Kinetic and potential energies of a propagating surface gravity wave are calculated for the orbiting fluid particles.These energies are then compared with the respective standard theoretical quantities.Based on earlier work, it is concluded that the two sets of energies will not agree.To substantiate the prediction observations are needed, or a new theory for the depth decay rate of the particle orbits would work.Considerably less algebraic effort is involved in the present analysis than what was done in the past.

One of Newton's mathematical solutions to a hypothetical orbital problem, recently verified by an independent physics model, is applied to the fluid particle motion in shallow water surface gravity waves.What is the functional form of the central force, with origin at the ellipse's center, which will keep a body in the orbit?Newton found out it is the spring force, which is linear.All fluid particles in shallow water waves move in ellipses.By a superposition of solutions in a linear problem, the application of Newton's result to shallow water waves is combined with a feature not noticed by Newton: the orbital period is independent of the semi-major and semi-minor axes.Two conclusions reached are that the wave period of shoaling waves should be constant and that there is no friction in these waves.

Within the two poleward wide warm surface currents that cross mid-latitudes on the eastern sides of the North and South Pacific Oceans, a single prediction is made that they have a horizontal velocity shear such that their mean speeds monotonically increase from east to west. This prediction is inspired mainly by a re-examination of the east/west asymmetric observations previously documented: the longitudinal maximum in sea surface temperature in the eastern parts of both oceans at mid-latitudes is located significantly west of the region of maximum mixed layer depths, which occur in the middle of these currents. Also the application of recent dynamical considerations discussed below stimulated the prediction, which include the application of Bernoulli’s law to streamlines in the flows as well as the geostrophic balance in the cross-stream direction. These caused the rethinking of an earlier explanation, which upon reflection now seems less suitable than the present one.

There is a long and wide continuous trough of deep mixed layers connecting the tropical western North Pacific Ocean with the offshore waters of the coast of California. Relatively warm water that is nearly uniform vertically fills the trough, which is concluded here to be a northeastward flow joining the wide warm surface current at mid-latitudes off California documented earlier. Evi-dence for the trough comes from a North Pacific atlas based on very many indi-vidual mixed layer depth data points, taken over a 27-year period, compiled (av-eraged) in monthly mean charts with contours of constant mixed layer depth dis-played. BTs (bathythermographs) were used to record temperature versus depth continuously from which the mixed layer depths were determined. Centerline curves, connecting the deepest mixed layer depths, which approximate the mid-dle of the troughs, are constructed from the atlas and are presented for all twelve months. In going from west to east, these curves bend counterclockwise, gradu-ally most of the way then more markedly near California. The curves for the summer months come closer to California than any of the other ones do, suggest-ing that the warm current itself is nearest to California in summer. Confirmation of the prediction awaits future efforts.

Two wooden buoyant croquet balls of identical weight (in air) were released simultaneously at the bottom of a swimming pool. One ball's surface had grooves that were arranged in concentric rings. Water resistant wood putty filled the grooves of the second ball which was then sanded to make a smooth spherical surface. Small holes were drilled through the balls along the axes of the concentric rings to guide their vertical movement up taut lines held fixed at the bottom of the pool and at the top above the water surface. Twenty runs were made: the grooved ball reached the surface first in every run by a significant time difference. It is concluded that grooves on the surface of a ball can substantially reduce the frictional interaction between the water and the ball, compared with that on a ball with a smooth surface. (C) 2015 Physics Essays Publication.

Based on available evidence, it is hypothesized that the net force of friction on a flat solid wall, when fluid flows steadily along it, is reduced by putting one or more grooves in the wall's surface oriented perpendicular to the mean flow.Among the convincing observations are the existence and history of golf balls which show that golf balls with dimples travel farther than golf balls without dimples.Also there is a laboratory experiment using streak photography of low Reynolds number flow along a straight wall with a square cavity in it, illustrating that the flow jumps right across the cavity's opening, strongly suggesting that there is no friction of the fluid on the wall in the region of the cavity.One forecast is that if grooves or dimples are made on the inside surface of pipes, the discharged rate of the pipe for fluid flow should become increased.

For large air bubbles rising steadily through still water, the upward reaction force on the spherical cap is calculated.When added to the buoyancy force on the roughly flat base of the bubble, the friction force at terminal velocity must be larger than it would be in the absence of the reaction force.Experimental data are used to estimate that the increase in the drag coefficient is expected to be about 4%.

Month to month changes in the SST of the North Pacific, on the eastern side at mid-latitudes, are studied based on 30 years of ship-injection temperatures. Along both 40 and 35 N the SST maximum shifts west in summer, but it starts west at 35 N two months sooner than at 40 N. In July the maximum at 40 N is at the same location as the maximum at 35 N was in June: 155 W. Since the longitudinal SST maximum in the eastern North Pacific has previously been identified as the signature of a very wide, warm and sluggish current permanently flowing northeast off California, the month to month SST changes are used to estimate its mean speed: 10 - 20 cm/sec. Also the month to month SST changes indicate that in summer a new body of warm water goes north, in a pulse- like movement, to the west of the existing wide warm current. This is consistent with the need of the western equatorial ocean to export more heat northward out of the tropics in summer due to the increased absorption of solar radiation in the surface layer in that season.

Depth decay rates for pressure and velocity variations of a propagating capillary wave are found to be significantly different from each other, and neither one is expected to have the classical exponential character. To obtain these results Bernoulli’s equation along streamlines in the steady reference frame is combined with the force balance on fluid particles in the cross-stream direction: a pressure gradient offsets the centrifugal force on particles moving along a curved path. The two starting equations for pressure and velocity are nonlinear, but two linear first order ordinary differential equations are produced from them, one for each variable, and they can be integrated immediately. A full solution awaits further information on the non-constant coefficient, the radius of curvature function for the streamlines, either from observations or another theory.

A major cooling down of the northwestern Indian Ocean’s surface, including the Arabian Sea, starts in May, according to a well-known world atlas of SSTs. This is before the southwest monsoon which usually begins in June. Also within one year, there are two surface temperature maxima and two minima, which is not typical for the northern hemisphere. A surface current, cooler than the surrounding water, crosses the equator in April and May heading north and east on the western side of the ocean. That proposal is consistent with the given SST information. The warmer surrounding water is then moved to east and south as a consequence. Since wind driving is not available for initiation, the relatively cool northeastward current is thought to be caused by a thermohaline force related to the unstable northward temperature gradient in the west, which is of constant sign right across the equator beginning in May: cool in the south monotonically increasing to warm in the north.

Watching the winds in northwest Iowa during more than 30 summers has led me to two conclusions about the local atmosphere at ground level: there is a net northward transport of heat and water taking place throughout the summer; warm humid winds from the south continually alternate with cool dry winds from the north. The proposed northward heat transfer is consistent with the constraint, placed on the motions of the oceans and the atmosphere, of the earth’s heat balance due to the increased absorption of solar radiation at low latitudes compared to that at high latitudes. At mid-latitudes in the interior of continents, like North America, it is the job of the atmosphere alone to constantly help satisfy the global heat balance. Although qualitative in nature, the predicted northward heat flux is strongly based on frequent observations over lengthy time intervals.

A point mass rotating and vibrating on one end of an idealized spring, fixed at the other end, is studied when the plane of motion is vertical and gravity is acting downward. In magnitude, the gravity force is taken small compared with the spring force. Calculations involving the force balance method and an energy budget predict that the general shape of the orbit has a slight top/bottom asymmetry: more pointed on top and blunter on the bottom. This asymmetry in the particle orbits is consistent with the wave profiles of propagating surface gravity waves which have often been observed to have narrow crests and broad troughs. It has not been possible theoretically to find the exact shape of the orbits by known analytical methods because of the interference of the gravity torque acting on the mass. (C) 2013 Physics Essays Publication.

Mean seasonal surface temperatures of the North Pacific are illustrated in three maps.Twenty nine years of ship-injection temperatures are used for the whole North Pacific (north of 20˚N).Map number two shows geographical regions of the month of highest sea surface temperature.There are two broad bands in the central and eastern basin, trending northeast/southwest, such that the September band lies east of the August band along a given latitude line.Map three depicts regions of the lowest monthly mean temperatures.March is the most common month, but in the middle of the ocean is a band of Februarys trending northeast/southwest.These features on maps two and three are interpreted in terms of the newly proposed wide warm surface current and its seasonal variations, mainly in horizontal position, flowing northeastward off California.It has not been found possible to compare maps two and three with the results from any earlier work.Map one shows the mean seasonal range of surface temperature, which has a character similar to maps going all the way back to the late 1800s, but is based on considerably more data.

A large-scale surface flow with a southward component is proposed for the central South Pacific Ocean based on an interpretation of existing closely spaced and accurately measured temperatures and salinities along two latitudes in two different southern hemisphere winters: 28o S (Scorpio) and five degrees south of that (WOCE). Such a southward flow is not predicted from theory nor is it shown on current charts and globes. The observed longitudinal maximum in surface temperature along 28o S is centered around 130o W and has an amplitude of at least 5o C and an east/west range of about 60o of longitude. This striking feature is most easily explained by horizontal transport from latitudes closer to the equator. Since temperature atlases show that equatorial surface temperatures are always highest in the west, the origin of the warm water probably is toward the western side of the ocean as well. Thus the surface flow surrounding the longitudinal temperature maximum should be directed to the southeast. Where the surface temperatures are maximum the mixed layer depths are relatively large in a convex downward lens with maximum depths of 100 m; a correlation that is consistent with warm water moving south and being cooled from above. Salinities are maximum near the temperature maximum, also suggesting that the source of the surface flow is at low latitudes, where evaporation is usually expected to exceed precipitation. It is conjectured that the large-scale southeastward flow of the South Pacific is the analogue of the northeastward wide warm current off California documented over 30 years ago.

A physical explanation is given for the existence of stable underwater bubbles in the form of a cylindrical column of air oriented vertically. If all the forces are balanced, it will not rise up against gravity in still water. Air compressibility is the key element of the explanation. When the rates of increase with increasing depth of the air pressure inside the cylinder and the water pressure outside the cylinder are equal, it is possible in theory for the bubble to be stationary, contrary to what intuition may suggest. (C) 2011 Physics Essays Publication. [DOI: 10.4006/1.3555766]

An elementary calculation is made of the drag coefficient, CD, for large bubbles rising in motionless water. The result is an algebraic expression involving two geometric properties easily measured in one still photograph. It is C-D=9h/4R, where h and R are the maximum vertical dimension and the radius of curvature of the spherical cap of the bubble, respectively. Thus, the drag coefficient is independent of the acceleration of gravity and of the Reynolds number. Typical data from the bibliography are used to evaluate the drag coefficient and they fall in the range 0.7-1.3 with 1.0 as the mean. For a solid sphere in a uniform flow at a Reynolds number equal to that obtained for a large bubble, the experimental drag coefficient is known to be 0.40. Higher drag for the bubble may be expected because of its shape, particularly the roughly flat bottom surface with turbulent eddy motion trailing behind it. (C) 2011 Physics Essays Publication. [DOI: 10.4006/1.3518268]

When plane surface gravity waves move into still deep water and there are no torques available to change the magnitude of the orbital angular momentum, then the angular momentum of the waves is conserved, meaning that the square of the amplitude divided by the frequency is constant at a fixed location as the waves pass by. Linear momentum is not conserved because the still environment exerts a reaction force on the advancing waves. From the balances of linear and orbital angular momentum come the conclusion that both the amplitude and the frequency must change as the waves travel into still water. Some ocean wave data agree qualitatively with the conservation of angular momentum. Quantitative comparisons between theory and measurement are left for the future. (C) 2011 Physics Essays Publication. [DOI: 10.4006/1.3592171]

The centrifugal force is used to increase the physical understanding of five examples taken from fluid dynamics, geophysics and the solar system, as well as four hypothetical orbital problems. Each example involves a balance of forces between the centrifugal force and one or two other forces, such as a pressure gradient and a component of the force of gravity. Among the examples chosen for examination are: the orbital motion of fluid particles in surface grav-ity waves, the boundary layer character of steady flow next to a curved rigid surface, the tornado, the rotating self-gravitating mass and the three-body problem.

Between the 1940s and the 1960s there was a significant lowering of the surface temperatures of the central North Pacific. This cool-down is discussed on the basis of analyses of a very large surface temperature data base, covering most of the North Pacific, which began in 1947 and continued for at least 30 years afterwards. A surface area more than 20 degrees of latitude by approximately 70 degrees of longitude, centered on 40°N, cooled down within about a ten year period by typically 0.5℃ and by as much as 1.0℃. Previously a permanent surface and near surface circulation was proposed in which a shallow very broad warm surface layer flows northeastward at mid-latitudes on the eastern side of the North Pacific while colder water returns southward to the east, west and underneath the warm surface current. It is suggested that variations in this hypothesized circulation, due to natural causes not yet completely understood, potentially provide a mechanism for producing a cooling down (or warming up) of a large region of the central North Pacific at mid-latitudes in a relatively short period of time (ten years or less).