Resultant-current vector

Fio. 4. Each line segment in the upper diagram shows the net flow of water over a 12.4-hr tidal period. The current meters were at elevations of 0.88rf (A), 0.46water depth. The lower diagrams show resultant current vectors obtained from meter A (the one nearest the surface) and, for comparison, the resultant surface wind for the same time intervals. The surface water follows the wind stress closely the flow near the bottom is unrelated to the wind stress. The meters were set 7.4 km north of Eatons Neck. 

The Ion current vector for the atomic numbers m (resulting from the contributions by the fragments of the Individual gases) Is equal to the fragment matrix times the vector of the sum of the flows for the Individual gases. 

The upper ocean wind-driven current was described realistically for the first time by Walfried Ekman s landmark theory of 1905. The velocity distribution in the near surface layer of the ocean cannot be determined without additional information about the variation of the Reynolds stress vector with depth. Ekman (1905) assumed the Reynolds stress vector to be equal to the vertical shear of the mean current vector times a constant vertical eddy viscosity. The resulting current profile below the sea surface is the well known Ekman spiral with current speed decreasing exponentially with depth and current direction turning clockwise linear with depth from 45° right-handed to the wind stress vector at the sea surface. 

I2 vectors in Fig. 6.15(a) to obtain Ir, then recognizing that the vertical component of Ir is the value of Ir at tj that is, Ir = Ir max sin (ajjtj + 0r), where 9r is the phase angle between the resultant current and the voltage. It is noted that the vector addition easily provides both the maximum value and the phase angle for the resultant current these quantities are all that are needed to fully describe the resultant current. 

We have previously reported that, although most storms do not alter the bottom-water resultant flow vectors, the probability of large water speeds over the bottom is increased (Bokuniewicz et ai, 1975b) when the wind stress is high. We now present further evidence on this effect. A periodogram calculated for a current meter record obtained in the western end of Long Island Sound is presented in Fig. 6. Three tidal peaks are... 

The procedure outlined in the Radiated Fields subsection may be followed to find an analytical expression for the uniform current vector potential integral of Eq. (13.66). This results in the following exact series representation for the near-zone of the loop ... 

As noted above, jC in Eq. (154) arises from terras in which p 7 v. The corresponding contribution to the four current was evaluated in [104,323] and was shown to yield the polarization cuirent. Our result is written in teims of the magnetic field H and the electric field E, as well as the spinor four-vector v / and the vectorial 2x2 sigma raatiices given in Eq. (151). 

Electron Nuclear Dynamics (48) departs from a variational form where the state vector is both explicitly and implicitly time-dependent. A coherent state formulation for electron and nuclear motion is given and the relevant parameters are determined as functions of time from the Euler equations that define the stationary point of the functional. Yngve and his group have currently implemented the method for a determinantal electronic wave function and products of wave packets for the nuclei in the limit of zero width, a "classical" limit. Results are coming forth protons on methane (49), diatoms in laser fields (50), protons on water (51), and charge transfer (52) between oxygen and protons. 

Let us lump together the m observations y (i = 1,..., m) into a vector y, the polynomial coefficients otj (/=0,...,n — 1) into a vector jc of unknowns, and define the (/—l)th power of the ith observable (uj> 1 as the current term atJ of the matrix Am, . We now apply the usual method. Polynomials of high degrees tend to generate nearly singular matrices A which result in excessive fluctuations. 

---