Turbulent Bottom Boundary Layer Research Articles

Evolution of water wave packets by wind in shallow water

We use the Korteweg–de Vries (KdV) equation, supplemented with several forcing/friction terms, to describe the evolution of wind-driven water wave packets in shallow water. The forcing/friction terms describe wind-wave growth due to critical level instability in the air, wave decay due to laminar friction in the water at the air–water interface, wave stress in the air near the interface induced by a turbulent wind and wave decay due to a turbulent bottom boundary layer. The outcome is a modified KdV–Burgers equation that can be a stable or unstable model depending on the forcing/friction parameters. To analyse the evolution of water wave packets, we adapt the Whitham modulation theory for a slowly varying periodic wave train with an emphasis on the solitary wave train limit. The main outcome is the predicted growth and decay rates due to the forcing/friction terms. Numerical simulations using a Fourier spectral method are performed to validate the theory for various cases of initial wave amplitudes and growth and/or decay parameter ranges. The results from the modulation theory agree well with these simulations. In most cases we examined, many solitary waves are generated, suggesting the formation of a soliton gas.

Effects of Bubble Plumes on Lake Dynamics, Near‐Bottom Turbulence, and Transfer of Dissolved Oxygen at the Sediment‐Water Interface

AbstractWe quantify the lake dynamics, near‐bottom turbulence, flux of dissolved oxygen (DO) across the sediment‐water interface (SWI) and their interactions during oxygenation in two lakes. Field observations show that the lake dynamics were modified by the bubble plumes, showing enhanced mixing in the near‐field of the plumes. The interaction of the bubble‐induced flow with the internal density structure resulted in downwelling of warm water into the hypolimnion in the far‐field of the plumes. Within the bottom boundary layer (BBL), both lakes show weak oscillating flows primarily induced by seiching. The vertical profile of mean velocity within 0.4 m above the bed follows a logarithmic scaling. One lake shows a larger drag coefficient than those in stationary BBLs, where the classic law‐of‐the‐wall is valid. The injection of oxygen elevated the water column DO and hence, altered the DO flux across the SWI. The gas transfer velocity is driven by turbulence and is correlated with the bottom shear velocity. The thickness of the diffusive boundary layer was found to be consistent with the Batchelor length scale. The dynamics of the surface renewal time follow a log‐normal distribution, and the turbulent integral time scale is comparable to the surface renewal time. The analyses suggest that the effect of bubble plumes on the BBL turbulence is limited and that the canonical scales of turbulence emerge for the time‐average statistics, validating the turbulence scaling of gas transfer velocity in low‐energy lakes.

Variations of Bottom Boundary Layer Turbulence under the Influences of Tidal Currents, Waves, and Raft Aquaculture Structure in a Shallow Bay

High-frequency measurements of tides, waves, and turbulence were made using the bottom-mounted tripod equipped with the Nortek 6-MHz acoustic Doppler velocimetry during 20–23 February 2016 (winter) and 12–26 June 2017 (summer) in Heini Bay, Yellow Sea. The synchro-squeezed wavelet transform was applied for wave-turbulence decomposition, and an iterative procedure was developed to identify the turbulence inertial subrange in the bottom boundary layer. The analysis results reveal the dependency of the inertial subrange on the tidal current and turbulence intensities. The flood-ebb tidal flows are different between the summer and winter seasons, without and with the presence of dense raft aquaculture for kelp, respectively. In summer, the turbulent kinetic energy (TKE), turbulent Reynolds stress (TRS), and dissipation rate (ε) of TKE increase smoothly with the increasing tidal flow magnitude, and ε is approximately in balance with TKE production related to the vertical shear. The presence of heavy kelp aquaculture in winter causes the reduction in flow speeds and TRS, while keeping TKE and ε at high levels.

On the formulation and implementation of the stress-free boundary condition over deformed bathymetry using a spectral-element-method-based incompressible Navier–Stokes equations solver

Various strategies are proposed for enforcing stress-free boundary conditions on deformed domains using a weak-form-based discretization in a Cartesian frame of reference. Due to the irregularity of the computational domain and the particular type of boundary condition, a coupling between the Cartesian velocity components is introduced. As such, a different computational kernel is required for the numerical solution of the associated vector Helmholtz equation, as contrasted to what is used for the scalar unknowns of the equations. Three approaches are presented, aimed towards the exact or approximate implementation of zero tangential stress (traction) at the deformed boundary while ensuring a decoupling of the velocity components in the solution of the vector Helmholtz equation. Two of these strategies, those which approximate the free slip boundary condition, are applied to the propagation of an internal solitary wave (ISW) of depression over a deformed bathymetry. The spatial structure and amplitude of the resultant pseudo-traction, which is accurately predicted by a simple scaling estimate, are explored as a function of the ISW-based Reynolds number, Re. For the Re values considered, the pseudo-traction is negligible with respect to the corresponding no-slip tangential shear stress. The pseudo-traction-induced, time-integrated loss of ISW energy is found to be significantly weaker than the associated viscous dissipation in the interior water column. Although, at laboratory-scale or oceanic Re, an approximate free-slip boundary condition is found to yield negligible pseudo-traction, this might not be the case when an elevated eddy viscosity is used in this context as a surrogate for no-slip turbulent bottom boundary layer dynamics.

Parameterization of oscillating boundary layers in lakes and coastal oceans

Oscillating turbulent bottom boundary layers (BBLs) occur in lakes and coastal oceans. At the mesoscale level, their kinematics are usually characterized by assuming either laminar or steady turbulent flow, and applying analytical solutions or semi-empirical correlations; e.g. log-law, Stokes’ second problem, inertial dissipation method (IDM), Batchelor fitting to temperature microstructure method (TMM). To investigate the ability of these models to capture oscillating turbulent BBLs, we have performed large eddy simulations (LES) and direct numerical simulations (DNS) for Reynolds numbers (Reδs; based on the Stokes layer thickness) between 20 and 3600. The velocity profiles showed logarithmic behavior throughout the cycle, in fully turbulent flows (error less than 2% for Reδs>3000), but the log-law was only accurate during turbulent bursts in the later stage of the acceleration phase for Reδs<550. Stokes’ second problem predicted the velocity profile in laminar or disturbed laminar flow (errors less than 10% for Reδs<500). At high Reynolds number (Reδs=3600), LES shows that the dissipation of turbulent kinetic energy from the IDM is more accurate than that from the log-law, particularly during changes in flow direction. The difference between the dissipation estimated from field observations (using IDM and TMM) and from idealized LES, however, suggest that measurement errors may predominate over uncertainties in simulation of boundary conditions and methodological errors in field applications.

Submesoscale Vortical Wakes in the Lee of Topography

AbstractAn idealized framework of steady barotropic flow past an isolated seamount in a background of constant stratification (with frequency N) and rotation (with Coriolis parameter f) is used to examine the formation, separation, instability of the turbulent bottom boundary layers (BBLs), and ultimately, the genesis of submesoscale coherent vortices (SCVs) in the ocean interior. The BBLs generate vertical vorticity ζ and potential vorticity q on slopes; the flow separates and spawns shear layers; barotropic and centrifugal shear instabilities form submesoscale vortical filaments and induce a high rate of local energy dissipation; the filaments organize into vortices that then horizontally merge and vertically align to form SCVs. These SCVs have O(1) Rossby numbers () and horizontal and vertical scales that are much larger than those of the separated shear layers and associated vortical filaments. Although the upstream flow is barotropic, downstream baroclinicity manifests in the wake, depending on the value of the nondimensional height , which is the ratio of the seamount height to that of the Taylor height , where L is the seamount half-width. When , SCVs span the vertical extent of the seamount itself. However, for , there is greater range of variation in the sizes of the SCVs in the wake, reflecting the wake baroclinicity caused by the topographic interaction. The aspect ratio of the wake SCVs has the scaling , instead of the quasigeostrophic scaling .

Energy Loss from Transient Eddies due to Lee Wave Generation in the Southern Ocean

ABSTRACTObservations suggest that enhanced turbulent dissipation and mixing over rough topography are modulated by the transient eddy field through the generation and breaking of lee waves in the Southern Ocean. Idealized simulations also suggest that lee waves are important in the energy pathway from eddies to turbulence. However, the energy loss from eddies due to lee wave generation remains poorly estimated. This study quantifies the relative energy loss from the time-mean and transient eddy flow in the Southern Ocean due to lee wave generation using an eddy-resolving global ocean model and three independent topographic datasets. The authors find that the energy loss from the transient eddy flow (0.12 TW; 1 TW = 1012 W) is larger than that from the time-mean flow (0.04 TW) due to lee wave generation; lee wave generation makes a larger contribution (0.12 TW) to the energy loss from the transient eddy flow than the dissipation in turbulent bottom boundary layer (0.05 TW). This study also shows that the energy loss from the time-mean flow is regulated by the transient eddy flow, and energy loss from the transient eddy flow is sensitive to the representation of anisotropy in small-scale topography. It is implied that lee waves should be parameterized in eddy-resolving global ocean models to improve the energetics of resolved flow.

Internal-Wave-Driven Mixing: Global Geography and Budgets

AbstractInternal-wave-driven dissipation rates ε and diapycnal diffusivities K are inferred globally using a finescale parameterization based on vertical strain applied to ~30 000 hydrographic casts. Global dissipations are 2.0 ± 0.6 TW, consistent with internal wave power sources of 2.1 ± 0.7 TW from tides and wind. Vertically integrated dissipation rates vary by three to four orders of magnitude with elevated values over abrupt topography in the western Indian and Pacific as well as midocean slow spreading ridges, consistent with internal tide sources. But dependence on bottom forcing is much weaker than linear wave generation theory, pointing to horizontal dispersion by internal waves and relatively little local dissipation when forcing is strong. Stratified turbulent bottom boundary layer thickness variability is not consistent with OGCM parameterizations of tidal mixing. Average diffusivities K = (0.3–0.4) × 10−4 m2 s−1 depend only weakly on depth, indicating that ε = KN2/γ scales as N2 such that the bulk of the dissipation is in the pycnocline and less than 0.08-TW dissipation below 2000-m depth. Average diffusivities K approach 10−4 m2 s−1 in the bottom 500 meters above bottom (mab) in height above bottom coordinates with a 2000-m e-folding scale. Average dissipation rates ε are 10−9 W kg−1 within 500 mab then diminish to background deep values of 0.15 × 10−9 W kg−1 by 1000 mab. No incontrovertible support is found for high dissipation rates in Antarctic Circumpolar Currents or parametric subharmonic instability being a significant pathway to elevated dissipation rates for semidiurnal or diurnal internal tides equatorward of 28° and 14° latitudes, respectively, although elevated K is found about 30° latitude in the North and South Pacific.

Bed Shear Stresses Parameterization in Wave–Current Interaction by k − ω Turbulence Model

For a flow generated by the wave–current interaction (WCI), an accurate estimate of the maximum ([Formula: see text]) and the mean ([Formula: see text]) bed shear stresses is important for the sediment transport calculation. These two parameters are usually estimated by numerical modeling which can prove to be difficult to implement and very costly in CPU time. This paper then proposes analytic parameterization of [Formula: see text] and [Formula: see text] by simple relationship depending on the current and wave shear stresses ([Formula: see text] and [Formula: see text]).The proposed parameterization was performed in two steps: the first step is to build a numerical database of [Formula: see text] and [Formula: see text] for different combinations of flow variables. This step was carried out by an one-dimensional vertical (1DV) model of turbulent bottom boundary layer using the [Formula: see text] turbulence model. The second step is to represent this database by predefined analytical relations. This step was performed by an optimization procedure adopting the GlobalSearch (GS) (function of Matlab software).The proposed parameterization based on the “[Formula: see text]/GS” combination provides very good estimations of [Formula: see text] and [Formula: see text]. These estimations are similar to those proposed by other authors who have studied the WCI by analytical models widely used by the marine science community.

Efficient boundary mixing due to near-inertial waves in a non-tidal basin: Observations from the Baltic Sea

Diapycnal mixing in large nontidal basins is often assumed to be related to the effect of near-inertial waves. While the role of near-inertial shear for the generation of shear instabilities in the stratified interior is relatively well understood, much less is known about the impact of near-inertial motions on boundary mixing processes in nontidal systems, mainly owing to the lack of appropriate observations. Here, an extensive data set is discussed, describing the variability of boundary mixing induced by near-inertial motions near the sloping topography of one of the main basins of the Baltic Sea. These data reveal the existence of a vigorously turbulent bottom boundary layer of a few meters thickness covering the entire slope region above and below the permanent halocline that constitutes the main obstacle for vertical transport in the Baltic Sea. Near-bottom turbulence was driven by the near-inertial shear in the frictional boundary layer rather than by breaking of near-inertial waves near critical slopes. Large regions of the bottom boundary layer remained strongly stratified, and therefore, different from the traditional view of inefficient boundary mixing, mixing efficiencies reached values typical for the ocean's interior.

GEOPHYSICAL ANALYSIS OF ABNORMAL SEISMIC (OCEANOGRAPHY) REFLECTION CHARACTERISTICS OF OCEANIC BOTTOM BOUNDARY LAYER

AbstractTraditional seismic oceanography researches dominantly pay attention to the oceanographic phenomena within the water column, such as internal wave, eddy, thermohaline fine structure, water mass boundaries, internal tide, thermohaline staircase, lee wave and so on, and could provide extra information quantitatively and qualitatively as compared with physical oceanography method. So far, very few researches try to study the water column near the seafloor, which is a significant boundary layer where water‐sediment dynamic interaction, cold seepage, hydrothermal vents, biochemical activities and energy dissipation of many oceanic processes may occur. To be different from previous seismic oceanography researches, this paper mainly focuses on seismic reflections of seawater columns near the seafloor, by reprocessing a large amount of seismic sections acquired in the west and north of the South China Sea.In this paper, conventional seismic facies analysis method is used to analyze, classify and summarize the external geometry, internal configuration, continuity, amplitude and apparent frequency of some complex seismic reflections of seawater column near the seafloor. Combined with the past research results of seismic oceanography, theory of bottom boundary layer and other various processes near the seafloor, this article not only classifies the reflection characteristics of meso‐scale eddies, internal solitary wave and Lee wave, but also speculates that some possible processes could result in a few of the newly discovered abnormal seismic reflections. For example, sheet seismic facies unit may reflect turbulent bottom boundary layer; hair‐like reflection configuration can be caused by the sediment resuspension, resulted from the interaction of bottom current and high frequency undulating seafloor, such as sand dunes; plume seismic facies unit indicates the characteristic of seep plume; and broom seismic facies unit could be associated with the upwelling currents and sediment resuspension in pockmarks. Results indicate that seismic oceanography can image not only processes of the ocean water column, such as internal wave and eddy, but also some complex processes near the seafloor, which greatly expands the research field of seismic oceanography and provides a new method and research perspective for the field observation of processes near the seafloor. Here, bottom boundary layer refers to the water column near the seafloor, and we call all the processes of this region “seafloor processes”.

Topographic vorticity generation, submesoscale instability and vortex street formation in the Gulf Stream

AbstractMeanders and eddies are routinely observed in the Gulf Stream along the South Atlantic Bight. We analyze here the instability processes that lead to the formation of submesoscale eddies on the cyclonic side of the Gulf Stream at the exit of the Florida Straits using very high resolution realistic simulations. The positive relative vorticity and potential vorticity on the cyclonic side of the Gulf Stream are strongly intensified in the Straits due to topographic drag along the continental slope. The bottom drag amplifies the cyclonic shear by generating large positive vertical vorticity values within the sloped turbulent bottom boundary layer. Downstream from the Straits the current becomes unstable to horizontal shear instability, rolls up, and forms a street of submesoscale vortices. The vortices expand as they propagate northward along the shelf, where they can generate large vertical displacements and enhance cross‐shelf exchanges.

Layered mixing on the New England Shelf in summer

AbstractThe layered structure of stratification and mixing on the New England Shelf (NES) in summer is examined by analyzing a comprehensive set of observations of hydrography, currents and turbulence. A clear distinction in mixing characteristics between the midcolumn water (consisting of subsurface stratification, middepth weak stratification and lower‐layer stratification) and a well‐mixed bottom boundary layer (BBL) is revealed. The combination of subtidal Ekman onshore bottom transport and cross‐shore density gradient created a lower‐layer stratification that inhibited the upward extension of the BBL turbulence. The BBL mixing was related to strong shear generated by bottom stress, and the magnitude and periodic variation of BBL mixing was determined by both the tidal and subtidal flows. Mixing in the midcolumn water occurred under stably stratified conditions and showed correspondence with the occurrence of near‐inertial and semidiurnal internal waves. Positive correlations between buoyancy frequency squared (N2) and shear variance (S2), S2 and dissipation rate (ε), N2 and ε are established in the midcolumn, but not in the BBL. The midcolumn ε was reasonably described by a slightly modified MacKinnon‐Gregg (MG) model.

Numerical simulations of larval transport into a rip‐channeled surf zone

Competent larvae of intertidal invertebrates have to migrate toward shore for settlement; however, their migration through the surf zone is not understood. We investigated larval transport mechanisms at a rip‐channeled beach. Because tracking larvae in the surf zone is infeasible, we used a three‐dimensional biophysical model to simulate the processes. The coupled model consists of a physical module for currents and waves, and a biological module for adding larval traits and behaviors as well as Stokes drift to Lagrangian particles. Model calculations were performed with and without onshore wind forcing. Without wind, wave‐driven onshore streaming occurs in the bottom boundary layer outside the surf zone. With onshore wind, onshore currents occur near the surface. In the surf zone, offshore‐directed rip currents and compensating onshore‐directed currents over shoals are formed in both no‐wind and wind cases. In the biological module, neutral, negative, and positive buoyant particles were released offshore. Additionally, particles either sank in the presence of turbulence or not. Two scenarios achieved successful onshore migration: Negatively buoyant larvae without wind forcing sink in the turbulent bottom boundary layer and are carried onshore by streaming; positively buoyant larvae drift toward shore in wind‐driven surface currents to the surf zone, then sink in the turbulent surf zone and remain near the bottom while transported shoreward. In both cases, the larval concentration is highest in the rip channel, consistent with field data. This successful result is only obtained if turbulence‐dependent sinking behavior and Stokes drift are included in the transport of larvae.

Deep‐water dynamics and boundary mixing in a nontidal stratified basin: A modeling study of the Baltic Sea

AbstractRecent results from a tracer release experiment have shown that, similar to many lakes and ocean basins, deep‐water mixing in the Baltic Sea is largely determined by mixing processes occurring in the energetic near‐bottom region. Due to the complexity and small vertical extent of this region, however, previous modeling studies of the Baltic Sea have so far not been able to provide a numerically and physically sound representation of boundary mixing. Here we discuss first results from a nested high‐resolution simulation of the central Baltic Sea that aims at a realistic description of the turbulent bottom boundary layer with the help of new numerical techniques (adaptive coordinates) and state‐of‐the‐art turbulence modeling. Using a comprehensive data set from the Baltic Sea Tracer Release Experiment, we show that the model is able to reproduce the key dynamical processes (near‐inertial waves, topographic waves, and a rim current) with excellent accuracy. Boundary mixing triggered by these processes was found to result in simulated basin‐scale mixing rates in close agreement with observations, including a seasonal variability that has been emphasized in previous studies. These results may be relevant also for the description of mixing in large lakes and other stratified basins.

Turbulence Process Domination under the Combined Forcings of Wind Stress, the Langmuir Vortex Force, and Surface Cooling

Abstract Turbulence in the ocean surface layer is generated by time-varying combinations of destabilizing surface buoyancy flux, wind stress forcing, and wave forcing through a vortex force associated with the surface wave field. Observations of time- and depth-averaged vertical velocity variance of full-depth turbulence in shallow unstratified water columns under destabilizing buoyancy forcing are used to determine when process domination can be assigned over a wide range of mixed forcings. The properties of two turbulence archetypes, one representing full-depth Langmuir circulations and the other representing full-depth convection, are described in detail. It is demonstrated that these archetypes lie in distinct regions of the plane of , where and are Langmuir and Rayleigh numbers, respectively, derived from scaling with surface stress velocity and a time scale characteristic of the growth of Langmuir circulation , where and are mean and Stokes velocities, respectively. Situations in which neither process dominates lie between the two end members, with relative dominance given by proximity to one or the other. Cases dominated by direct stress forcing are conspicuous by their absence. In cases of Langmuir domination, surface Stokes velocity is linearly related to , making it impossible to differentiate between scaling depth-averaged vertical velocity variance with , and any other scaling involving both and . A third nondimensional parameter is introduced and used to assess the importance of bottom boundary layer turbulence in a depth-limited system. Questions of time dependence and applicability of results to the open ocean surface boundary layer are considered.

On the use of the Stokes number to explain frictional tidal dynamics and water column structure in shelf seas

Abstract. In recent years coastal oceanographers have suggested using the "Strouhal" number or its inverse, the "Stokes" number, to describe the effect of bottom boundary layer turbulence on the vertical structure of both density and currents. These are defined as the ratios of the frictional depth (δ) to the water column depth (h) or vice versa. Although many researchers have mentioned that the effects of the earth's rotation should be important, they have tended to omit it. Rotation may have an important influence on tidal currents, as the frictional depth from a fully cyclonic to a fully anticyclonic tidal ellipse can vary by up to an order of magnitude at mid latitudes. The Stokes number might appear smaller for cyclonic current ellipses (larger for anticyclonic) than it is without rotation, resulting in frictional effects being underestimated (overestimated). Here, a way to calculate a Stokes number is proposed, in which the effect of the earth's rotation is taken into account. The standard Stokes and the rotational Stokes numbers are used as predictors for the position of the tidal mixing fronts in the Irish Sea. Results show that use of the rotational number improves the predictions of fronts in shallow cyclonic areas of the eastern Irish Sea. This suggests that the effect of rotation on the water column structure will be more important in shallow shelf seas and estuaries with strong rotational currents.

PREDICTION OF SEDIMENT TRANSPORT DUE TO IRREGULAR WAVE MOTION

&lt;p&gt;In general, waves in coastal environments are irregular and have a random shape with a height and period that was not constant. The accuracy of sediment transport rate prediction is the most important stages in the study of morphology and coastal marine environments. In addition, the predictive model of coastal morphology is more efficient to use the bottom shear stress calculation approach for practical purposes rather than a more complex approach to the modeling of two phases. In this paper, the calculation of sediment transport was based on the bottom shear stress modelling purposed with data validation from the experimental results in the turbulent bottom boundary layer over rough bed under irregular waves. The new approach to estimate the bottom shear stress was based on combining velocity and acceleration terms. Furthermore, a new approach of the bottom shear stress was applied to formulate the sheet flow sediment transport rate for irregular waves by using the experimental data from Dibadjnia and Watanabe (1998) and the empirical formula was found.&lt;/p&gt; &lt;p&gt;Keywords: sediment transport, bottom shear stress, irregular waves&lt;/p&gt;

PREDICTION OF SEDIMENT TRANSPORT DUE TO IRREGULAR WAVE MOTION

In general, waves in coastal environments are irregular and have a random shape with a height and period that was not constant. The accuracy of sediment transport rate prediction is the most important stages in the study of morphology and coastal marine environments. In addition, the predictive model of coastal morphology is more efficient to use the bottom shear stress calculation approach for practical purposes rather than a more complex approach to the modeling of two phases. In this paper, the calculation of sediment transport was based on the bottom shear stress modelling purposed with data validation from the experimental results in the turbulent bottom boundary layer over rough bed under irregular waves. The new approach to estimate the bottom shear stress was based on combining velocity and acceleration terms. Furthermore, a new approach of the bottom shear stress was applied to formulate the sheet flow sediment transport rate for irregular waves by using the experimental data from Dibadjnia and Watanabe (1998) and the empirical formula was found. Keywords: sediment transport, bottom shear stress, irregular waves

The impact of the spatial variability in bottom roughness on tidal dynamics and energetics, a case study: the M 2 surface tide in the North European Basin

A modified version of the 3D finite-element hydrostatic model QUODDY-4 is used to quantify the changes in the dynamics and energetics of the M 2 surface tide in the North European Basin, induced by the spatial variability in bottom roughness. This version differs from the original one, as it introduces a module providing evaluation of the drag coefficient in the bottom boundary layer (BBL) and by accounting for the equilibrium tide. The drag coefficient is found from the resistance laws for an oscillatory rotating turbulent BBL over hydrodynamically rough and incompletely rough underlying surfaces, describing how the wave friction factor as well as other resistance characteristics depend on the dimensionless similarity parameters for the BBL. It is shown that the influence of the spatial variability in bottom roughness is responsible for some specific changes in the tidal amplitudes, phases, and the maximum tidal velocities. These changes are within the model noise, while the changes in the averaged (over a tidal cycle) horizontal wave transport and the averaged dissipation of barotropic tidal energy may be of the same orders of magnitude as are the above energetic characteristics as such. Thus, contrary to present views, ignoring the spatial variability in bottom roughness at least in the North European Basin is only partially correct: it is valid for the tidal dynamics, but is liable to break down for the tidal energetics.