Jeff Polton: Talk, in theme 2, with the aim of elucidating for a non specialist audience
"Tidally induced mean flow over bathymetric features - A steady state Huthnance
legacy". This would not be new work, more of a homage.
Tidally induced mean flow over bathymetric features A steady state Huthnance legacy
Theme 2 - (John Simpson's session)
Scope:
What it is & how it works.
Literature review with the aim of elucidating the process for a non specialist audience.
(I wouldn't intend to present new work - which would probably be a distraction from the
key principles)
Abstract:
When oscillating tides flow over undersea features mean flows are induced that flow
along contours of constant depth. Huthnance (1973) investigated this effect with
reference to tides over sandbanks and attributed the induced mean flow around the bank
to the effects of friction and planetary rotation. These interesting physical principles are
presented along with the developments of subsequent authors.
Outline (by papers):
Huthnance, J. M. (1973). Tidal current asymmetries over the Norfolk Sandbanks. Estuarine
and Coastal Marine Science, 1, 89–99.
Looks at tidally induced mean flow along topography that is uniform in one direction.
Identifies two mechanisms for inducing mean flow:
1) convective / friction effects: The argument is that in shallow water friction plays a larger role balancing the
acceleration (along with pressure). But in deep fluid friction is less important. For a tidal flow that has both
along and across shelf components, excess along shelf momentum is advected on shelf in the flood (which is
not compensated for on the ebb). And a deficit of negative along shelf momentum is advected off shelf during
the ebb. The net effect is an along slope mean current
2) Coriolis effect: The argument here is a bit opaque. However it seems consistent with the frictionless arguement that
conserves vorticity for flows being advected on and off shelf. The result is the same as for the friction: inducing a
clockwise circulation around N Hem topographic features.
This work is then 'schematically' developed by Zimmerman, which significantly helps with the
interpretation of John's equations!
Zimmerman, J. T. F. (1981). Dynamics, diffusion and geomorphological significance of tidal
residual eddies. Nature, 290, 549–555.
Pretty neat summary / interpretation of Huthnance ’73 physical processes. Reduces the mean 2D residual circulation to
vorticity considerations, giving 4 regimes: 1) closed channel; 2) headland; 3&4) submarine ellipsoids mounds skewed
to left and right of the reciprocating tide.
Mean circulation in the closed channel and headland case are explained using circulation argument (circulation is
computed by the flux of vorticity into the closed contour).
Mean circulation around the submarine ellipsoid has two parts i) a Coriolis part (which looks like PV conservation
when H varies - though it is presented using Bernoulli acceleration and consequent variable Coriolis deflection
language, varying with H). The Coriolis part is always clockwise in NHem. ii) A frictional torque. The sense of the
frictional torque depends whether the ellipsoid is skewed to the left or right of the tidal flow.
It is my impression that the Coriolis and frictionally induced circulations are the analysis from Huthnance 73.
The paper goes on to present the idea of Residual Eddy diffusion - diffusion of parcels from a closed residual path.
The paper also calculates how induced flow varies with tidal flow for various parameters (H & h, tidal excusion over
topo wavelength.) Suggest that a model grid resolution of half the tidal displacement to capture most of the induced
mean residual flow. [NB they compute circulations for the Coriolis and frictional processes but using circular
bathymetry I do not see how a non-zero frictional circulation can arise as there is no break in the symmetry of the
problem - Coriolis has an inherent asymmetry)
Then tackle Robinson 1981 and Loder, 1980
Robinson, I. S. (1981). Tidal vorticity and residual circulation. Deep Sea Research Part A.
Oceanographic Research Papers, 28(3), 195–212.
Formulate 2D vorticity equation. Introduce ‘Residual Vorticity’ as a general means for inferring the residual
circulation. Residual vorticity is generated from ‘vorticity sources’. Realistic scenarios can be computed as a
superposition of sources. This work is not that dissimilar to Zimmerman ’81, though it is grounded in a
vorticity balance. Has useful scale analysis method for relative sizes of contributions e.g. estimate for size of
induced velocity from frictionless PV conservation
Loder, J. W. (1980). Topographic rectification of tidal currents on the sides of Georges
Bank. Journal of Physical Oceanography, 10, 1399–1416.
Higher order tidal harmonic expansion of the Huthnance ‘73 (2D) work. Also including 2D tidal ellipse solutions.
Discussion about cross shelf flow being link to vertical structure.
Estimates baroclinic exchange at shelf edge due to bed friction + ssh gradient, wherein the bed flow (due to friction) is
not geostrophically balance resulting in an across slope pressure driven flow.
Deals with the Stokes drift effect of the tidal waves.
Include elements where time permits from other works that guid on John's 73 paper:
Dong, C., Ou, H.-W., Chen, D., & Visbeck, M. (2004). Tidally Induced Cross-Frontal Mean
Circulation: Analytical Study. Journal of Physical Oceanography, 34, 293–305.
Young, W. R. (1983). Topographic rectification of tidal currents. Journal of Physical
Oceanography, 13, 716–721.
Ou, H.-W. (1999). A Model of Tidal Rectification by Potential Vorticity Mixing. Part I:
Homogeneous Ocean. Journal of Physical Oceanography, 29, 821–827.
Ou, H.-W. (2000). A Model of Tidal Rectification by Potential Vorticity Mixing. Part II:
Frontal Regime. Journal of Physical Oceanography, 30, 564–571.
Wright, D. G., & Loder, J. W. (1985). A Depth-dependent Study of the Topographic
Recification of Tidal Currents. Geophysical & Astrophysical Fluid Dynamics, 31,
169–220.
Garrett, C. J. R., & Loder, J. W. (1981). Dynamical Aspects of Shallow Sea Fronts.
Philosophical Transactions of the Royal Society A: Mathematical, Physical and
Engineering Sciences, 302, 563–581.
Pingree, R. D., & Maddock, L. (1979). Tidal flow around an island with a regularly sloping
bottom topography. J. Mar. Biol. Assoc. UK, 59, 699–710.
Zimmerman, J. T. F. (1978b). Dispersion by Tide-Induced Residual Current Vortices. In
Hydrodynamics of Estuaries and Fjords, Proceedings of the 9th International Liege
Colloquium on Ocean Hydrodynamics (Vol. 23). Elsevier.