A Coupled-Mode Shallow-Water Model for Tidal Analysis: Internal Tide Reflection and Refraction by the Gulf Stream

Abstract

A hydrostatic, coupled-mode, shallow-water model (CSW) is described and used to diagnose and simulate tidal dynamics in the greater Mid-Atlantic Bight region. The reduced-physics model incorporates realistic stratification and topography, internal tide forcing from a priori estimates of the surface tide, and advection terms that describe first-order interactions of internal tides with slowly varying mean flow and mean buoyancy fields and their respective shear. The model is validated via comparisons with semianalytic models and nonlinear primitive equation models in several idealized and realistic simulations that include internal tide interactions with topography and mean flows. Then, 24 simulations of internal tide generation and propagation in the greater Mid-Atlantic Bight region are used to diagnose significant internal tide interactions with the Gulf Stream. The simulations indicate that locally generated mode-one internal tides refract and/or reflect at the Gulf Stream. The redirected internal tides often reappear at the shelf break, where their onshore energy fluxes are intermittent (i.e., noncoherent with surface tide) because meanders in the Gulf Stream alter their precise location, phase, and amplitude. These results provide an explanation for anomalous onshore energy fluxes that were previously observed at the New Jersey shelf break and linked to the irregular generation of nonlinear internal waves.

Semidiurnal internal tide incoherence in the equatorial Pacific

“…[], Kelly and Lermusiaux [], and Kelly et al . [], who show that mesoscale structures such as eddies and jets can decohere, reflect, refract, and scatter the internal tides. We observe all of these mechanisms in the equatorial jet region, but we do not detect clear examples of wave reflections.…”

“…Kelly et al . [] and Kelly and Lermusiaux [] show that these dipoles are balanced by energy terms related to energy advection by the mean flow. We do not compute these terms here; this work is saved for a future paper.…”

“…First, the internal tide generation (barotropic to baroclinic conversion) may vary in time with the tidal forcing due to local changes in stratification and/or remotely generated incoherent internal tides [ Chavanne et al ., ; Nash et al ., ; Kelly et al ., ; Pickering et al ., ; Kerry et al ., ]. After generation, the internal tides propagate through mesoscale flows, and the associated spatial and temporal variability in stratification, currents, and vorticity may cause time variable refraction of the internal gravity wave fields [ Park and Watts , ; Rainville and Pinkel , ; Ward and Dewar , ; Zaron and Egbert , ; Dunphy and Lamb , ; Ponte and Klein , ; Kelly and Lermusiaux , ; Kelly et al ., ; Kerry et al ., ; Magalhaes et al ., ]. Hence, the internal tides become phase incoherent with the tidal forcing at a given location in the ocean.…”

“…There are few studies that have looked into the interaction between the equatorial jets and the internal tides from the FPI and Hawaii. However, the interaction between midlatitude jets and internal tides has been studied in numerical model experiments [ Ponte and Klein , ; Kelly and Lermusiaux , ; Kelly et al ., ]. Magalhaes et al .…”

Long‐Range Radiation and Interference Pattern of Multisource M2 Internal Tides in the Philippine Sea

“…Internal tide dissipation can result from breaking near the continental slopes (Klymak et al, ), topographic scattering in the deep ocean (Mathur et al, ; Wang et al, ), and cascading to smaller scales via wave‐wave interactions (Henyey et al, ; Müller et al, ). In addition, the refraction/reflection processes that result from subtidal velocities and density gradients associated with background flows transform some internal tide energy into incoherent and temporally variable energy and modulate the propagation path and energy flux pattern (Kelly et al, ; Kerry et al, ; Zilberman et al, ). However, the propagation path of low‐mode internal tides is only slightly affected by typical background currents in the energetic internal tide areas, although the phase becomes increasingly incoherent as the propagation distance increases (Rainville et al, ; Rainville & Pinkel, ).…”