Mean Horizontal Velocity Research Articles

The critical layer for internal gravity waves in a shear flow

Internal gravity waves of small amplitude propagate in a Boussinesq inviscid, adiabatic liquid in which the mean horizontal velocity U(z) depends on height z only. If the Richardson number R is everywhere larger than 1/4, the waves are attenuated by a factor $\exp\{-2\pi(R - \frac{1}{4})^{\frac{1}{2}}\}$ as they pass through a critical level at which U is equal to the horizontal phase speed, and momentum is transferred to the mean flow there. This effect is considered in relation to lee waves in the airflow over a mountain, and in relation to transient localized disturbances. It is significant in considering the propagation of gravity waves from the troposphere to the ionosphere, and possibly in transferring horizontal momentum into the deep ocean without substantial mixing.

Accelerated diffusion in the skewed shear flow of lake currents

When the direction as well as the magnitude of the horizontal mean velocity (e.g., in a lake or ocean current) changes with the vertical coordinate, the horizontal diffusion of a batch of ‘marked’ fluid is greatly accelerated, as compared with diffusion in uniform flow. When, in addition, temporal changes are superimposed on this pattern, further dispersing effects appear. The net result is that, as observed during diffusion experiments in Lake Huron, apparent horizontal diffusivities increase steeply in complex currents. Theoretically some light may be thrown on this rather involved problem by several approximate measures: (1) by considering the kinematics of skewed, unsteady currents, (2) by calculating effective lateral or longitudinal diffusivities using a technique originated by G. I. Taylor in 1954, and (3) by calculating first and second moments of the concentration distribution in shear flow using the diffusion equation. Numerical estimates obtained in this manner of ‘acceleration’ effects show order of magnitude agreement with observations. From a practical point of view the interesting conclusion emerges that a low vertical eddy diffusivity tends to produce a high apparent horizontal diffusivity, owing to acceleration of diffusion by the greater complexity of the current, so that over-all dilution rates vary less than one would otherwise expect.

A turbulent equatorial jet

A recent study of a laminar jet in a rotating spherical shell of fluid is extended to the case of a turbulent planetary jet at the equator of a rotating, stratified atmosphere or ocean. General forms of the velocity, density and pressure functions of both the mean motion and the turbulence are derived by a dimensional analysis applied to the mean and perturbation equations. The horizontal and vertical dimensions are estimated, based on the three characteristic constants of the problem, which are the momentum transfer, the stability and a rotation parameter. The estimates are in good agreement with the dimensions of the Cromwell current, i.e. the equatorial undercurrent of the Pacific Ocean.To the first order of approximation, the mean axial velocity in the theory is independent of distance along the jet axis. The mean horizontal transverse velocity component is much smaller and decreases upstream. The mean vertical velocity is extremely small, also decreasing upstream. The two horizontal velocity components of the turbulence are of the same order and, in the undercurrent, are about one-fourth the mean axial velocity. The vertical turbulent component is much smaller. Finally, it is shown that the eddy-viscosity concept is inappropriate for this problem because at least one of the eddy coefficients would have to be negative.

The Mean Vertical Velocity and Heat Supply during the Rainy Season Near Japan

In section 2, the physical significance of the time-averaged equations of motion is discussed. In the time averaged vorticity equation, the terms expressing the vertical transport of vorticity, the dissipation of vorticity due to friction, and so on, become important in their magnitude. As for the time-averaged thermodynamic equation, the magnitude of the term expressing the heat transfer due to horizontal disturbances is about the same order as that due to mean horizontal velocity. On the contrary, the heat transfer due to vertical disturbances is extremely small as compared with that due to mean vertical velocity.In section 3, we compute the mean vertical velocity and the mean supply of heat during the rainy season. An interesting feature in the patterns is the existence of a marked zone of cooling and of a pronounced downward motion near the so-called Okhotsk high.In section 4, the mean stream function and the mean velocity potential are obtained. Utilizing the mean velocity potential, the vertical distributions of divergence at the southwestern part of the Okhotsk high are analyzed.

On the law of the resistance of the air to rifled projectiles

At the beginning of this month Lieut.-Col. H. R. Halford applied to the author to obtain for him the law of atmospheric resistance resulting from his experiments in shooting with Metford’s match-rifle, a small bore with increasing pitch. Col. Halford had determined by experiment the elevations required for the ranges 100, 200, &c. up to 1100 yards, each determination being derived from a very large number of shots; and the table of experimental elevations, corresponding to these various ranges, formed the datum furnished to the author. As all the trajectories were very low, the greatest elevation amounting to only 2° 35' 30”, the author assumed, as a sufficiently close approximation that the vertical motion was determined solely by the force of gravity, and that the effect of the resistance of the air on the velocity was the same as if the projectile had moved strictly in a horizontal line. Consequently the depression of the point in which the target is struck, below the initial tangent to the path, becomes a measure of the time of flight, according to the usual law of falling bodies; and the mean horizontal velocity being thus known for a series of different ranges, we can calculate the mean velocity for every 100 yards of a long range, and thence determine the resistance.