Forced double Kelvin waves in a stratified ocean

This paper examines the linear response of a two-layer uniformly rotating ocean of infinite horizontal extent with a discontinuity in depth to a divergence-free transient wind stress. Initially the ocean is at rest and the wind stress is directed perpendicular to the escarpment. A rigid lid is employed to filter out the external double Kelvin wave and an analytic solution is derived, using transform techniques, for the forced internal double Kelvin wave which is trapped along the depth discontinuity. Parameter values are chosen which most accurately model the Mendocino escarpment oriented almost zonally off the northern California coast. Soon after the wind stress is applied a single large wave is generated in the neighborhood of the wind stress curl origin. The wave has a maximum amplitude of 3 m, a phase speed of approximately 2.2 km day–1 and a wavelength in the order of 200 km. Furthermore the forced double Kelvin wave is found to exhibit a 6 day oscillation which is independent of the e-folding time scale of the wind stress. At any fixed location along the escarpment the solution also displays amplitude modulation. An investigation of how sensitive the solutions are to the upper layer depth and stratification is presented. A brief discussion of the response produced by a time-periodic spatially independent wind stress directed parallel to the escarpment and suddenly applied to a quiescent ocean, is also presented. It is suggested that double Kelvin waves may perhaps be detected from deep-sea buoy measurements

The clubhead and hand planes in golf draw and fade shots.

Swing planes in golf have become a popular area of research. Cochran and Stobbs (1968) examined the motion of the clubhead and hands qualitatively. Subsequent quantitative analyses have included investigations of the planarity of the whole club (Coleman & Anderson, 2007) and clubhead (Shin, Casebolt, Lambert, Kim, & Kwon, 2008). The aim of this study was to investigate the motion of the clubhead and hands in the downswing quantitatively, and to compare these motions for the fade and draw (as suggested by Coleman and Anderson, 2007). In conclusion, both the clubhead and hand planes in the late downswing were found to differ significantly in relation to the target line between the draw and fade shots. Greater differences were found between golfers, rather than between shots, in the relationship between the clubhead and hand motion during the downswing. Nevertheless, further detailed analysis is warranted of how the motions around impact – especially the clubface orientation – differ between the two types of shot

The clubhead swing plane in golf draw and fade shots

It has become popular to characterise a golf shot in terms of a ‘swing plane’. However Coleman and Anderson (2007) showed that the motion of the whole club in the downswing could not be represented by a single plane in all players. Shin et al. (2008) found that the clubhead motion was consistently planar between the club being horizontal in the downswing and follow-through. Coleman and Anderson (2007) also suggested that the club plane might differ between draw and fade shots. The purpose of this study was to compare draw and fade shots, with a focus on the clubhead motion in the late downswing. The late downswing clubhead plane differs between a draw and a fade shot, even when differences in address angles are accounted for

Steady, barotropic wind and boundary-driven circulation on a polar plane

Steady, linear, barotropic wind and boundary forced circulation solutions in the presence of linear bottom friction are analytically derived in a circular basin of uniform depth on a polar tangent plane in which only first order effects of the Earth’s curvature are retained. Approximate solutions are constructed by using the well known method of aggregating the interior inviscid Sverdrup balance solution and the frictional wall boundary layer solution. In contrast to the width of mid-latitude frictional western boundary layers that scale as , the width of the polar frictional boundary layer adjacent to the basin wall is wider, scaling as , where is the bottom friction coefficient, is the coriolis parameter. Solutions are presented for a variety of wind stress curl distributions and for a prescribed inflow/outflow representative of the exchange of water masses between the Arctic and Atlantic basins. Boundary forced solutions are also derived in a basin with a uniform width step shelf. For this basin geometry the flow is mainly confined to the shelf, although a parameter regime is identified that supports significant flow in the deep basin

Competitive swimmers modify racing start depth upon request

To expand upon recent findings showing that competitive swimmers complete significantly shallower racing starts in shallower pools, 12 more experienced and 13 less experienced swimmers were filmed underwater during completion of competitive starts. Two starts (1 routine and 1 “requested shallow”) were executed from a 0.76 m block height into water 3.66 m deep. Dependent measures were maximum head depth, head speed at maximum head depth, and distance from the starting wall at maximum head depth. Statistical analyses yielded significant main effects (p < 0.05) for both start type and swimmer experience. Starts executed by the more experienced swimmers were deeper and faster than those executed by the less experienced swimmers. When asked to dive shallowly, maximum head depth decreased (0.19 m) and head speed increased (0.33 ms-1) regardless of experience. The ability of all swimmers to modify start depth implies that spinal cord injuries during competitive swimming starts are not necessarily due to an inherent inability to control the depth of the start

Block height influences the head depth of competitive racing starts

The purpose of this study was to determine whether or not starting block height has an effect on the head depth and head speed of competitive racing starts. Eleven experienced, collegiate swimmers executed competitive racing starts from three different starting heights: 0.21 m (pool deck), 0.46 m (intermediate block), and 0.76 m (standard block). One-way repeated measures ANOVA indicated that starting height had a significant effect on the maximum depth of the center of the head, head speed at maximum head depth, and distance from starting wall at maximum head depth. Racing starts from the standard block and pool deck were significantly deeper, faster, and farther at maximum head depth than starts from the intermediate block. There were no differences between depth, speed, or distance between the standard block and pool deck. We conclude that there is not a positive linear relationship between starting depth and starting height, which means that starts do not necessarily get deeper as the starting height increases

Racing start safety: head depth and head speed during competitive backstroke starts

Research on competitive swim start safety has focused on starts involving a dive from above the water surface. The purpose of this study was to determine the depths, speeds, and distances attained when executing backstroke starts, which begin in the water, and to investigate whether or not these variables are a function of age. Backstroke starts (n = 122) performed in 1.22 m of water during competition were stratified according to age group (8&U, 9-10, 11-12, 13-14, and 15&O). Dependent measures were maximum depth of the center of the head (MHD), head speed at maximum head depth (SPD), and distance from the wall at maximum head depth (DIST). Main effects were shown for age group for MHD (F = 8.86, p < 0.05), SPD (F = 4.64, p < 0.05), and DIST (F = 17.21, p < 0.05). Because they performed starts that were deeper and faster than the younger swimmers, the older swimmers seem to be at a greater risk for injury when performing backstroke starts in shallow water

Racing start safety: head depth and head speed during competitive starts into a water depth of 1.22 m

From the perspective of swimmer safety, there have been no quantitative 3-dimensional studies of the underwater phase of racing starts during competition. To do so, 471 starts were filmed during a meet with a starting depth of 1.22 m and block height of 0.76 m. Starts were stratified according to age (8 & U, 9–10, 11–12, 13–14, and 15 & O) and stroke during the first lap (freestyle, breaststroke, and butterfly). Dependent measures were maximum head depth, head speed at maximum head depth, and distance from the wall at maximum head depth. For all three variables, there were significant main effects for age, F(4, 456) = 12.53, p < .001, F(4, 456) = 27.46, p < .001, and F(4, 456) = 54.71, p < .001, respectively, and stroke, F(2, 456) = 16.91, p < .001, F(2, 456) = 8.45, p < .001, and F(2, 456) = 18.15, p < .001, respectively. The older swimmers performed starts that were deeper and faster than the younger swimmers and as a result, the older swimmers may be at a greater risk for injury when performing starts in this pool depth

Water depth influences the head depth of competitive racing starts

Recent research suggests that swimmers perform deeper starts in deeper water (Blitvich, McElroy, Blanksby, Clothier, & Pearson, 2000; Cornett, White, Wright, Willmott, & Stager, 2011). To provide additional information relevant to the depth adjustments swimmers make as a function of water depth and the validity of values reported in prior literature, 11 collegiate swimmers were asked to execute racing starts in three water depths (1.53 m, 2.14 m, and 3.66 m). One-way repeated measures ANOVA revealed that the maximum depth of the center of the head was significantly deeper in 3.66 m as compared to the shallower water depths. No differences due to water depth were detected in head speed at maximum head depth or in the distance from the wall at which maximum head depth occurred. We concluded that swimmers can and do make head depth adjustments as a function of water depth. Earlier research performed in deep water may provide overestimates of maximum head depth following the execution of a racing start in water depth typical of competitive venues

Start depth modification by adolescent competitive swimmers

To expand upon previous studies showing inexperienced high school swimmers can complete significantly shallower racing starts when asked to start “shallow,” 42 age group swimmers (6-14 years old) were filmed underwater during completion of competitive starts. Two starts (one normal and one “requested shallow”) were executed from a 0.76 m block into 1.83 m of water. Dependent measures were maximum depth of the center of the head, head speed at maximum head depth, and distance from the starting wall at maximum head depth. Statistical analyses yielded significant main effects (p < 0.05) for start type and age. The oldest swimmers’ starts were deeper and faster than the youngest swimmers’ starts. When asked to start shallowly, maximum head depth decreased (0.10 m) and head speed increased (0.32 ms-1) regardless of age group. The ability of all age groups to modify start depth implies that spinal cord injuries during competitive swimming starts are not necessarily due to age-related deficits in basic motor skills