Homogeneous Ocean Research Articles

The generalized eastern boundary conditions and the three‐dimensional structure of the ideal fluid thermocline

A generalized eastern boundary condition of no net zonal flux is applied to a continuously stratified model of the ideal fluid thermocline. Assuming that vertical exchange of water masses at the eastern boundary can be realized by the effect of mixing, water particles can move into or out of the eastern boundary in the form of vertical modes of no net zonal flux. For a purely wind‐driven model, a simple mode with the upper layer water moving into the eastern boundary and the lower layer water coming back into the interior is consistent with the assumption that vertical velocity is everywhere nonpositive within the subtropical interior. The stratification at the eastern boundary is an inseparable part of the global dynamics of the subtropical gyre and thus cannot be specified a priori. In fact, the eastern boundary stratification should be determined as part of a solution. One numerical example shows that relaxing the strict no‐zonal‐flux eastern boundary condition releases the nonphysical constraint over the upper surface density gradient near the intergyre boundary and gives rise to sloping isopycnals in the upper ocean and a vast zone of the eastern boundary ventilated thermocline in the southeastern basin. Therefore in contrast to the passive role played in the previous homogeneous ocean circulation models, the eastern boundary layer in a continuously stratified model plays an active role of setting up the global structure of the subtropical gyre. The dynamics of the eastern boundary layer which can transport the vertical mass exchange remains an issue for further study.

Gaussian beam method for underwater acoustic reflection from an elastic bottom

The Gaussian beam method furnishes a potentially useful numerical algorithm for modeling propagation in an inhomogeneous ocean environment. However, the paraxially approximated beams in the heuristically discretized stack suffer from spectral deficiencies that are problem dependent and make a priori predictability uncertain. Understanding these deficiencies may provide clues as to how to deal with them. The present test environment is a line source excited homogeneous ocean with a solid bottom that gives rise to two distinct critical reflections associated with the compressional (P) and vertical (SV) waves, respectively. Stacks of narrow beams, which have localizing advantages, have previously been found incapable of accounting for the critical angle (head wave) effects when the relevant wave phenomena involve only P or SV (horizontal shear), respectively [I.T. Lu, L. B. Felsen, and Y. Z. Ruan, Geophys. J. R. Astron. Soc. 89, 915–932 (1987)]. It is confirmed here that this situation persists in the presence of P‐SV coupling. As before, very wide paraxial beams or narrow beams with full spectra remove these effects, but tracking the latter is computationally more difficult, while tracking the former is inconvenient and uncertain for successive encounters with an environment. Various alternative options are examined to cope with these difficulties. [Work supported by NOSC.]

Generation and propagation of non-linear internal waves induced by the tide over a continental slope

A model is constructed to simulate the generation and propagation of non-linear internal waves being induced over a shelf break as a result of the propagation of the barotropic tidal wave in a two-layer ocean. Assuming a perfect fluid, the internal motion, taken as a disturbance with respect to the motion in a homogeneous ocean, is governed by Euler's and continuity equations. Assuming small baroclinic variations in the level of the free surface, the equations for the two layers are coupled through the relationship between the pressure gradients in these layers. The amplitude of the internal waves can reach up to 30 m at the shelf edge. It is found to increase linearly with the thickness of the upper layer, to decrease when stability increases, and to decrease away from the shelf edge on both sides. Very different wave shapes are found over the continental shelf and over the abyssal plain. Averaged over a period, group and phase velocities are close to the values predicted by the linear theory. The interaction between the internal wave and the barotropic tide, together with the asymmetry of the forced wave near the shelf edge, result in a continuous current parallel to the shelf break showing spatially periodic changes in its characteristics with about the same wavelength as the internal waves. Evidence for such a current is found in the data from a recent cruise.

On the inertial motion of a homogeneous ocean

An investigation of properties of the solutions of the steady state inviscid barotropic vorticity equation in a rectangular basin was performed for various functional relationships between potential vorticity and the streamfunction. All computed solutions which have slow interior flow and satisfy Arnol'd-Blumen condition are qualitatively similar to Fofonoff's inertial gyre. A new class of solutions with a small vortex near the boundary current is described. Such solutions are not stable under finite amplitude perturbations and instability is manifested in the drift of the vortex. It is shown that the vortex is robust and decays only after collision with the boundary or under the influence of very large perturbations. We also show that the inertial boundary current may be much wider than in Fofonoff's model due to the appearance of a countercurrent on its seaward side.

On the inertial motion of a homogeneous ocean

On the inertial motion of a homogeneous ocean

Closing the oceanic circulation

Two examples of circulation in a homogeneous ocean driven by balanced evaporation-precipitation and closed by a Fofonoff-type inertial current on the western side are given. The balances that obtain in the vorticity equation in different regions are discussed.

Ship perturbation of irradiance measurements at sea 1: Monte Carlo simulations

Most in-water irradiance and radiance measurements at sea are carried out by suspending an instrument from a hydrocable located relatively close to the ship, the presence of which can severely perturb the in-water light field. This paper describes Monte Carlo techniques which have been developed specifically to assess such perturbations. Sample computations of the perturbation to the upward and downward irradiances due to the presence of the ship are presented for the case of a homogeneous ocean. The results reveal situations in which the downward irradiance, in the case of collimated illumination, is relatively unperturbed, while large effects are observed in the case of diffuse illumination. Conversely, the upwelled irradiance just beneath the surface is seen to be strongly influenced by the ship’s presence for both types of illumination.

On the propagation of topographically trapped waves

Abstract In the context of ageostrophic theory in a homogeneous ocean, a nondimensional number is determined which corresponds to the Ursell number for long gravity waves. It is defined as Q = NL 2/h 3, where N is the amplitude of the wave travelling along the long length-scale direction, L is its length and h (which for gravity waves is the water depth) is given by h=(l 4 f 2/g)1/3. where l is the short length-scale, f the Coriolis parameter and g the acceleration due to gravity. The physical meaning of Q is as follows: if Q≪ O(1) the free evolution of the wave is linear and weakly dispersive, if Q = O(1) nonlinear and dispersive effects balance out and finally if Q ≫O(1) the evolution is nonlinear and non-dispersive. Expressions for the time scales for the development of dispersive and nonlinear effects are also determined. These results apply to topographically trapped waves, namely barotropic continental shelf and double Kelvin waves travelling along a rectilinear topographic variation.

Propagation of acoustic normal modes in a homogeneous ocean overlaying layered anisotropic porous beds

Attenuation of acoustic normal modes propagating in a shallow ocean overlaying naturally consolidated anisotropic sand beds is calculated using Biot’s theory for porous media. The propagator matrix method is utilized in the analysis to model layered transverse isotropic porous media. The effects of anisotropies in permeability and elastic moduli are studied numerically. It is found that the effect of the hydraulic anisotropy (permeability) of the sand bed on the acoustic attenuation is significant whereas the effect of the elastic anisotropy of the sand bed is not very important. The principle of relaxation is used to interpret the results. It is observed that the energy loss is maximum at a certain frequency which coincides with the relaxation frequency fr of the porous media given by fr=βν/3π ks. Here, β is the porosity, ν is the kinematic viscosity of the pore fluid, and ks is the coefficient of permeability.

Ocean response to low frequency wind forcing with application to the seasonal variation in the Florida Straits — Gulf Stream transport

The linear response of a two layer ocean model to a periodic wind stress curl in the presence of bottom photography has been invesrigated. For periods much less than the time taken for the wind generated baroclinic Rossby waves to pass over the topography (i.e. ‘short’ periods), the ocean response is primarily that for a homogenous ocean and thus strongly modified by topography. For periods much longer than this time (i.e. ‘long’ periods), the Rossby waves compensate for the effect of topography and the non-topographic Sverdrup balance holds. At intermediate periods, the phase and amplitude of the transport variations over topography can be understood in terms of a non-equilibrium baroclinic response forcing the barotropic mode over topography with relatively little feedback from the barotropic mode.a The bottom topography therefore imposes a low pass filter on the transport variations. For the Atlantic at 25°N, the long period limit is of the order of years to decades, depending on the location of the wind stress variability, so at annual period the non-topographic Sverdrup balance is not applicable. Variations in transport can be forced by a wind stress over varying topography, and by the passage of a coastal baroclinic Kelvin wave over topography. At short periods (including the annual), the effect of strong bottom topography is similar to that of an island. It was found that both with and without associated bottom topography a north-south island acts as a spatial filter such that wind stress forcing of larger north-south scale to the east of the island contributes proportionately more to transport variations to the west of the island than forcing of smaller north-south scale.

A numerical world ocean general circulation model Part I. Basic design and barotropic experiment

A new six-layer world ocean general circulation model based on the primitive system of equations is described in detail and its performance in the case of a homogeneous ocean is described. These test integrations show that the model is capable of reproducing the observed mean barotropic or vertically-integrated transport, as well as the seasonal variability of the major ocean gyres. The surface currents, however, are dominated by the Ekman transport, and such non-linear features as the western boundary currents and the equatorial countercurrents are poorly represented. The abyssal boundary countercurrents are also absent due to the lack of thermohaline forcing. The most conspicuous effect of the bottom topography on a homogeneous ocean is seen in the Southern ocean where the calculated Antarctic circumpolar transport through the Drake passage ( ≈ 10 Sv, with bathymetry included) greatly underestimates the observed transport (≈ 100 Sv).

Estimation of the influence of a current on the pressure field of a monochromatic point source in a homogenous ocean

Estimation of the influence of a current on the pressure field of a monochromatic point source in a homogenous ocean

Effects of Continental Slope on the Mean Shelf Circulation

Csanady's (1978) theory on the mean shelf circulation in a homogeneous ocean was re-examined by including effects of a continental slope. The results suggested that the mean southwestward flow on the Mid-Atlantic Blight is driven by an inflow from the Georges Bank.

Acoustic propagation in the ocean with a porous bottom

Biot's theory was directly incorporated with the normal mode analysis of acoustic propagation in the ocean with a porous elastic bottom. The complex dispersion relations was obtained in a closed form for the case of a homogeneous ocean with a poro-elastic half-space. The attenuation data from the shallow water experiments in the Mediterranean Sea were compared with the theoretical calculations. The 100-m water/sandy bottom data showed an optional transmission frequency of about 250 Hz. The theoretical analysis using the sediment data revealed that the attenuation of the high-frequency components are mainly due to the seepage of pore water through the sand (the slow compressional wave effect) and the attenuation of the low-frequency components are owing to the energy dissipation of the shear waves by the Coulomb friction in the consolidated sand. As a result, the intermediate frequency components have minimum overall attenuations and result into the optimal transmission frequencies. The agreements between the theory and the experiments are good. [Work supported by NSF.]

The Generation of Diurnal Period Shelf Waves by Tidal Currents

Abstract Continental shelf waves of diurnal period are shown to be generated by tidally induced Reynolds stresses within a bottom Stokes-scale boundary layer. The theory is applicable to a uniformly rotating, homogeneous ocean of two-dimensional depth variability in which alongshore variations occur over scales large compared to the shelf width. Explicit solutions are derived for the shelf wave velocity components and for the cross-shelf sea surface slope in the case of a traveling Kelvin wave forcing. Numerical values are presented for an exponential depth profile H = H0 exp(−2αx), where x is the coordinate normal to the coast. Results indicate that the amplitude of the shelf wave current can exceed that of the astronomical tidal current and that the alongshore component of the shelf wave current will consistently lead the alongshore component of the tidal current by 180° to 0° over one, wavelength in the direction of phase propagation.

Underwater sound from surface waves according to the Lighthill-Ribner theory

The acoustic source density given by Ribner’s version of the Lighthill theory is calculated for a stochastic surface gravity wavefield. A Green function gives the acoustic farfield, as a volume integral. The method eliminates some of the complications involving the moving ocean surface. For a homogeneous ocean, the farfield acoustic spectrum agrees with the spectrum of Hughes [J. Acoust. Soc. Am. 60, 1032–1039 (1976)], and at low frequencies with the spectrum of Brekhovskikh [Izv. Atmos. Ocean Phys. 2, 582–587 (1966)], after certain corrections are applied to their results. At high frequencies, the Brekhovskikh spectrum is larger by a factor (5/4)2.

A linear stratified ocean model of the equatorial undercurrent

A linear stratified ocean model is used to study the wind-driven response of the equatorial ocean. The model is an extension of the Lighthill (1969) model that allows the diffusion of heat and momentum into the deeper ocean, and so can develop non-trivial steady solutions. To retain the ability to expand solutions into sums of vertical normal modes, mixing coefficients must be inversely proportional to the square of the back ground Väisälä frequency. The model is also similar to the earlier homogeneous ocean model of Stommel (i960). He extended Ekman dynamics to the equator by allowing his model to generate a barotropic pressure field. The present model differs in that the presence of stratification allows the generation of a baroclinic pressure field as well. The most important result of this paper is that linear theory can produce a realistic equatorial current structure. The model Undercurrent has a reasonable width and depth scale. There is westward flow both above and below the Undercurrent. The meridional circulation conforms to the ‘classical’ picture suggested by Cromwell (1953). Unlike the Stommel solution, the response here is less sensitive to variations of parameters. Ocean boundaries are not necessary for the existence of the Undercurrent but are necessary for the existence of the deeper Equatorial Intermediate Current. The radiation of equatorially trapped Rossby and Kelvin waves is essential to the development of a realistic Undercurrent. Because the system supports the existence of these waves, low-order vertical modes can very nearly adjust to Sverdrup balance (defined below), which in a bounded ocean and for winds without curl is a state of rest. As a result, higher-order vertical modes are much more visible in the total solution. This property accounts for the surface trapping and narrow width scale of the equatorial currents. The high-order modes tend to be in Yoshida balance (defined below) and generate the characteristic meridional circulation pattern associated with equatorial Ekman pumping.

Resonance of Poincaré waves on a continental shelf

The response of a continental shelf to incident Poincaré waves in a homogeneous ocean rotating about a vertical axis is considered, linear friction being incorporated in the model. The shelf is shown to resonate at the usual 'quarter-wavelength' frequencies, but surprisingly, the maximum energy absorption at resonance occurs for a particular value of the relation between the friction parameter and the shelf geometry.

Variation of the vertical directionality of noise with depth in the North Pacific

A vertical array of 20 vibration isolated hydrophones was suspended from the Research Platform FLIP at various depths from 713 to 4816 m. Preformed sets of beams were formed with a digital beamformer to observe the vertical noise distribution at several frequencies between 23 and 100 Hz. Directional spectra derived from 10-min samples of digital records are presented. Interpretation of the data set leads to a model for the vertical noise directional spectrum as a function of depth which indicates a reduction of a factor of 2 in the vertical extent of the noise window as depth increases from the sound channel axis to the critical depth. This reduction in width is accompanied by a reduction in the maximum level of about 4 dB. The effect is essentially independent of frequency over the observed range of 23 to 100 Hz. No horizontal null in the directional spectrum of the noise, as predicted by ray theory for a horizontally homogeneous ocean, was observed in the data.

The transient response of the North Atlantic: Some model studies

Four numerical experiments have been designed to clarify the role of stratification and topography on the transient response of the ocean to a change in wind forcing. The geometry and topography appropriate to the North Atlantic between the equator and 50°N are used to make the study more appropriate to a real ocean. In all four experiments, zonally symmetric wind stresses are ‘switched on’ at the upper surface of a resting model ocean. Two short experiments, 1 and 2, with a duration of 100 days, are first discussed. These are for a homogeneous ocean with and without topography. The response in the flat‐bottomed case can be described either in terms of planetary waves or basin modes, but when topography is present, no obvious wave propagation was identified. Higher‐frequency basin modes are detectable, but their amplitude is much lower than that in the flat‐bottomed case. They are damped out on a time scale of ∼50 days. Two longer experiments, 3 and 4, are then analyzed. These are the analogs of 1 and 2, but stratification was included. The introduction of stratification for the ocean with topography leads to a new, longer time scale, not just for the baroclinic modes, but also for the barotropic. Despite the presence of topography, modal analysis was found useful in analyzing the results. Propagation effects are analyzed, both on the moderately fast time scale of internal Kelvin waves and on the slow time scale of internal planetary waves. Kelvin waves are apparent along the equator, the northern boundary, and on the eastern coast in the Gulf of Guinea from the equator to 20°N. They are not clearly visible anywhere on the west coast. Planetary waves can be detected in the interior both in the presence and absence of topography. When topography is present without stratification, the transport of the Gulf Stream is reduced from 30 to 14 million tons per second. This is a well‐known result. With stratification there is no significant difference in transport between the case with or without topography.