by bottom friction and eddy diffusion. Particles released at various locations showed a net upstream drift, produced by the combined effects of: (1) shear in the vertical profile of horizontal velocity; and (2) tidally-induced vertical motion. Velocity of upstream drift could partially offset net downstream transport by river flow. This velocity increased with distance downstream, providing a mechanism tending to stabilize positions of larvae in the basin. Tidal vertical migration of mud crab larvae in nature is in phase with, and presumably reinforced by, the predicted tide-induced vertical motions of the water. The passive, tidally-induced upstream drift could provide an important mechanism, in addition to larval behaviour, for the retention of larvae in estuaries.

Shear Instability of Internal Inertia-Gravity Waves

Abstract Local shear and convective instabilities of internal inertia-gravity waves (IGW) are examined assuming a steady, plane-parallel flow with vertical profiles of horizontal velocity and static stability resembling an IGW packet in a basic state at rest, without mean vertical shear. The eigenproblem can be described in terms of a nondimensional rotation rate R = f/ω0 < 1, where f is the Coriolis parameter, ω0 is IGW intrinsic frequency, and IGW amplitude is a, such that a = 1 for convectively neutral waves. In the nonrotating case, shear instability is possible only for convectively supercritical waves, with horizontal wavevector aligned parallel or nearly parallel to the plane of IGW propagation. Transverse convection, with wavevector aligned perpendicular to the plane of IGW propagation, displays faster growth than parallel shear or convective instability at any horizontal wavenumber. For intermediate R, eigenmodes in supercritical IGW are characterized at small horizontal wavenumber k by a trans...

A numerical model of the combined wave and current bottom boundary layer

A numerical model of oscillatory rough‐turbulent boundary layer flow, featuring closure via the turbulent energy equation, is used to examine the principal features of wave‐current interaction above the seabed. Results are presented from case studies carried out with water depth of 10 m, bed roughness of 0.5 cm and wave period of 8 s. The steady surface current in the absence of waves is nominally 100 cm/s, and waves having near‐bottom velocity amplitudes of 50, 100, and 150 cm/s are superimposed on this current at angles ϕ = 0, π/4, and π/2. Velocity, turbulent energy, shear stress, and eddy viscosity distributions are compared for the steady current alone, for waves alone, and for waves superimposed on the current, and the interaction in the wave‐current boundary layer is examined. Cycle‐averaged vertical profiles of horizontal velocity illustrate the extent to which the mean flow is retarded by wave‐current interaction. For the general case in which the waves are superimposed at an arbitrary angle ϕ, the mean current veers to form an angle with the wave direction greater than that of the initial steady current. Finally, the enhancement of the bed shear stress and the increase in oscillatory boundary layer thickness associated with wave‐current interaction are both quantified.

A model of oscillatory rough turbulent boundary layer flow

Approximate analytical solutions of the boundary layer equation are obtained in closed form for oscillatory rough turbulent flow. The solutions are based on a time-varying eddy viscosity, and the aim of the study is to assess the effects of these time variations on the properties of the wave boundary layer. The flow and the eddy viscosity are made interdependent by a closure assumption which relates the peak value of viscosity in the wave cycle to the peak value of shear velocity. Instantaneous vertical profiles of horizontal velocity and shear stress, and time series of the bed shear stress, are presented for a typical case study. In addition, the wave drag coefficient, the boundary layer thickness and the phase lead of peak bed shear stress over peak free-stream velocity, are determined as functions of both the relative roughness and the parameter governing the magnitude of the time variations in viscosity. Reasonable agreement is demonstrated with previous experimental and theoretical results.

A numerical model of the wave boundary layer

A numerical model of deep, uniform, oscillatory, rough-turbulent boundary-layer flow is described. The model is based upon the governing horizontal momentum equation and a closure scheme involving the turbulent-energy equation and various turbulence-scaling laws. Finite difference solutions of these equations are obtained for a range of values of the ‘relative roughness’ (A 0/k s), whereA 0 is the excursion amplitude of the water particles in the free-stream flow andk s is the ‘equivalent bed roughness’. Typical vertical profiles of horizontal velocity, turbulence energy and eddy viscosity, and time-series of the bed shear stress are presented. The model results are then used to determine the wave drag coefficient, boundary-layer thickness and phase lead of the bed shear stress over the free-stream velocity, each as a function ofA 0/k s. These results are shown to be in generally good agreement with previous experimental and theoretical results. Finally, the model is used to test for the existence of a universal velocity distribution for uniform oscillatory (sinusoidal) rough-turbulent flow. The ‘law of the wall’ and the ‘defect law’ proposed by Jonsson (1980, Ocean Engineering, 7, 109–152) are well supported by the model, and the existence of a logarithmic ‘velocity overlap layer’ in which both of these laws are valid is demonstrated forA o/k s≳30.