Current Velocity Vector Research Articles

Curvilinear parabolic approximation for surface wave transformation with wave–current interaction

The direct coordinate transformation method, which only transforms independent variables and retains Cartesian dependent variables, may not be an appropriate method for the purpose of simplifying the curvilinear parabolic approximation of the vector form of the wave–current equation given by Kirby [Higher-order approximations in the parabolic equation method for water waves, J. Geophys. Res. 91 (1986) 933-952]. In this paper, the covariant–contravariant tensor method is used for the curvilinear parabolic approximation. We use the covariant components of the wave number vector and contravariant components of the current velocity vector so that the derivation of the curvilinear equation closely follows the higher-order approximation in rectangular Cartesian coordinates in Kirby [Higher-order approximations in the parabolic equation method for water waves, J. Geophys. Res. 91 (1986) 933-952]. The resulting curvilinear equation can be easily implemented using the existing model structure and numerical schemes adopted in the Cartesian parabolic wave model [J.T. Kirby, R.A. Dalrymple, F. Shi, Combined Refraction/Diffraction Model REF/DIF 1, Version 2.6. Documentation and User’s Manual, Research Report, Center for Applied Coastal Research, Department of Civil and Environmental Engineering, University of Delaware, Newark, 2004]. Several examples of wave simulations in curvilinear coordinate systems, including a case with wave–current interaction, are shown with comparisons to theoretical solutions or measurement data.

全方向移動ロボットのための２輪キャスタ型オドメータの開発

This paper proposes a two wheels caster type odometer to estimate the current position and orientation of omnidirectional vehicles. The proposed odometer is composed of two passive wheels and one passive rotational axis. The two passive wheels rotate independently, and the passive rotational axis changes the odometer's orientation. Angular velocities of the two wheels and rotational axis are measured by three rotary encoders. In order to solve an encoder's wiring problem by increasing rotation of the rotational axis, a mechanism of a gear train is proposed. Using measured values of the three encoders, the current velocity vector of an omni-directional vehicle is calculated by kinematics of the proposed odometer. Using the velocity vector, the position and orientation of the omni-directional vehicle are estimated by dead-reckoning. An experimental two wheels caster type odometer is developed. Experimental results of localization by the developed odometer are shown in this paper.

An Assessment of Surface – Dynamics Observed Offshore Ancona with HF Radar

Abstract. An assessment is made of the dominant processes governing the circulation in a 30 × 30 km area off the coast of Ancona, where surface current velocity vectors have been obtained using an HF Coastal Dynamics Applications Radar (CODAR). Throughout one year of measurements (September 1997–August 1998), certain aspects of the surface dynamics in this area have been analysed. In winter the surface circulation is intensified and mainly concentrated close to the coast (within 15–20 km from it); in the spring and summer months, surface currents are much weaker, and between summer and autumn, a single cyclonic eddy further offshore often dominates surface circulation. In this paper the CODAR velocity data have been used to compute the surface vorticity and divergence fields offshore Ancona. The vorticity field is shown to have generally well‐defined patterns that are trackable in time despite the influence of winds and tides. The divergence field tends to be more variable spatially and temporally. However, it is an important descriptor of the irrotational motion and it is used, together with vorticity of the rotational flow, to illustrate the regional dynamics. In order to better visualize the rotary nature of the semidiurnal currents over the whole first year of study, these are presented in terms of ellipses. The direction of the semi‐major axis shows a preferential behaviour parallel to the coastline over the entire study area.

The near-surface current velocity determined from image sequences of the sea surface

A method to measure the ocean's near-surface current velocity vector based on the analysis of remote sea-surface image sequences was developed. The spatial and temporal records were transformed to the wavenumber-frequency domain, resulting in a three-dimensional (3-D) image power spectrum. In the spectrum, the signal energy of the waves is localized on a shell defined by the dispersion relation of surface waves. The sum of the sensor's velocity and the near-surface current profile deforms the dispersion shell due to the Doppler-frequency shift. An iterative least-squares fitting technique and an error-estimation model was implemented. To improve the method's accuracy, spectral wave energy found in higher harmonics of the dispersion shell and aliasing effects are taken into account. The most important nonlinear mechanism leading to higher harmonics is explained as resulting from wave shadowing due to the low grazing angles typical for ground- or ship-based radars. The improved method is examined analytically and is tested with Monte Carlo simulations. The variation of the shape of the measured or simulated 3-D image spectra, especially the peak wavenumber, the directional spread, and the main travel direction, controls the behavior and accuracy of the technique. A comparison of velocities acquired by nautical radar and independent Doppler log current measurements is presented. The technique's accuracy, its limits, and its adaptability are discussed. Additional improvements are proposed.

An assessment of local coastal dynamics observed with high‐frequency radar

An assessment is made of the dominant processes governing the circulation in a 30 km by 40 km area off the coast of Cape Hatteras, North Carolina, where surface current velocity vectors have been obtained using shore‐based high‐frequency radars in the High Resolution Remote Sensing experiment in 1993. Although the currents in this region are constantly under the influence of winds and tides, frequent intrusion of energetic flows into the area, apparently mostly of Gulf Stream origin, is shown to have a strong influence on the current variability. Analysis of vorticity and divergence shows that the flow intruding into the area is strongly rotational with positive vorticity. This rotational motion is not in geostrophic balance with the surface pressure gradient, and an inertial oscillation is often excited as a result, with vorticity and divergence oscillating 90° out of phase. On average the geostrophic imbalance generates a net surface flow divergence, which, in turn, induces negative vorticity that more than offsets the positive vorticity advected into the region. However, vertical viscous transfer of positive vorticity from subsurface to surface is shown to be required to complete the surface vorticity balance; the same energetic cyclonic shear flows that intrude into the area are suggested as the source of the subsurface vorticity as these flows of Gulf Stream origin are known to be subducted under buoyant shelf water.

Correction of the spectral characteristics of hydrophysical fields registered by a moving instrument

A method for the correction of the tensor which characterizes the spectrum of pulsations of the multi-dimensional hydrophysical processes in the invariant form recorded by a moving instrument is considered. The possibility of correct suppression of noise conditioned by the contribution of the instrument's proper motions to the spectral estimates of the small-scale (of the order of 10−2−102 m) pulsations of the processes investigated is shown when rather simple and effective construction approaches are used. Being derived using field data as an example, the spectral estimates for the pulsations of temperature, sound speed, and the three-dimensional current velocity vector, which linearly independent of the instrument's proper motions, indicate the essential (20–70% on average) reduction of the outside noise conditioned by the violation of the main requirement to the Eulerian form for the description of the variability of the hydrophysical processes investigated.

Mean current velocity measurement from a movable base

This paper discusses the possibility of measurement of the current velocity vector characteristics averaged over the time of continuous regular down-up probings from a moving carrier. The measurements can be carried out either from a moving vessel or from a helicopter, floating on or hovering above the sea surface. As an illustration for the suggested technique,in situ observations compiled by a free-component (±XYZ) VEGA-3 probe in the Guiana current region in March 1990 are provided. Comparison of the results with buoy data shows good agreement within the accuracy limits of the instruments employed.

Studies of Bottom Ekman Layer Processes and Mid-Lake Upwelling in the Laurentian Great Lakes

Abstract Profiles of horizontal current velocity have been measured over long time intervals across bottom Ekman layers in Lake Michigan. Measurements at offshore locations in water depths greater than 100 m have disclosed current speeds exceeding 25 cm s"1 at 1 m above the lake floor during winter storms when the lake water is unstratified. Counterclockwise veering of the current velocity vector occurs as the bottom is approached, with the veering being most rapid close to the bottom. Measurements of currents during winter and spring have shown prevailing cyclonic circulation at all water depths. This is true of the other deep Great Lakes as well. Mass conservation calculations with the current meter data yield upwelling velocities on the order of 1 m day'1 in the center of the lake during winter. Water temperature data have been obtained from thermistor strings attached to meteorological buoys moored in the center of the lake by the National Data Buoy Center, Bay St. Louis, Mississippi. Simulations of the temperature data with four different one-dimensional mixed layer models were all premature in timing the onset of stratification. Additional simulations of the temperature data were made with a constant upwelling velocity imposed through late spring. Results of the new simulations were significantly improved over those neglecting upwelling. These results emphasize the importance of Ekman pumping in retarding the start of stratification in large lake basins.

Transfer Function Model for Current to Wind

Abstract In some cases it may be useful to study the dependence of physical variables, like the current velocity or the depth of an isotherm in a lake, on the wind velocity from experimental data. In this study a transfer function model is applied to the current velocity vector for three separate cases. The first case concerns the hypolimnetic current in a sound between two basins (surface areas of 26.4 km2 and 52.1 km2) of a large lake in the temperature-stratified situation. In the second case, time series analysis is applied to the oscillatory currents in the hypolimnion of a stratified lake (surface area of 13.6 km2), and the third case concerns near surface currents in a homogeneous lake (surface area of 154 km2). The results of the transfer function may be used for computation of steady-state current due to long periods of constant wind, and also for comparison of measured and computed oscillatory characteristics of current velocity. The results from each of the computations were rather promising.

Least-squares methods for the extraction of surface currents from CODAR crossed-loop data: Application at ARSLOE

Least-squares methods are demonstrated that extract surface current radial velocities from first-order Coastal Ocean Dynamics Applications Radar (CODAR) sea-echo Doppler spectra for the compact crossed-loop/monopole antenna system. Based on the known physics of first-order sea scatter at HF, these techniques, implemented as software, are objective and automatic in that they: a) determine from the sea-echo phase and amplitude correction factors for the antenna elements; b) separate the first-order spectrum from the surrounding continuum for arbitrarily varying current conditions; c) using statistical hypothesis testing, select and use either a single or dual-angle model for radial current patterns, whichever best fits the data; d) calculate angles associated with given radial velocities; e) combine the data into a polar-coordinate map of radial velocity versus position; and f) calculate radial velocity uncertainties at each point on the map. In addition, as interpretive aids, two methods are evaluated and compared that provide total current vectors from single-site CODAR data, along with their uncertainties: model fitting and the application of the equation of continuity. It is shown how these methods can be applied to the older, CODAR 4-element antenna system, however, the following advantages of the crossed-loop/monopole system are discussed: it is physically more compact; analysis procedures are more efficient; resulting current velocities are more accurate, because there are no side-lobe problems; and finally, it also gives the ocean wave-height directional spectrum. These methods are tested and optimized against data taken during the Atlantic Remote Sensing Land Ocean Experiment (ARSLOE) storm (October 23-27, 1980), when surface currents varied in speed between 0-50 cm/s and over nearly 300° in angle. Current velocities were measured to a range of 36 km from the radar. Standard deviations in angle are typically 1°-3°; these translate to 2-3 cm/s rms radial velocity uncertainties over most of the coverage area, with decreased accuracy in angular sectors nearest the coast. Total current velocity vectors in strips parallel to shore obtained from model fitting have typical speed and angle uncertainties of 4 cm/s and 12°, respectively. Of the several formulations for the equation of continuity evaluated here, the best gave uncertainties of 5 cm/s, 12° at the closest range cells; these values increase rapidly with range to exceed 20 cm/s, 30° for distances greater than 20 km. The surface currents were observed to follow the wind throughout most of the storm at ARSLOE, but the current was almost always more closely parallel to the shore than the wind. An interesting exception occurred when the onshore storm wind that had prevailed for two days ceased; there was a rush of surface current directly offshore as the storm-surge sea level dropped. The surface current speed measured by CODAR in the upper meter of the ocean was, on the average, 2.1 percent of the windspeed.

An Investigation of Vertical Structure in Shelf Circulation

Abstract Recording current meter data from four levels are used to describe the vertical structure of the circulation of mid shelf waters 33 m deep off the central Texas Gulf coast. Resultant current velocity vectors for the 41-day study indicate a strong onshore mass flux past the study site, with the cross-isobath deflection increasing with height above the bottom. Both the resultant current speed and direction vary approximately linearly when plotted against the natural log of the depth. Statistically significant coherences are computed for time scales in excess of one day for longshore motion through the lowest three-fourths of the water column, and for both longshore and cross-shelf motion in a layer 7 m thick just above mid depth.

Some exact solutions of a system of equations of electrohydrodynamics: PMM Vol. 37, N°1, 1973, pp. 48–56

A class of exact solutions of a system of equations of electrohydrodynamics is studied for which the electric current is directed along streamlines of the hydrodynamic flow. In the two-dimensional case the solution is written down explicitly. It is shown how to construct other exact solutions for which the collinearity conditions of the electric current density and velocity vectors has not been satisfied, by using the solutions obtained, as an illustration, an exact solution for the flow of a unipolarly charged fluid in a channel with electrode-walls is constructed. It is shown that for a particular kind of hydrodynamic eddy current the solution of the two-dimensional system of equations can be reduced in some cases to finding the solution of a system of ordinary differential equations.