TY - JOUR
T1 - A coupled model for laplace's tidal equations in a fluid with one horizontal dimension and variable depth
AU - Kelly, Samuel M.
AU - Jones, Nicole L.
AU - Nash, Jonathan D.
PY - 2013
Y1 - 2013
N2 - Tide-topography interactions dominate the transfer of tidal energy from large to small scales. At present, it is poorly understood how low-mode internal tides reflect and scatter along the continental margins. Here, the coupling equations for linear tides model (CELT) are derived to determine the independent modal solutions to Laplace's Tidal Equations (LTE) over stepwise topography in one horizontal dimension. CELT is (i) applicable to arbitrary one-dimensional topography and realistic stratification without requiring numerically expensive simulations and (ii) formulated to quantify scattering because it implicitly separates incident and reflected waves. Energy fluxes and horizontal velocities obtained using CELT are shown to converge to analytical solutions, indicating that "flat bottom'' modes, which evolve according to LTE, are also relevant in describing tides over sloping topography. The theoretical framework presented can then be used to quantify simultaneous incident and reflected energy fluxes in numerical simulations and observations of tidal flows that vary in one horizontal dimension. Thus, CELT can be used to diagnose internal-tide scattering on continental slopes. Here, semidiurnal mode-1 scattering is simulated on the Australian northwest, Brazil, and Oregon continental slopes. Energy-flux divergence and directional energy fluxes computed using CELT are shown to agree with results from a finite-volume model that is significantly more numerically expensive. Last, CELT is used to examine the dynamics of two-way surface-internal-tide coupling. Semidiurnal mode-1 internal tides are found to transmit about 5% of their incident energy flux to the surface tide where they impact the continental slope. It is hypothesized that this feedback may decrease the coherence of sea surface displacement on continental shelves.
AB - Tide-topography interactions dominate the transfer of tidal energy from large to small scales. At present, it is poorly understood how low-mode internal tides reflect and scatter along the continental margins. Here, the coupling equations for linear tides model (CELT) are derived to determine the independent modal solutions to Laplace's Tidal Equations (LTE) over stepwise topography in one horizontal dimension. CELT is (i) applicable to arbitrary one-dimensional topography and realistic stratification without requiring numerically expensive simulations and (ii) formulated to quantify scattering because it implicitly separates incident and reflected waves. Energy fluxes and horizontal velocities obtained using CELT are shown to converge to analytical solutions, indicating that "flat bottom'' modes, which evolve according to LTE, are also relevant in describing tides over sloping topography. The theoretical framework presented can then be used to quantify simultaneous incident and reflected energy fluxes in numerical simulations and observations of tidal flows that vary in one horizontal dimension. Thus, CELT can be used to diagnose internal-tide scattering on continental slopes. Here, semidiurnal mode-1 scattering is simulated on the Australian northwest, Brazil, and Oregon continental slopes. Energy-flux divergence and directional energy fluxes computed using CELT are shown to agree with results from a finite-volume model that is significantly more numerically expensive. Last, CELT is used to examine the dynamics of two-way surface-internal-tide coupling. Semidiurnal mode-1 internal tides are found to transmit about 5% of their incident energy flux to the surface tide where they impact the continental slope. It is hypothesized that this feedback may decrease the coherence of sea surface displacement on continental shelves.
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U2 - 10.1175/JPO-D-12-0147.1
DO - 10.1175/JPO-D-12-0147.1
M3 - Article
AN - SCOPUS:84883765673
SN - 0022-3670
VL - 43
SP - 1780
EP - 1797
JO - Journal of Physical Oceanography
JF - Journal of Physical Oceanography
IS - 8
ER -