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James L. Hench
and
Richard A. Luettich Jr.

Abstract

An analysis of transient momentum balances is carried out to elucidate circulation, dynamics, and exchange mechanisms at shallow barotropic tidal inlets. Circulation is computed using a depth-integrated, fully nonlinear, time-stepping, finite-element model with variably spaced grids having horizontal resolution down to 50 m. Velocity and elevation fields from the model are used to directly evaluate the contribution of each term in the momentum equations to the overall momentum balance. A transformation of the xy momentum terms into an sn coordinate system is used to simplify the interpretation of the dynamics and provide vivid illustrations of the forces and resulting accelerations in the flow. The analysis is conducted for an idealized inlet and contrasted with a highly detailed model of Beaufort Inlet, North Carolina. Results show that momentum balances in the immediate vicinity of these inlets vary significantly in time and space and oscillate between two dynamical states. Near maximum ebb or flood, the alongstream momentum balances are dominated by advective acceleration, pressure gradient, and bottom friction. Cross-stream balances are dominated by centrifugal acceleration and pressure gradients. Near slack, balances more closely follow linear wave dynamics, with local accelerations balancing pressure gradients, and (to a lesser degree) Coriolis. Comparisons between the idealized inlet and Beaufort Inlet show broad similarities in these momentum balances. However, natural inlet geometry and bottom topography, as well as the tidal transmission characteristics of the sounds behind Beaufort Inlet produce strong asymmetries. Moreover, momentum balances are highly localized, often with subkilometer length scales. The dynamics are used to explain the physical mechanisms for inlet exchange. In particular, the results indicate that the cross-stream dynamics generate a “wall” along the length of an inlet during the stronger phases of the tide. The wall is established by opposing cross-inlet pressure gradients and centrifugal forces, and it poses a significant barrier to cross-inlet exchange during the stronger phases of the tide but is absent near slack.

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Richard A. Luettich Jr.
,
Julia C. Muccino
, and
Michael G. G. Foreman

Abstract

The vertical velocity, w, in three-dimensional circulation models is typically computed from the three-dimensional continuity equation given the free-surface elevation and depth-varying horizontal velocity. This problem appears to be overdetermined, since the continuity equation is first order, yet w must satisfy boundary conditions at both the free surface and the bottom. At least three methods have been previously proposed to compute w: (i) a “traditional” method that solves the continuity equation using only the bottom boundary condition, (ii) a “vertical derivative” method that solves the vertical derivative of the continuity equation using both boundary conditions, and (iii) an “adjoint” method that solves the continuity equation and both boundary conditions in a least squares sense. The latter solution is equivalent to the traditional solution plus a correction that varies linearly over the depth.

It is shown here that the vertical derivative method is mathematically and physically inconsistent if discretized as previously proposed. However, if properly discretized it is equivalent to the adjoint method if the boundary conditions are weighted so that they are satisfied exactly. Furthermore, if the surface elevation and horizontal velocity fields satisfy the depth-integrated continuity equation locally, one of the boundary conditions is redundant. In this case, the traditional, adjoint, and properly discretized vertical derivative approaches yield the same results for w. If the elevation and horizontal velocity are not locally mass conserving, the mass error is transferred into w. This is important for models that do not guarantee local mass conservation, such as some finite element models.

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Cristina Forbes
,
Richard A. Luettich Jr.
,
Craig A. Mattocks
, and
Joannes J. Westerink

Abstract

The evolution and convergence of modeled storm surge were examined using a high-resolution implementation of the Advanced Circulation Coastal Ocean and Storm Surge (ADCIRC) model for Hurricane Gustav (2008). The storm surge forecasts were forced using an asymmetric gradient wind model (AWM), directly coupled to ADCIRC at every time step and at every grid node. A total of 20 forecast advisories and best-track data from the National Hurricane Center (NHC) were used as input parameters into the wind model. Differences in maximum surge elevations were evaluated for ensembles comprised of the final 20, 15, 10, and 5 forecast advisories plus the best track. For this particular storm, the final 10–12 forecast advisories, encompassing the last 2.5–3 days of the storm’s lifetime, give a reasonable estimate of the final storm surge and inundation. The results provide a detailed perspective of the variability in the storm surge due to variability in the meteorological forecast and how this changes as the storm approaches landfall. This finding is closely tied to the consistency and accuracy of the NHC storm track forecasts and the predicted landfall location and, therefore, cannot be generalized to all storms in all locations. Nevertheless, this first attempt to translate variability in forecast meteorology into storm surge variability provides useful insights for guiding the potential use of storm surge models for forecast purposes. Model skill was also evaluated for Hurricane Gustav by comparing observed water levels with hindcast modeled water levels forced by river flow, tides, and several sources of wind data. The AWM (which ingested best-track information from NHC) generated winds that were slightly higher than those from NOAA’s Hurricane Research Division (HRD) H*Wind analyses and substantially greater than the North American Mesoscale (NAM) model. Surge obtained using the AWM more closely matched the observed water levels than that computed using H*Wind; however, this may be due to the neglect of the contribution of wave setup to the surge, especially in exposed areas. Several geographically distinct storm surge response regimes, some characterized by multisurge pulses, were identified and described.

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