Longshore Wind Research Articles

A Simple Model of Lake Ontario's Coastal Boundary Layer

An empirical forced wave model of currents and thermocline displacements in the coastal zone of Lake Ontario is derived from data from the International Field Year for the Great Lakes (1972). The model consists of three linear wave equations for predicting the depth of the thermocline, its slope and the longshore volume transport from the wind. The empirical phase speeds are consistent with internal Kelvin wave and topographic wave theory and the response to a unit longshore wind stress is consistent with cross-section models of long lakes.

Intermittent ‘full’ upwelling in Lake Ontario

A strong enough longshore impulse leaving the coast to the left (looking downwind) generates ‘Full’ upwelling in which the thermocline comes to intersect the free surface. This problem is beyond the scope of linearized (small displacement) theory, but it may be treated as a simple geostrophic adjustment problem in which the wind stress is supposed to be exerted impulsively on a two-layer fluid. A minimum impulse is found to be necessary for a full upwelling to develop from hydrostatic equilibrium, the magnitude of which is close to the product of top layer depth and propagation velocity of long waves on the thermocline. When the upwelling-favoring wind impulse is greater than the minimum, the upwelled front moves offshore by a distance proportional directly to the extra impulse (above the minimum) and inversely to top layer depth times Coriolis parameter. Upwelling episodes observed in Lake Ontario during the International Field Year for the Great Lakes (IFYGL) and feasibility studies before IFYGL show a frontal behavior in good quantitative agreement with the simple theoretical model. The offshore component of the impulsively exerted wind leaves the position of the front unaffected. However, a sustained offshore wind increases somewhat the offshore displacement due to a prior longshore impulse. The effect is relatively weak, and an offshore wind alone rarely produces full upwelling. A sustained longshore wind acting on an already upwelled thermocline generates considerable negative potential vorticity. Adjustment following such a ‘second’ longshore impulse produces a more complex thermocline shape and under certain conditions a frontal countercurrent. In a closed basin, full upwelling following a wind stress impulse occurs over only a portion of the shoreline. Given quiescent conditions, the upwelled front may be expected to propagate alongshore, somewhat as an internal Kelvin wave. Observations in October 1972 in Lake Ontario show frontal motions resembling internal Kelvin waves. However, only one half of the wave propagates, that half in which particle velocities have the same direction as the wave propagation velocity. Furthermore, the propagating warm zone is much narrower than the cold upwelled zone which developed under a succession of previous wind impulses.

Mean circulation in shallow seas

The mean circulation of shallow seas arises as the residue of chaotic first-order flow episodes created by winds, tides, and river inflow. The average effect of many such episodes is to generate an internal pressure and shear stress distribution which may differ significantly from a steady solution of the equations of motion. Within the coastal boundary layer (of about 10-km width), complex average effects of variable flow probably dominate. However, in mid-shelf regions of the Mid-Atlantic Bight, for example, classical steady state models adequately describe the main features of the mean circulation. The statistical effects of variable first-order flow even bring about some simplifications of the theory, i.e., linear internal and bottom friction laws and a decoupling of salt transport from the mean circulation. The mid-shelf circulation of the Mid-Atlantic Bight is thus found to consist of four additive components, each driven by offshore wind, longshore wind, longshore pressure gradient, and density contrasts caused by freshwater influx. The longshore pressure gradient enters the theory as a parameter necessary for describing the interaction of a portion of the continental shelf with the rest of the ocean. The pressure gradient driven flow component is responsible for some notable circulation features such as the line of divergence in bottom drift at about the 60-m isobath. The wind-driven and thermohaline flow components are familiar in character. Quantitatively, the four components together account satisfactorily for the observed mean shelf circulation.

Spin-up of a stratified ocean, with applications to upwelling

The method by which an ocean, initially stratified but motionless, adjusts to a suddenly applied wind stress is examined. For wind stress in the east-west direction, the zonal velocity in the ocean interior builds up linearly with time until a long planetary wave arrives from the eastern boundary. Then the interior flow stops increasing and oscillates about a steady value. At the west, a boundary layer forms and gets progressively thinner. The rate of thinning of this boundary layer is reduced by the arrival of long planetary waves from the east but is not stopped. A comparison is made between the barotropic and baroclinic responses. A comparison is also made between the upwelling at the eastern boundary induced by a longshore wind stress when there are no planetary waves (f-plane) and when there are planetary waves (ß-plane). In the former, upwelling is restricted to within a distance of ∼ 3 km of the coast, whereas when planetary waves are included the width of the upwelling zone increases with time. On both f- and ß-plane, Kelvin waves carry energy poleward along the eastern boundary. For a wind stress which varies sinusoidally with y this results in the mean upwelling being nearly 90° out of phase with the wind stress. The amplitude of the Kelvin wave is damped on the ß-plane but suffers no attenuation on the f-plane. The difference between the results for coastal upwelling on an f-plane and that on a ß-plane increases as the north-south scale of the forcing is increased. In the case where the scale is infinite, the f-plane upwelling increases indefinitely with time whereas the ß-plane solution attains a steady value.

Relation between mean sea level, current and wind stress on the east coast of Australia

Five-day mean sea level differences between Evans Head (29� 07'S.) and Coffs Harbour 30� 19'S.), and between Coffs Harbour and Crowdy Head (31� 50'S.) were regressed on estimates of longshore current acceleration, mean longshore current and longshore wind stress, with the following results: (i) A relation was found between sea level difference from Coffs Harbour to Crowdy Head, and current acceleration. There was no similar relation for the section Evans Head to Coffs Harbour, and no reason could be found for the difference in behaviour between the two sections. (ii) A weakly defined relation was found, in both sections of the coast, between sea level difference and the square of the mean longshore current (a friction effect). (iii) An apparent relation was found, again in both sections of the coast, between sea level difference and longshore wind stress. This relation was more marked than expected from theory. The longshore currents were obtained from ships' drift, and covered a period of 2 years. The current data show a southward drift of current pattern, at an average rate of 9 km day-1. They also show a clear correlation between currents at the shelf edge (approximately 19 km offshore) and currents nearer shore (approximately 6.5 km offshore). It was found that the nearer-shore currents lagged the shelf-edge currents by between 7 and 10 days. Time and space correlations of the shelf-edge currents confirm earlier estimates from similar data. A frequency spectrum of the shelf-edge currents showed a broad maximum in the period range 50-170 days.

Poleward shift of the coastal upwelling region off the California coast

Yoshida (1967) pointed out that the coastal upwelling region may not coincide with the intense longshore wind region and shift poleward. In order to clarify this poleward shift from the existing data, the monthly mean distributions of the offshore Ekman transport and the coastal upwelling intensity are estimated along the California coast from U. S. Daily Weather Maps and from the CCOFI data in 1949, respectively. The results show that the center of the coastal upwelling region is generally shifted to the north from the position of the maximum offshore Ekman transport. The detailed discussions are given for the case of August 1949 when the shift is seen most clearly.

Diurnal variations of winds over an upwelling region off Oregon

The diurnal variation of surface winds off the coast of Oregon is described and compared with a recent analysis of winds off the coast of Peru. The Oregon wind speeds have a distinct 24-h periodicity, while the Peru wind speeds were reported to have an irregular 12-h variation. The long-and trans-shore components of both winds exhibit 24-h periodicities; the ratio of the long-shore to trans-shore diurnal amplitudes off Oregon is 2.8, twice the ratio found off Peru. Although meteorological conditions off Oregon were quasi-stationary during the period investigated, there were considerable day-to-day variations in diurnal amplitudes and phases. Diurnal amplitudes were found to be correlated with the daily mean long-shore winds.

On the Circulation of a Homogeneous Ocean Induced by the Presence of Continental Slopes

<section class="abstract"><h2 class="abstractTitle text-title my-1" id="d14249249e50">Abstract</h2> The three-dimensional circulation of a steady, frictional, homogeneous ocean forced by a wind stress varying sinusoidally in the northward direction is examined, with reference to the effects of continental slopes. It is found that the local circulation pattern is considerably altered by the presence of slopes, although the global pattern is not. Moderately strong eastern boundary currents, of order 1–3 cm sec⁻¹, are predicted, flowing in the same direction as those observed. Areas of secondary up- or downwelling are found near the bottom of the continental slope, even in the absence of a local long-shore wind stress, again agreeing qualitatively with observations. The northward, intense (linear) return flow on the western boundary is again modified. It consists of a wide weak flow over the slope, and a narrower strong flow over the flat bottom; both flows have a northward flux of the same order, however. </section>

The Effect of Bathymetry on the Coastal Upwelling of Homogeneous Water

The influence of bathymetry upon the wind-driven, steady-state coastal upwelling motion of homogeneous water is investigated. The motion occurs in two principal layers, a divergent surface Ekman layer and a subsurface return flow. The restriction that the surface layer depth be always a small fraction of the total depth permits the retention of the surface layer solution developed in a previous paper by the author where bathymetry was not treated. The subsurface motion is affected by bathymetry, but the governing equations can he simplified for bottom topographies of slopes characteristic of continental slopes and shelves. The velocity and pressure fields are deduced by a combination of analytic and numerical means. The principal physical effects of bathymetry are two-fold. Shoaling uplifts and compresses the streamline field in the return flow. The resulting acceleration of the flow toward shore induces a jet in the longshore velocity field for the subsurface layer. This motion occurs in the direction of the longshore wind component and exceeds the surface layer longshore movement in mass flux.

On the generation of Kelvin-type waves by atmospheric disturbances

This paper considers the surface response of a semi-infinite, uniformly rotating, constant depth, homogeneous ocean to a variable atmospheric force. For a general wind and pressure system it is shown that forced Kelvin-type waves can be generated and that only the longshore wind component and the pressure can generate them. In particular a semi-infinite wind and moving pressure pattern are shown to generate Kelvin waves that travel away from the force discontinuities at the speed of shallow-water waves. The waves in the latter case exhibit a frequency shift typical of non-dispersive waves from a moving source. Some numerical values for the amplitudes of the Kelvin waves are also given.