The influence of a geostrophic current on the internal tide generation

2021 ◽  
Author(s):  
Yangxin He ◽  
Kevin Lamb
Keyword(s):  
Conversion Rate ◽  
Gaussian Function ◽  
Internal Tide ◽  
Maximum Velocity ◽  
Propagation Path ◽  
Geostrophic Current ◽  
Total Conversion ◽  
Shelf Slope ◽  
Baroclinic Energy Conversion ◽  
Linear Slope

<p>We investigate the influence of a barotropic geostrophic current on<br>internal tide (IT) generation over a shelf slope.<br>The current $V_g(x)$ is modeled as an idealized Gaussian function centered at<br>$x_0$ with width $x_r$ and maximum velocity $V_{max}$.<br>The bathymetry is modelled as a linear slope with smoothed corners.<br>We calculate the total barotropic-to-baroclinic energy conversion $C =<br>\int \overbar{C} \,dx = \int \int \rho' g W \,dx\, dz$. <br>$\overbar{C}(x,t)$ can be either positive or negative. Positive (negative) conversion means energy is<br>converted from barotropic to baroclinic (baroclinic to barotropic)<br>waves. <br>The main conclusions are: 1) $V_g(x)$ changes the effective<br>frequency $f_{eff}$. This has a direct impact on the slope of the IT<br>characteristics and the slope criticality, which affects the total<br>conversion rate;<br>2) Since $(V_g)_x$ is not a constant value, $f_{eff}$ varies along the<br>slope. This has a significant effect on the IT beam generation<br>location and its propagation path. If the current is strong enough so<br>that $f_{eff}$ is greater than the barotropic tidal frequency $\sigma_T$, a blocking<br>region is formed where the conversion vanishes and IT propagation is blocked;<br>3) Changes of sign in $\bar{C}(x,t)$ correspond to the locations where<br>IT beams reflect from the boundaries. As a result, the total conversion rate $C$ is<br>also strongly affected by the IT beam pattern.<br>In conclusion, the total conversion rate $C$ is affected by a<br>combination of three factors: slope criticality, size and location of the blocking<br>region and the IT beam patterm, all of which can be varied by changing<br>the strength, width and location of the geostrophic current $V_g(x)$.</p>

scholarly journals Internal Wave Reflection on Shelf Slopes with Depth-Varying Stratification

2013 ◽  
Vol 43 (2) ◽  
pp. 248-258 ◽  
Author(s):  
Rob A. Hall ◽  
John M. Huthnance ◽  
Richard G. Williams
Keyword(s):  
Internal Wave ◽  
Internal Waves ◽  
Energy Flux ◽  
Internal Tide ◽  
Shelf Break ◽  
Maximum Slope ◽  
Near Surface ◽  
Shelf Slope ◽  
Linear Slope ◽  
Horizontal Wavelength

Abstract Reflection of internal waves from sloping topography is simple to predict for uniform stratification and linear slope gradients. However, depth-varying stratification presents the complication that regions of the slope may be subcritical and other regions supercritical. Here, a numerical model is used to simulate a mode-1, M2 internal tide approaching a shelf slope with both uniform and depth-varying stratifications. The fractions of incident internal wave energy reflected back offshore and transmitted onto the shelf are diagnosed by calculating the energy flux at the base of slope (with and without topography) and at the shelf break. For the stratifications/topographies considered in this study, the fraction of energy reflected for a given slope criticality is similar for both uniform and depth-varying stratifications. This suggests the fraction reflected is dependent only on maximum slope criticality and independent of the depth of the pycnocline. The majority of the reflected energy flux is in mode 1, with only minor contributions from higher modes due to topographic scattering. The fraction of energy transmitted is dependent on the depth-structure of the stratification and cannot be predicted from maximum slope criticality. If near-surface stratification is weak, transmitted internal waves may not reach the shelf break because of decreased horizontal wavelength and group velocity.

The Mechanism of Internal Tide Generation over Weak Topography

2012 ◽  
Vol 588-589 ◽  
pp. 1972-1978
Author(s):  
Li Dan Wu ◽  
Chun Bao Miao
Keyword(s):  
Energy Conversion ◽  
Conversion Rate ◽  
Internal Tide ◽  
Baroclinic Mode ◽  
Resonance Case ◽  
Numerical Techniques ◽  
Barotropic Tide ◽  
Baroclinic Energy Conversion ◽  
Baroclinic Modes ◽  
Perturbation Pressure

Here the process of internal tide generation over idealized (sinusoidal) topography was investigated using numerical techniques, in which the barotropic-to-baroclinic energy conversion was discussed. The result shows that when the wavenumber of the sinusoidal topography, ktopo, is equal to the horizontal wavenumber of the m-th baroclinic mode km, the conversion from the barotropic tide to the m-th baroclinic mode is enhanced with the increase of topography length; When the wavenumber of the sinusoidal topography is not equal to horizontal wavenumbers of any baroclinic modes, ktopo≠km(m=1,2,...), conversion from the barotropic energy to baroclinic modes is decreased with the increase of topography length. Furthermore, it shows that in resonance case, the phase of the perturbation pressure gradually agrees with the phase of the truncated sinusoidal topography, and the conversion rate is always positive over the topography, thus the baroclinic mode which matches with the wavenumber of the sinusoidal topography persists in absorbing energy from the barotropic tide, and the conversion rate is increased.

Effects of an along-shelf current on the generation of internal tides near the critical latitude

2021 ◽  
Vol 932 ◽  
Author(s):  
Yangxin He ◽  
Kevin G. Lamb
Keyword(s):  
Conversion Rate ◽  
Internal Tide ◽  
Internal Tides ◽  
Horizontal Shear ◽  
Background Current ◽  
Baroclinic Energy Conversion ◽  
Internal Wave Generation ◽  
Spatially Varying ◽  
Beam Patterns ◽  
Critical Latitude

The effects of along-shelf barotropic geostrophic currents on internal wave generation by the $K_1$ tide interacting with a shelf at near-critical latitudes are investigated. The horizontal shear of the background current results in a spatially varying effective Coriolis frequency which modifies the slope criticality and potentially creates blocking regions where freely propagating internal tides cannot exist. This paper is focused on the barotropic to baroclinic energy conversion rate, which is affected by a combination of three factors: slope criticality, size and location of the blocking region where the conversion rate is extremely small and the internal tide (IT) beam patterns. All of these are sensitive to the current parameters. In our parameter space, the current can increase the conversion rate up to 10 times.

scholarly journals Investigation of the Internal Tides in the Northwest Pacific Ocean Considering the Background Circulation and Stratification

2020 ◽  
Vol 50 (11) ◽  
pp. 3165-3188
Author(s):  
Pengyang Song ◽  
Xueen Chen
Keyword(s):  
Pacific Ocean ◽  
Ocean Circulation ◽  
Conversion Rate ◽  
Internal Tide ◽  
Internal Tides ◽  
Global Ocean ◽  
Northwest Pacific ◽  
Northwest Pacific Ocean ◽  
Baroclinic Tide ◽  
The Northwest Pacific Ocean

AbstractA global ocean circulation and tide model with nonuniform resolution is used in this work to resolve the ocean circulation globally as well as mesoscale eddies and internal tides regionally. Focusing on the northwest Pacific Ocean (NWP, 0°–35°N, 105°–150°E), a realistic experiment is conducted to simulate internal tides considering the background circulation and stratification. To investigate the influence of a background field on the generation and propagation of internal tides, idealized cases with horizontally homogeneous stratification and zero surface fluxes are also implemented for comparison. By comparing the realistic cases with idealized ones, the astronomical tidal forcing is found to be the dominant factor influencing the internal tide conversion rate magnitude, whereas the stratification acts as a secondary factor. However, stratification deviations in different areas can lead to an error exceeding 30% in the local internal tide energy conversion rate, indicating the necessity of a realistic stratification setting for simulating the entire NWP. The background shear is found to refract propagating diurnal internal tides by changing the effective Coriolis frequencies and phase speeds, while the Doppler-shifting effect is remarkable for introducing biases to semidiurnal results. In addition, nonlinear baroclinic tide energy equations considering the background circulation and stratification are derived and diagnosed in this work. The mean flow–baroclinic tide interaction and nonlinear energy flux are the most significant nonlinear terms in the derived equations, and nonlinearity is estimated to contribute approximately 5% of the total internal tide energy in the greater Luzon Strait area.

scholarly journals Internal tide energy flux over a ridge measured by a co-located ocean glider and moored acoustic Doppler current profiler

Ocean Science ◽  
2019 ◽  
Vol 15 (6) ◽  
pp. 1439-1453 ◽  
Author(s):  
Rob A. Hall ◽  
Barbara Berx ◽  
Gillian M. Damerell
Keyword(s):  
Energy Flux ◽  
Internal Tide ◽  
Acoustic Doppler Current Profiler ◽  
Small Scale ◽  
Negative Bias ◽  
Potential Density ◽  
Shelf Slope ◽  
Current Profiler ◽  
Circle Diameter ◽  
Horizontal Wavelength

Abstract. Internal tide energy flux is an important diagnostic for the study of energy pathways in the ocean, from large-scale input by the surface tide to small-scale dissipation by turbulent mixing. Accurate calculation of energy flux requires repeated full-depth measurements of both potential density (ρ) and horizontal current velocity (u) over at least a tidal cycle and over several weeks to resolve the internal spring–neap cycle. Typically, these observations are made using full-depth oceanographic moorings that are vulnerable to being “fished out” by commercial trawlers when deployed on continental shelves and slopes. Here we test an alternative approach to minimize these risks, with u measured by a low-frequency acoustic Doppler current profiler (ADCP) moored near the seabed and ρ measured by an autonomous ocean glider holding station by the ADCP. The method is used to measure the semidiurnal internal tide radiating from the Wyville Thomson Ridge in the North Atlantic. The observed energy flux (4.2±0.2 kW m−1) compares favourably with historic observations and a previous numerical model study. Error in the energy flux calculation due to imperfect co-location of the glider and ADCP is estimated by subsampling potential density in an idealized internal tide field along pseudorandomly distributed glider paths. The error is considered acceptable (<10 %) if all the glider data are contained within a “watch circle” with a diameter smaller than 1∕8 the mode-1 horizontal wavelength of the internal tide. Energy flux is biased low because the glider samples density with a broad range of phase shifts, resulting in underestimation of vertical isopycnal displacement and available potential energy. The negative bias increases with increasing watch circle diameter. If watch circle diameter is larger than 1∕8 the mode-1 horizontal wavelength, the negative bias is more than 3 % and all realizations within the 95 % confidence interval are underestimates. Over the Wyville Thomson Ridge, where the semidiurnal mode-1 horizontal wavelength is ≈100 km and all the glider dives are within a 5 km diameter watch circle, the observed energy flux is estimated to have a negative bias of only 0.4 % and an error of less than 3 % at the 95 % confidence limit. With typical glider performance, we expect energy flux error due to imperfect co-location to be <10 % in most mid-latitude shelf slope regions.

Generation of Internal Tides by Tide-Topography Resonance over Weak Topography: Analytical Calculation

2012 ◽  
Vol 588-589 ◽  
pp. 1964-1971
Author(s):  
Li Dan Wu ◽  
Chun Bao Miao
Keyword(s):  
Conversion Rate ◽  
Mode Conversion ◽  
Bottom Topography ◽  
Analytical Calculation ◽  
Internal Tide ◽  
Resonant Mode ◽  
Internal Tides ◽  
Resonant Modes ◽  
Minimum Amplitude ◽  
Baroclinic Modes

Internal tides generated by the interaction of the barotropic tide with bottom topography are studied by using an analytical solution. Tide-topography resonance takes place when the wavenumber of the truncated sinusoidal topography is equal to that of one baroclinic mode. The minimum amplitude of the resonant mode increases from the center of the domain to both sides of the topography; while the maximum keeps the same. Amplitudes of the internal tides and mode conversion rate are analyzed as a function of the length and wavenumber of the topography. For non-resonant modes, the amplitudes are weak and vary periodically with the extending of the topography, and are exactly zero when the length of topography is integral times of the mode-1 wavelength. For resonant modes, the amplitudes increase with the length of the topography. For each internal tide mode, there is a response zone, where the amplitude for one mode is obviously larger than other baroclinic modes. The response zones for high modes are wider than those for low modes. Mode conversion rate is obviously high when the wavenumber of the topography is equal to that of the baroclinic modes; otherwise it is almost zero. Furthermore, mode conversion rate for small topography wavenumber is more than that for large topography wavenumber with the same number of the sinusoidal topography, and is less with the same topography length.

scholarly journals Internal Tides in Monterey Submarine Canyon

2011 ◽  
Vol 41 (1) ◽  
pp. 186-204 ◽  
Author(s):  
Rob A. Hall ◽  
Glenn S. Carter
Keyword(s):  
Energy Conversion ◽  
Energy Flux ◽  
Internal Tide ◽  
Submarine Canyon ◽  
Ocean Model ◽  
Internal Tides ◽  
Remote Areas ◽  
Order Of Magnitude ◽  
Baroclinic Energy Conversion

Abstract The M2 internal tide in Monterey Submarine Canyon is simulated using a modified version of the Princeton Ocean Model. Most of the internal tide energy entering the canyon is generated to the south, on Sur Slope and at the head of Carmel Canyon. The internal tide is topographically steered around the large canyon meanders. Depth-integrated baroclinic energy fluxes are up canyon and largest near the canyon axis, up to 1.5 kW m−1 at the mouth of the upper canyon and increasing to over 4 kW m−1 around Monterey and San Gregorio Meanders. The up-canyon energy flux is bottom intensified, suggesting that topographic focusing occurs. Net along-canyon energy flux decreases almost monotonically from 9 MW at the canyon mouth to 1 MW at Gooseneck Meander, implying that high levels of internal tide dissipation occur. The depth-integrated energy flux across the 200-m isobath is order 10 W m−1 along the majority of the canyon rim but increases by over an order of magnitude near the canyon head, where internal tide energy escapes onto the shelf. Reducing the size of the model domain to exclude remote areas of high barotropic-to-baroclinic energy conversion decreases the depth-integrated energy flux in the upper canyon by 20%. However, quantifying the role of remote internal tide generation sites is complicated by a pressure perturbation feedback between baroclinic energy flux and barotropic-to-baroclinic energy conversion.

scholarly journals Low-mode internal tide generation by topography: an experimental and numerical investigation

2009 ◽  
Vol 636 ◽  
pp. 91-108 ◽  
Author(s):  
PAULA ECHEVERRI ◽  
M. R. FLYNN ◽  
KRAIG B. WINTERS ◽  
THOMAS PEACOCK
Keyword(s):  
Large Scale ◽  
Internal Tide ◽  
Finite Depth ◽  
Internal Tides ◽  
Nonlinear Phenomena ◽  
Nonlinear Behaviour ◽  
Mode Structure ◽  
Channel Depth ◽  
Ocean Ridges ◽  
Baroclinic Energy Conversion

We analyse the low-mode structure of internal tides generated in laboratory experiments and numerical simulations by a two-dimensional ridge in a channel of finite depth. The height of the ridge is approximately half of the channel depth and the regimes considered span sub- to supercritical topography. For small tidal excursions, of the order of 1% of the topographic width, our results agree well with linear theory. For larger tidal excursions, up to 15% of the topographic width, we find that the scaled mode 1 conversion rate decreases by less than 15%, in spite of nonlinear phenomena that break down the familiar wave-beam structure and generate harmonics and inter-harmonics. Modes two and three, however, are more strongly affected. For this topographic configuration, most of the linear baroclinic energy flux is associated with the mode 1 tide, so our experiments reveal that nonlinear behaviour does not significantly affect the barotropic to baroclinic energy conversion in this regime, which is relevant to large-scale ocean ridges. This may not be the case, however, for smaller scale ridges that generate a response dominated by higher modes.

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