The propagation of tides near the critical latitude

Middleton, Jason H.; Denniss, Tom

doi:10.1080/03091929308203559

Cited by 8 publications

(6 citation statements)

References 10 publications

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“…Diurnal internal tide generation should be weak and any diurnal baroclinic tides will be bottom-trapped and will not propagate freely according to linear internal wave theory (i.e., Middleton and Denniss 1993). The model response basically followed this theory with weak baroclinic tides generated over the rim and upper flank of the guyot trapped at the bottom at ∼500-800 m (Fig.…”

Section: Baroclinic Tides For the Best Casementioning

confidence: 99%

Modeling internal tides over Fieberling Guyot: resolution, parameterization, performance

Robertson

2006

Ocean Dynamics

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Terrain-following ocean models are being used to simulate baroclinic tides and provide estimates of the tidal fields for circulation and mixing studies. These models have successfully reproduced elevations with most of the remaining inaccuracies attributed to topographic errors; however, the replication of barotropic and baroclinic velocity fields has not been as robust. Part of the problem is the lack of an adequate observational dataset in the simulated regions to compare the models. This problem was addressed using a dataset collected during the Flow over Abrupt Topography initiative at Fieberling Guyot. To evaluate the capability of the Regional Ocean Model System (ROMS) to simulate baroclinic tidal velocities, the combined tides for four constituents, M 2 , S 2 , K 1 , and O 1 , were modeled over Fieberling Guyot. Model inputs, numerical schemes, and parameterizations were varied to improve agreement with observations. These included hydrography, horizontal resolution, and the vertical mixing parameterization. Other factors were evaluated but are not included in this paper. With the best case, semidiurnal baroclinic tides were well replicated with RMS differences between the model estimates and the observations of 1.85 and 0.60 cm s −1 for the major axes of the tidal ellipses for M 2 and S 2 , respectively. However, diurnal K 1 baroclinic tides were poorly simulated with RMS differences of 4.49 cm s −1 . In the simulations, the K 1 baroclinic tides remained bottom-trapped unlike the observed fields, which had free waves due to the contribution of the mean velocity to the potential vorticity. The model did not adequately simulate the mean velocity, and the K 1 tides remained trapped. A resolution of 1 km most accurately reproduced the major axes and mean velocities; however, a 4-km resolution was sufficient for a qualitative estimate of where baroclinic tidal generation occurred. Nine vertical mixing parameterizations were compared. The vertical mixing parameterization was found to have minor effects on the velocity fields, with most effects occurring over the crown of guyot and in the lower water column; however, it had dramatic effects on the estimation of vertical diffusivity of temperature. Although there was no definitive best performer for the vertical mixing parameterization, several parameterizations could be eliminated based on comparison of the vertical diffusivity estimates with observations. The best performers were Mellor-Yamada and three generic length scale schemes.

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Section: Baroclinic Tides For the Best Casementioning

confidence: 99%

Modeling internal tides over Fieberling Guyot: resolution, parameterization, performance

Robertson

2006

Ocean Dynamics

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“…Theories of internal waves indicate that the propagation of internal tides has an obvious latitude dependence (Hibiya et al, ; Middleton & Denniss, ). According to the dispersion relation, internal wave beams propagate with a slope of

tan α = \sqrt{\frac{ω^{2} - f^{2}}{N^{2} - ω^{2}}} .

…”

Section: Introductionmentioning

confidence: 99%

“…Here ω , f , and N are the tidal frequency, Coriolis frequency, and buoyancy frequency, respectively. From equation , the propagation slope of internal wave beams becomes more horizontal, as the latitude increases toward the critical latitude where the inertial frequency equals the tidal frequency (Middleton & Denniss, ; Robertson, ). At the critical latitude, the propagation slope will become completely horizontal, internal tides are not predicted to propagate according to linear internal wave theory, and any internal waves generated poleward of the critical latitude will have their internal tidal energy locally trapped.…”

Section: Introductionmentioning

confidence: 99%

Impacts of Mesoscale Currents on the Diurnal Critical Latitude Dependence of Internal Tides: A Numerical Experiment Based on Barcoo Seamount

et al. 2019

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Critical latitudes are a significant area of tidal dissipation. Generally, critical latitudes are taken to be the exact latitude where the tidal frequency equals the inertial frequency. However, the key is really where the tidal frequency equals the combination of planetary vorticity and relative vorticity from background currents. Although the influence of background currents on critical latitude effects and nonlinear interactions have been noted for many years, their exact impacts are not well known. The latitude dependence of critical latitude impacts on the tides, internal tides, and internal waves in the presence of background currents was investigated using the Regional Ocean Modeling System by shifting a small domain including a seamount from 20.6° to 38.6°S and comparing simulations with and without background currents. The diurnal kinetic energy with mesoscale currents was relatively unchanged for most latitudes, except for a slight decrease 1–4° poleward of the critical latitude. However, the semidiurnal and high‐frequency (≥3 cycles per day) kinetic energy increased with the presence of mesoscale currents, especially within the diurnal critical latitude range. Spectral and nonlinear analyses indicated mesoscale currents broadened the range of critical latitude effects and enhanced energy transferring from diurnal frequencies to semidiurnal and high frequencies and from low to high mode waves. Local diffusivities increased, roughly an order of magnitude, when mesoscale currents were present. The impacts of mesoscale currents on the broadening of the critical latitude range and enhancement of nonlinear interactions were attributed to the additional relative vorticity and near‐inertial internal waves generated by mesoscale currents.

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“…Although these parameterizations are an important improvement, they ignore critical latitude effects. Here the critical latitude is defined as the latitude where the inertial frequency equals the tidal frequency (e.g., Furevik & Foldvik, ; Middleton & Denniss, ; Robertson, ), although others define it as the latitude with half the tidal frequency (e.g., MacKinnon et al, ; see Table ). Critical latitudes affect ocean dynamics in several ways.…”

Section: Introductionmentioning

confidence: 99%

“…They have been observed to be a key factor in energy transfer and dissipation (Hibiya et al, ). They strongly influence generation and propagation of internal tides (e.g., Middleton & Denniss, ; Robertson, ). Tides become resonant near critical latitude, increasing generation and energy transfers to harmonics.…”

Section: Introductionmentioning

confidence: 99%

Diurnal Critical Latitude and the Latitude Dependence of Internal Tides, Internal Waves, and Mixing Based on Barcoo Seamount

2017

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Vertical mixing is a key issue in ocean circulation modeling today. Mixing, particularly tidal mixing, is poorly represented in ocean and climate models, which generally ignore critical latitude effects. Critical latitude is the latitude where the inertial frequency equals the tidal frequency and differs for each tidal constituent. Critical latitudes strongly influence generation and propagation of internal tides. Using a model, latitude effects on tidal interactions with a seamount were examined by varying the latitude from 20° to 38°, through the range of the diurnal critical latitudes. The diurnal critical latitudes were found to strongly influence propagation of the diurnal internal tides, the magnitude of the semidiurnal tides, the energy in the harmonic and higher frequencies, the barotropic mean flow, and the diffusivities. The strongest effects occurred between the K1 and O1 critical latitudes. Here the semidiurnal tides, harmonics, and high frequencies were enhanced, barotropic mean velocities weakened, energy at the harmonics and higher frequencies increased, and diffusivities increased. Spectral techniques indicate that most of these impacts are the result of nonlinear wave‐wave interactions and resonant phenomena with the prominent mechanism harmonic transfers. There was no evidence of parametric subharmonic instabilities. The semidiurnal tides indicated a resonant response at 20°S, which is near the latitude for the combined M2 and K1 tidal period, ∼19°S.

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The propagation of tides near the critical latitude

Cited by 8 publications

References 10 publications

Modeling internal tides over Fieberling Guyot: resolution, parameterization, performance

Modeling internal tides over Fieberling Guyot: resolution, parameterization, performance

Impacts of Mesoscale Currents on the Diurnal Critical Latitude Dependence of Internal Tides: A Numerical Experiment Based on Barcoo Seamount

Diurnal Critical Latitude and the Latitude Dependence of Internal Tides, Internal Waves, and Mixing Based on Barcoo Seamount

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