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Chris Garrett

Abstract

The effectiveness of mixing near a sloping boundary is reduced not just by the ratio of the stratification there to that in the interior but by the square of this ratio. This result has previously been derived and interpreted by invoking the upgradient vertical buoyancy flux associated with secondary circulation as this opposes the downgradient vertical diffusive flux. Here it is shown that the result may be derived very simply by considering the diffusive flux across an isopycnal, rather than a horizontal, surface. The reduction in the buoyancy flux comes from the increased isopycnal spacing and the reduced distance to the boundary. Derivation of the secondary circulation in the isopycnal/diapycnal framework is more subtle, however, as it involves allowing for the curvilinear nature of the coordinates.

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Chris Garrett

Abstract

The “near-inertial” part of the internal wave continuum is dominant and also different from the rest of the spectrum. A simple possible reason for the difference is that waves generated at the surface are not reflected or scattered from the seafloor until they have propagated equatorward to a latitude where their frequency exceeds the local inertial frequency. This excess is easily estimated and is of the order of 10% of f at midlatitudes. The estimate is in reasonable agreement with data on the depth dependence of the peak frequency over smooth topography and on the frequency band within which there is little upward propagating energy. Internal wave propagation and interactions with bottom topography may thus be just as important as wave–wave interactions in controlling the energetic parts of the internal wave spectrum and, hence, in determining mixing rates in the ocean.

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Chris Garrett and Theo Gerkema

Abstract

The generation of internal tides can be ascribed to the action of a buoyancy force caused by the flow of the barotropic tide over topographic features. It is commonly assumed that the barotropic flow can be taken as hydrostatic, but it is shown here that this leads to a linearized governing equation for the baroclinic tide that is only valid if the baroclinic tide is also hydrostatic. A governing equation for the baroclinic tide, valid for any situation, is derived here and is shown to be exactly equivalent to a simple transformation of the governing equation for the combined barotropic and baroclinic tides.

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Konstantin Zahariev and Chris Garrett

Abstract

The temperature dependence of the expansion coefficient of seawater can lead to a nonzero annual-average surface buoyancy flux even if the annual-average heat flux is zero. In the Mediterranean Sea, for example, this effect apparently gives the same buoyancy flux into the sea as a heat flux of 6 W m−2. This does not, however, lead to an increase in the surface layer buoyancy over the course of a year; compensating cabbeling occurs mainly in the winter and spring when there is intensive mixing. The magnitude of the apparent buoyancy flux is proportional to the area inside the hysteresis loop of the seasonal cycle of the sea surface temperature versus the total heat content of the ocean. The output of a simple mixed layer model, however, shows only a weak sensitivity of mixed layer properties, such as depth, to inclusion of the nonlinearity in the equation of state.

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Myriam Bormans and Chris Garrett

Abstract

The inviscid two-layer hydraulic model of Farmer and Armi has two types of solution in the eastern end of the Strait of Gibraltar for flow that is critical at Camarinal Sill. The solution corresponding to maximal exchange has a fast supercritical flow with a shallow interface whereas the solutions corresponding to submaximal exchange show a much slower subcritical flow with a rather deep interface. We extend their model to include physically important effects such as nonrectangular cross section, friction and barotropic fluctuations. Allowing for realistic cross sections reduces the exchange and raises the interface everywhere along the strait. Realistic interfacial friction has little influence on the exchange but lateral friction at the sloping sides of the cross sections has a significant effect on the flow and brings the two solutions (supercritical and subcritical) closer together. The effect of the earth's rotation is also summarized but dealt with in more detail in a companion paper by Bormans and Garrett.

Low-frequency barotropic fluctuations significantly alter the volume flux and the interface depth everywhere along the strait and so should be taken into account in any comparison between theory and observations. They also affect sea-level differences across and along the strait, with a ratio of these that is positive for maximal exchange and negative for submaximal exchange. This provides a useful diagnostic using sea level data alone.

It appears that the exchange through the Strait of Gibraltar alternates between periods of maximal and submaximal exchange, although we do not yet know the frequency of, or conditions for, each state.

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Johannes Gemmrich and Chris Garrett

Abstract

Extreme, or “rogue,” waves are those in the tail of the probability distribution and are a matter of great concern and considerable research. They may be partly associated with non-Gaussian behavior caused by resonant nonlinear interactions. Here it is shown that even in a Gaussian sea, “unexpected” waves, in the sense of, for example, waves twice as large as any in the preceding 30 periods, occur with sufficient frequency to be of interest and importance. The return period of unexpected waves is quantified as a function of the height multiplier and prior quiescent interval for various spectral shapes, and it is shown how the return period is modified if allowance is made for nonlinear changes in wave shape and/or a buildup of one or more waves prior to the unexpected wave. The return period of “two-sided” unexpected waves, with subsequent as well as prior quiescence, is also evaluated.

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Myriam Bormans and Chris Garrett

Abstract

Gull's theory for rotating hydraulics is applied, as a reduced gravity model, to the surface inflow through the Strait of Gibraltar into the Mediterranean as it is shown that rotation is mostly important east of Tarifa Narrows where only the upper layer is active. Details of the flow depend on the volume flux, Q, and on the potential vorticity of the inflow. We examine two extreme cases for this. In both examples the model predicts that supercritical inflow separates from the north share about half way between Tarifa and Gibraltar, so that at Gibraltar the flow is separated. The comparison of (i) conditions for criticality, (ii) separation widths and (iii) interface depths and velocities in midstrait, between this 2D model and the ID models of Farmer and Armi and of Bormans and Garrett suggests that the use of a simple 1D model is appropriate for the Strait of Gibraltar for both subcritical and separated supercritical flows. However, for the latter, the prediction of the point of separation and of the interface depth using the 1D model requires allowance for the effect of rotation.

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Johannes Gemmrich and Chris Garrett

Abstract

The roughness of the sea surface can be affected by strong currents. Here, long records of surface wave heights from buoy observations in the northeastern Pacific Ocean are examined. The data show the influence of tidal currents, but the first evidence of wave-height modulation (up to 20%) at a frequency that is slightly higher than the local inertial frequency is also found. This finding shows the effect on surface waves of near-inertial currents, which are typically the most energetic currents in the open ocean. The result has implications for wave forecasting but also provides valuable information on the frequency, strength, and intermittency of the associated near-inertial motions.

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Darek Bogucki and Chris Garrett

Abstract

Internal solitary waves (ISWs) are a common feature of the coastal zone and marginal seas, especially close to shelf breaks, and are observed to mix the water column at the depth of maximum density gradient. For a two-layer system separated by a thin interface with a finite density gradient, the Richardson number in the interface fails below 1/4 if, in the simplest case, the ISW amplitude exceeds 2(hH 1)1/2, where h is the interface thickness and H 1 the thickness of the upper layer. Assuming that mixing then thickens the interface and that the potential energy for this comes from the ISW, we derive formulas for the damping rate of the ISW.

The model is generalized to allow for a stratified upper layer; a Richardson number of less than 1/4 now requires that the displacement of the base of the upper layer exceeds 0.82 times the thickness of the layer. The ISW damping rate is sensitive to the ratio of the mixing depths above and below the base of the upper layer but can be plausibly matched to field observations.

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Amit Tandon and Chris Garrett

Abstract

A recent parameterization of mesoscale eddies by Gent and McWilliams (GMc) represents their effects as advective and diffusive fluxes along isopycnals. The form chosen for the added transport velocity due to eddies flattens isopycnals as in baroclinic instability but implicitly assumes purely viscous dissipation of the available potential energy released. If, however, the energy dissipation occurs in the ocean interior due to a process such as internal wave breaking, it is likely to cause diapycnal mixing. The implied diffusivity is large in a frontal situation, but the analysis of the spindown equation for a quasigeostrophic front shows that it causes only small changes in the frontal evolution. The spindown equation also permits analysis of the relative importance of various terms describing subgrid-scale fluxes of momentum and buoyancy, and may be interpreted in terms of Eliassen–Palm fluxes. Another possibility for the dissipation of the eddy energy that is generated from the mean available potential energy in the GMc mechanism involves air–sea interaction and subsequent water mass modification, but this is also clearly diabatic across mean isopycnals. The GMc parameterization does accomplish diabatic transfer across mean isopycnals near the surface due to the boundary conditions on the advective eddy flux, though it is not clear that this is the same as if the effect air–sea interaction on the eddies were treated explicitly. The cross-frontal volume flux must be compatible with the buoyancy budget. In the case of the Southern Ocean, this may require the net meridional circulation cell to be weak if the air–sea buoyancy flux is small.

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