Topographic Rectification of Tidal Currents on the Sides of Georges Bank

Loder, John W.

doi:10.1175/1520-0485(1980)010<1399:trotco>2.0.co;2

Cited by 290 publications

(241 citation statements)

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“…More recently, Padman et al [1992] reported an anticyclonic flow around the Yermak plateau area in the eastern Arctic. They attributed the rectification process to tidal forcing, similar to the analysis by Loder [1980] for Georges Bank.…”

Section: Introductionsupporting

confidence: 61%

A laboratory study of mean flow generation in rotating fluids by Reynolds stress gradients

McGuinness¹,

Boyer²,

Fernando³

2001

J. Geophys. Res.

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Abstract. Laboratory experiments were conducted that demonstrate that a mean azimuthal flow can be produced by introducing Reynolds stress gradients to a rotating fluid with zero initial mean flow. This mechanism may play a role in the generation of mean currents in coastal regions. The experiments entail the establishment of turbulence in a thin annular-shaped region centered within a cylindrical test cell through the use of a vertically oscillating grid. This region rests in a horizontal plane perpendicular to the vertical axis of the tank, and the entire system is placed on a turntable to simulate background rotation. Flow visualization techniques are used to depict qualitative features of the resulting flow field. Measurements of the mean and turbulent velocity fields are performed using a two-component laser-Doppler velocimeter. The results show how rectified currents (mean flows) can be generated via Reynolds stress gradients induced by periodic forcing of the grid. In the absence of background rotation, rectified flow is observed in the radial and vertical directions only. The presence of background rotation tends to organize these motions in that the flow tends to move parallel to the turbulent source, i.e., in the azimuthal direction, with the source (strong turbulence) located to the right, facing downstream. The influence of rotation on the Reynolds stresses and their gradients as well as on the ensuing mean flow is evaluated, and the observations are examined by considering individual contributions of the terms in the Reynolds-averaged momentum equations. IntroductionLargely because of environmental concerns, there has been an increased interest over the past decade in better understanding, and eventually predicting, the characteristics of current systems in coastal oceans. One goal, for example, is to develop the knowledge base necessary to improve the prediction of the transport of pollutants and marine biota. The present study considers the question of generating mean (or rectified) currents in fluid systems that sustain turbulent Reynolds stress gradients in the presence of background rotation. In this context a mean or rectified flow is defined as one for which a fluid forcing (with a zero temporal average) leads to persis- respectively. Note that for an experiment starting at t = 0 with U1-= Uo = W --0 and imposing Reynolds stress gradients, OUo/Ot = 0, and hence Uo remains zero at all times. The radial and vertical velocities, however, can be developed via the Reynolds stress gradient terms on the right-hand side of (12) Nonrotating CaseFor the nonrotating case (i.e., f --0), axisymmetry and scaling arguments can be explored to simplify further the dynamical equations. If one follows a turbulent fluid parcel (e.g., u '1-) in the horizontal plane as it moves radially away from the gap, no preferential direction is associated with its motion along an azimuth; that is, the axisymmetry of the system necessitates that the particle will just as likely move in the positive as in the negative 0 dire...

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Section: Introductionsupporting

confidence: 61%

A laboratory study of mean flow generation in rotating fluids by Reynolds stress gradients

McGuinness¹,

Boyer²,

Fernando³

2001

J. Geophys. Res.

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“…In particular, the tidal rectification due to the stretching mechanism of the water columns is considered dominant compared to the ones due to the bottom friction of the tidal current. It is well known that the bottom friction plays an important role in coastal seas [Robinson, 1981] or over such topographic features as the Georges Bank [Loder, 1980], where the bottom depth is <40 m. However, in our case the bottom depth near the shelf break of the Bay of Biscay is much deeper (of the order of 200 m). The mathematical approach is based on the spectral method introduced by Zimmerman [1978Zimmerman [ , 1980 and developed by Maas et al [1987]; then Zhang et al [1996] extended the model, which was initially applied to small-amplitude topography [Maas et al, 1987], to a realistic topography such as the continental slope.…”

Section: Paper Number 1999jc900050contrasting

confidence: 52%

“…However, the difference between the observed residual and the theoretical value is approximately the same at the two moorings with a value between 4 and 5 cm/s (Table 5). This suggests that this difference could not result from another process associated with the tidal rectification since the forcing parameters of the tidal rectification are drastically different at both locations (see section 3.2); note that this argument also applies to the friction-based models developed by Huthnance [1973] and Loder [1980]. The difference between the model output and observations is more likely to come from a current which is not linked to tidal rectification.…”

Section: Spatial Evolution Of the Rectified Tidementioning

confidence: 92%

“…Thus, once the model assumptions are accepted, the mathematical solution given by the spectral method is considered as exact; that is, it is not confined to a limited domain of the physical parameters. This is an advantage compared to earlier barotropic rectification models [Huthnance, 1973;Loder, 1980] whose harmonic truncation method associated with various bottom friction parametrizations did not induce convergence of the solutions in the frictionless limit (see the discussions by Garreau Our model is applied to the realistic case of the continental slope in the northern Bay of Biscay with (1) tidal rectification due to the Coriolis mechanism, (2) a large-amplitude topography, and (3) a forcing term with both M2 and S2 tidal waves. The paper is organized as follows: the data processing is presented in section 2, and the observations are analyzed in section 3.…”

Section: Paper Number 1999jc900050mentioning

confidence: 99%

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Effect of barotropic tidal rectification on low‐frequency circulation near the shelf break in the northern Bay of Biscay

Pérenne¹,

Pichon²

1999

J. Geophys. Res.

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Abstract. Current meter data collected in the Bay of Biscay are used with a barotropic model to study the effect of the tidal rectification on the low-frequency circulation near the shelf break. Data collected at two different locations are analyzed and show that the tidal forcing terms and the low-frequency circulation are completely different at the two locations. In order to obtain a quantitative interpretation of these differences, a tidal forcing with both M2 and S2 waves is introduced in a barotropic tidal rectification model. We focus on the rectification process due to the "stretching of the water columns" alone, in the realistic case of large-amplitude topography. A first theoretical result is that the bichromatic forcing generates a nonlinear variation of the residual current which depends on only one nondimensional parameter. This parameter is a function of the barotropic flow and of the wave frequencies. A second result is that the low-frequency circulation generated by such a rectification process (including the two waves) is twice as large in spring tide than in neap tide. Finally, the model applied to both moorings confirms that the tidal rectification is much weaker at one mooring, the northwest one, than at the other, where the tidal rectification can explain 50% of the observed low-frequency circulation.

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“…This evidently implies an "ultraviolet catastrophe" if the bottom topographic length scale becomes very small (the slope going to infinity), an indication of the invalidity of the primitive series for stronger nonlinearities, although the horizontally integrated mass-transport given by Huthnance ( 1973) remains finite for small topographic length scales. Loder (1980) improved the theory by including feed back of the generated residual currents to the tidal velocity field. This method, which is in fact not a perturbation approach but a harmonic truncation in the frequency domain, surprisingly removes the catastrophic behaviour of the response for small topographic length scales, leading to results that seem to be uniformly valid for all strengths of the nonlinear interactions concerned.…”

Section: Introductionmentioning

confidence: 99%

On the exact shape of the horizontal profile of a topographically rectified tidal flow

1987

Deep Sea Research Part B. Oceanographic Literature Review

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Starting from the nonlinear shallow water equations of a homogeneous rotating fluid we derive the equation describing the evolution of vorticity by a fluctuating bottom topography of small amplitude, using a multiple scale expansion in a small parameter, which is the topographic length scale relative to the tidal wave length. The exact response functions of residual vorticity for a sinusoidal bottom topography are compared with those obtained by a primitive perturbation series and by harmonic truncation, showing the former to be invalid for small topographic length scales and the latter to be only a fair approximation for vorticity produced by planetary vortex stretching. In deriving the exact shape of the horizontal residual velocity profile at a step-like break in the bottom topography, it is shown that the Lagrangian profile only exists in a strip having the width of the amplitude of the tidal excursion at both sides of the break, and that it vanishes outside that interval. Moreover, in the limit of small amplitude topography at least, it vanishes altogether for the generation mechanism by means of planetary vortex stretching. The Eulerian profile is shown to extend over twice the interval of the Lagrangian profile both for production by vortex stretching 106L. R. M. MAAS, J. T. F. ZIMMERMAN AND N. M. TEMME and by differential bottom friction. These finite intervals over which the residual velocity profiles exist for a step-like topography are not reproduced by harmonic truncation of the basic equation. This method gives exponentially decaying profiles, indicating spurious horizontal diffusion of vorticity. In terms of orders of magnitude, the method of harmonic truncation is reliable for residual velocity produced by vortex stretching but it overestimates the residual velocity produced by differential bottom friction by a factor 2.

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Topographic Rectification of Tidal Currents on the Sides of Georges Bank

Cited by 290 publications

References 0 publications

A laboratory study of mean flow generation in rotating fluids by Reynolds stress gradients

A laboratory study of mean flow generation in rotating fluids by Reynolds stress gradients

Effect of barotropic tidal rectification on low‐frequency circulation near the shelf break in the northern Bay of Biscay

On the exact shape of the horizontal profile of a topographically rectified tidal flow

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