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Will Perrie and Bechara Toulany

Abstract

We present the variation that results when fetch relations for wind-generated wave spectra are sealed by the friction velocity component in the dominant wave direction rather than the magnitude of the friction velocity, using the data collected during the Canadian Atlantic Storms Program (CASP). The effects of three possible drag coefficients are considered. the usual constant drag coefficient, the open-ocean long fetch drag coefficient, and finally, the wave age dependent drag coefficient for growing waves recently measured by Smith and Anderson in HEXOS.

Contributions to the correlation coefficients for dimensionless variables due to both scaling variables and dimensional variables are computed. We find that the friction velocity component in the dominant wave direction rather than the friction velocity magnitude should be used as the scaling variable. The self-correlation introduced to the correlation coefficients is then less than that resulting from the friction velocity magnitude.

Balance relations among physical fetch relations support this conclusion and imply that the wave age dependent drag coefficient for growing waves is the appropriate drag coefficient to use in scaling variables. We generalize Snyder et al.'s parameterization of the wind input energy and derive a functional form for Phillips’ equilibrium range α-function.

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Bechara Toulany and Christopher Garrett

Abstract

A simple model in which the cross-strait sea surface slope is geostrophically balanced and the along-strait slope is balanced by acceleration and friction, is shown to be supported by the results of Buchwald and Miles for fluctuating flow through a gap between two semi-infinite oceans. For a narrow gap (compared with the Rossby radius and the scale of the motion in the far field), the transport through it is exactly the same as that predicted by the model, provided that the gap is regarded as having an elective length as determined in this paper. The importance of the models is that they demonstrate that, at low frequency, the flow may be “geostrophically controlled” and the transport limited to a value much less than that which would arise in a nonrotating system. The neglect of nonlinear advective terms in the models is justified by a comparison or the Bernoulli set-down in the strait with the driving head and the mean water depth. The formula for the flux through a strait may be applied in studies of the forced of ocean basins connected by straits. In particular, we draw attention to the existence of damped low-frequency normal modes for two connected (but frictionless) ocean basins.

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William Perrie and Bechara Toulany

Abstract

Field experiments, in the years since the JONSWAP results, have established fetch- and duration-limited relations for wave parameters such as total energy E 0, peak frequency fp, and the Phillips α coefficient. The Canadian Atlantic Storms Program (CASP) Experiment of 1986 also found that the wind speed profile appropriate for the fetch-limited wave relations is a function of fetch, due to the change in surface roughness at the shoreline. Moreover, the fetch-limited wave relations may be altered by assuming differing wind speed variations with fetch. Inverting accepted fetch-limited wave relation the authors inter a fetch-limited relation for wind speed (or friction velocity) in terms of spectral wave parameters such as wave age. These relations are verified from measurements collected during CASP.

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Will Perrie and Bechara Toulany

Abstract

Spatial correlations for sea level pressures, during the Canadian Atlantic Storms Program of January-April 1986, were computed. We initially modeled these correlations using isotropic negative squared exponential, and second- and third-order autoregressive correlation functions. Allowances for variations due to latitude were made by partitioning the pressure stations north of 44°N from those south of 44°N and parameterizing observed correlations in each group using isotropic correlation functions. Tomporal variations were accommodated by separating pressure reports of the period early January to middle February from the period middle February to early April and parameterizing as before. Anisotropy was displayed by modeling the whole dataset using anisotropic second- and third-order autoregressive correlation functions.

These model correlation functions, which are used in optimal statistical estimation methods for the assimilation of data, were related to dynamical processes of the planetary boundary layer.

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Christopher Garrett and Bechara Toulany

Abstract

The Green's function for a semi-infinite ocean with depth a function of distance from the boundary is developed numerically for the M2 frequency and with Coriolis frequency and depth profile appropriate to the continental slope off the Gulf of Maine. This involves numerical integration of the linearized shallow water equations for all longshore wavenumbers, followed by numerical Fourier transformation. This variable-depth Green's function is approximately equal to Buchwald's (1971) constant-depth Green's function for distances along the boundary greater than the width of the slope, and at very short range tends to limiting values which can be approximated analytically.

The Green's function, when combined with currents from Greenberg's (1979) numerical model of the Bay of Fundy and Gulf of Maine, is used to explain substantial observed variations in M2 amplitude and phase along the edge of the shelf off the Gulf of Maine; the variable-depth Green's function produces significantly better results than the constant-depth Green's function. The results support the basic premise that the M2 elevation at the shelf edge in the absence of the Gulf of Maine would be fairly constant, and suggest ways of deriving open boundary input for tidal models of coastal seas with a minimum of offshore gaging.

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William Perrie and Bechara Toulany

Abstract

A model is developed for the response of waves to turning wind, which we denote as the fetch relaxation model. Comparison is presented with the standard 𝒷 relaxation model pioneered by Hasselmann et al. The fetch relaxation model is shown to surpass the standard 𝒷 model, with respect to observations collected during the Canadian Atlantic Storm Program (CASP) of 1986. Both models are based on the premise that the net growth of energy due to the wind is centered on the wind direction. The fetch relaxation model also conforms to relations for fetch-limited growing waves derived from the CASP observations. Moreover, the fetch relaxation model is shown to provide estimates for the role of the drag coefficient in turning wind situations.

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Bechara Toulany, Brian Petrie, and Chris Garrett

Abstract

We present an analysis of 84 days of current meter, sea level and hydrographic data collected in the Strait of Belle Isle, a long, narrow strait which connects the Atlantic Ocean and the Gulf of St. Lawrence. Along-strait currents are highly coherent throughout the entire cross section of the strait at all frequency, but the ratio of near-bottom to near-surface flows shows a well defined increase with increasing frequency. This frequency dependence is compared to the model of Garrett and Petrie after modification to allow for the finite thickness of the bottom Ekman layer. The model can best account for the frequency-dependent amplitude ratio if the spindown time in the strait is 4 hours.

We also compare the model predictions to observations of the ratio of the surface minus bottom pressure fluctuation on the north side of the strait to the pressure fluctuation difference across the strait at the surface. We again find reasonable agreement with theory for a friction parameter corresponding to a spindown time of 4–6 hours, equivalent to a quadratic bottom drag coefficient of about 5–8 × 10−3.

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