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Michael W. Stacey

Abstract

The interaction of the tides with the sill of a tidally energetic inlet, Observatory Inlet, British Columbia, is studied. Because of temporal variations in the stratification of the inlet, a substantial seasonal variation is observed in the power withdrawn from the barotropic tide. Vigorous, nonlinear, internal motions occur in the region of the sill, but most of the withdrawn tidal power is fed into a progressive, linear internal tide. The first two modes, which contain almost all of the energy, respond very differently to changes in stratification. The energy flux of the first mode is insensitive to changes in surface stratification but increases dramatically as a result of deep water renewal. The energy flux of the second mode exhibits the reverse behavior, being insensitive to the occurrence of deep water renewal but being a strong positive function of the surface stratification. Even though the inlet has a distinct surface layer in summer and appears to be a two-layer system, the second mode contains almost as much power as the first, a characteristic not indicative of simple two-layer flows.

The nonlinear sill processes induce a significant baroclinic flow at the beat frequency of the M2 and S2 tides. This flow is most vigorous near the surface of the inlet where it is greater in magnitude than the M2 barotropic current.

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Michael W. Stacey

Abstract

Month-long observations of along-channel velocity made close to the surface of Knight Inlet are used with a numerical model to estimate the roughness length z 0 on the water side of the air–sea interface. In analogy with a very common parameterization for z 0 on the air side of the air–sea interface, z 0 is parameterized in the numerical model as z 0 = au2/g where u∗ = (τ/ρ)1/2 is the friction velocity, g is the acceleration due to gravity, τ is the wind stress, ρ is the density of water, and a is an empirical constant. It is found that aO(105) for the dataset from Knight Inlet, a value four orders of magnitude larger than the value commonly used to estimate z 0 on the air side of the air–sea interface. When compared to empirical estimates of the significant wave height H s, it is found that z 0O(H s). Further evidence is provided that a numerical model that uses the Mellor–Yamada level 2.5 turbulence closure scheme can simulate the near-surface, wind-forced circulation quite well.

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Michael W. Stacey

Abstract

The interaction of the tides with the sill of Knight Inlet, a fjord located on the coast of British Columbia, is investigated. The seasonal variation in the stratification of the inlet causes a large seasonal variation in the power withdrawn from the barotropic tide. Usually, most of the withdrawn tidal power can be accounted for by a simple model of the internal tide.

Obviously, the model composition of the internal tide in an inlet is a function both of the inlet topography and the stratification. In particular, when there is a thin but distinct surface layer, caused possibly by river runoff, both first and second modes can transport significant amounts of energy away from the sill. When this is the case, the surface layer as well as the underlying stratification must be taken into account when calculating the amount of energy being transported by the internal tide.

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Michael W. Stacey and S. Pond

Abstract

A two-dimensional (i.e., laterally averaged) numerical model of the circulation in Burrard Inlet and Indian Arm near British Columbia, Canada, is used to examine the sensitivity of deep-water renewal events in Indian Arm to the turbulent mixing in the lee of the narrow sills in Burrard Inlet. Horizontal variations in the flow field can have an important influence on the production of turbulent kinetic energy near the sills and therefore also on the renewal events in Indian Arm. An ad hoc modification to the expression for the production of turbulent kinetic energy, required to obtain an acceptable simulation downstream of Second Narrows in Burrard Inlet, also results in a reasonable simulation of the observed circulation in Indian Arm. The modified laterally averaged model can reproduce the main features of the circulation away from the narrow sills. However, it seems that a three-dimensional model will be required if the circulation is to be simulated with greater accuracy and without the ad hoc modification, which has a free parameter.

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Michael W. Stacey and S. Pond

Abstract

A laterally integrated (two dimensional) nonlinear numerical model is used to examine the flux of M2 tidal energy in Knight Inlet. The simulated flux of tidal energy into the inlet is somewhat smaller than that estimated using the change in phase of the M2 tidal height along the inlet, a method that does not account for the effect of the internal tide on the surface elevation. The simulated energy flux into the inlet is close to the energy flux of the internal tide away from the sill determined from observations using an acoustic Doppler current profiler (ADCP). The net flux due to the internal tide is significantly less than (<1/2 of) the rate at which energy is removed from the surface tide. Earlier linear models of the internal tide produced energy fluxes that agreed with those estimated from the phase change of the tidal height but were larger than the fluxes that could be found in the observations. The reason for this discrepancy is not that these simple models neglected nonlinear effects, but rather that they did not take reflections of the internal tide into account. Also, the simulated flux of energy into the inlet less the net flux of internal tidal energy away from the sill is about equal to the simulated dissipation within 2 km on either side of the sill. The simulated net flux of internal tidal energy away from the sill is in agreement with the flux determined from the ADCP observations on the downinlet side of the sill, but not on the upinlet side of the sill. A possible explanation is that only the first internal mode (which is surface intensified) was important on the downinlet side but the first three internal modes were important on the upinlet side. The flux calculation using the ADCP observations took variations in the inlet width into account but did not take depth variations into account; thus, the reflection coefficients of the second and third modes may have been underestimated.

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Michael W. Stacey and S. Pond

Abstract

Observations of the circulation in a hole near a constriction in Burrard Inlet are simulated using a two-dimensional (i.e., laterally integrated) numerical model. The model uses a level-2 version of the Mellor–Yamada turbulence closure scheme. During spring tides, when mixing is at its most intense, the density in the hole decreases (increases) during the large (small) floods, and there is an up-inlet current pulse into the hole during each flood regardless of the flood's strength. During the large floods in particular, the simulation is significantly improved if the explicit influence of horizontal spatial variations on the production of turbulent kinetic energy is taken into account. During neap tides the simulated density is much less variable, and the currents in the hole are much weaker, in agreement with the observations. The model differs from the observations in that the simulated current pulses are significantly weaker than the observed pulses, possibly because the cross-channel averages computed by the model may not be a good estimate of the observed currents.

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Michael W. Stacey and Stephen Pond

Abstract

A numerical model that uses a level-2½ turbulence closure scheme is used to compare two boundary conditions for the turbulent energy at the air–sea interface. One boundary condition, the most commonly used, sets the turbulent kinetic energy proportional to the friction velocity squared, while the other sets the vertical diffusive flux of turbulent kinetic energy proportional to the friction velocity cubed. The first boundary condition arises from consideration (simplification) of the turbulence closure scheme near boundaries, and the second arises from consideration of the influence of surface gravity waves on the transfer of turbulent kinetic energy from the wind to the water. Simulations using these two boundary conditions are compared to month-long observations of velocity, temperature, and salinity (as shallow as 2 m from the surface) from Knight Inlet, British Columbia, Canada. The circulation in the inlet is strongly influenced by the wind, tides, and freshwater runoff. The two boundary conditions produce simulations that are different down to a depth of at least 5 m. Somewhat more accurate simulations are produced by the second boundary condition. Also, simulations using the second boundary condition are more sensitive to variations in the roughness length. Based on the simulations, roughness lengths as large as 1 m (or greater) are possible.

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Michael W. Stacey and Yves Gratton

Abstract

A laterally integrated, two-dimensional numerical model is used to examine the influence of the M 2 tide on the circulation in the Saguenay Fjord, a two-silled fjord (with a “large” inner and a “small” outer basin) located on the north shore of the St. Lawrence Estuary. It is found that the M 2 tide is more vigorous in the outer than in the inner basin and that more vertical mixing occurs in the outer basin. Therefore, the density at depth in the outer basin decreases faster than it does in the inner basin, and the resulting horizontal pressure gradient causes a bottom flow of water from the inner to the outer basin across the inner sill. This “reverse renewal” is evident in both the available observations and the simulation.

According to the model, much of the M 2 energy withdrawn from the surface tide is fed into the internal tide. Significant tidal energy is also advected by the mean flow velocity. Approximately 25% of the net energy flux into the fjord is dissipated within 2 km of the outer sill.

Because of the baroclinic pressure (i.e., the total pressure but with the influence of the surface displacement removed) the subtidal circulation is associated with very large energy fluxes within the fjord. These fluxes are much larger than the net rate at which tidal energy enters the fjord and they are greater than the subtidal, advective energy flux. They represent a large redistribution of energy within the fjord and their horizontal divergence along the fjord is almost in balance with the time rate of change of potential energy.

When a flux Richardson number is calculated for the inner basin below sill depth, a value of 0.075 is obtained, which is close to values found for other fjords.

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Shawn M. Donohue and Michael W. Stacey

Abstract

A numerical model, the Parallel Ocean Program (POP), is used to run a 46-yr simulation of the North Pacific Ocean beginning in January 1960. The model has 0.25° horizontal resolution and 28 vertical levels, and it employs spectral nudging, which, unlike standard nudging, nudges only specific frequency and wavenumber bands. This simulation is nudged to the mean and annual Levitus climatological potential temperature and salinity. The model was forced with National Centers for Environmental Prediction (NCEP) mean monthly winds, sea level pressure, net heat flux, and rain rate.

The simulated mixed layer depths (MLD) suggest significant shoaling of the MLD between 1970 and 2006, with faster rates in the northern Gulf of Alaska and slower rates to the west and south of Line Papa. The rates are of similar magnitude to those found in past studies and are consistent with the observed freshening and warming of the upper waters in the Gulf of Alaska. The rates are not spatially uniform, and the simulated MLD in the northeast Pacific actually deepens with time at some locations. These regions of increase form zonal bands in the simulation. The simulated MLD at Ocean Weather Station Papa (OWSP) shoals on average, but it is located close to one of these deepening bands.

On average, the simulated, low-frequency MLD at OWSP gives a good indication of the MLD along Line Papa and in the Gulf of Alaska near Line Papa’s latitude. The correlation coefficient between the MLD at OWSP and the latitudinal average of the MLD within the greater Gulf of Alaska (with OWSP removed) is 0.7 at zero lag. The correlation coefficient between the MLD at OWSP and the latitudinal average along Line Papa alone (with OWSP removed) is 0.6 at zero lag. Observed variability of the MLD along Line Papa and at OWSP is reproduced by the model. However, there is considerable spatial variability in the simulated MLD in the Gulf of Alaska as a whole, so MLD variability at OWSP is not necessarily a good indicator of the MLD variability throughout the region. Over the span of the simulation, the low-frequency MLD variability in the Gulf of Alaska is better correlated to the North Pacific Gyre Oscillation (NPGO) than to either the Pacific decadal oscillation (PDO) or Southern Oscillation index (SOI).

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Shawn M. Donohue and Michael W. Stacey

Abstract

A numerical model, the Parallel Ocean Program (POP), with 0.25° horizontal spatial resolution and 28 vertical levels is used to simulate the circulation of the North Pacific Ocean for the time period 1960–2006. Spectral nudging is used so that model drift of the mean state over the 46-yr time period of the simulation is prevented while allowing for the prognostic evolution of the circulation at time scales that are not nudged. The simulation successfully reproduces a southward shift in the North Pacific Current in 2002–03 as calculated from scalar observations. It is suggested that this calculated shift may not be solely due to meridional current drift but also a consequence of the shifting intensity of two eastward-moving current bands separated by 300–500 km, a distance consistent with the Rhines scale (the scale at which the 2D turbulence cascade tends to be arrested), which implies an influence from Rossby waves that are heavily affected by nonlinearities. The simulation suggests that the North Pacific Current may indeed have been influenced by a Rossby wave–like disturbance. This disturbance could have been forced to a significant extent by the local winds, but there is also evidence in the model for a coastally generated Rossby wave–like disturbance. This coastal disturbance was generated during the 1997/98 ENSO and traveled westward from the coast at about 1 cm s−1, taking 3–5 yr to travel into the region of the North Pacific Current. The noncoastal portion of the disturbance, which was generated by the local winds away from the coast, propagated westward at about 1 cm s−1 as well.

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