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A Regime Diagram for Internal Lee Waves in Coastal Plain Estuaries

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  • 1 Horn Point Lab University of Maryland Center for Environmental Science P.O. BOX 775 Cambridge, MD 21613, U.S.A.
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Abstract

Using an idealized channel representative of a coastal plain estuary, we conducted numerical simulations to investigate the generation of internal lee waves by lateral circulation. It is shown that the lee waves can be generated across all salinity regimes in an estuary. Since the lateral currents are usually subcritical with respect to the lowest mode, mode-2 lee waves are most prevalent but a hydraulic jump may develop during the transition to subcritical flows in the deep channel, producing high energy dissipation and strong mixing. Unlike flows over a sill, stratified water in the deep channel may become stagnant such that a mode-1 depression wave can form higher up in the water column. With the lee wave Froude number above 1 and the intrinsic wave frequency between the inertial and buoyancy frequency, the lee waves generated in coastal plain estuaries are nonlinear waves with the wave amplitude scaling approximately with 𝑉/N¯ where V is the maximum lateral flow velocity and N¯ is the buoyancy frequency. The model results are summarized using the estuarine classification diagram based on the freshwater Froude number Frf and the mixing parameter M. Δh decreases with increasing Frf as stronger stratification suppresses waves, and no internal waves are generated at large Frf. Δh initially increases with increasing M as the lateral flows become stronger with stronger tidal currents, but decreases or saturates to a certain amplitude as M further increases. This modeling study suggests that lee waves can be generated over a wide range of estuarine conditions.

Corresponding author: Renjian Li, Horn Point Lab., University of Maryland Center for Environmental Science, 2020 Horns Point Road, Cambridge, MD 21613, U.S.A. Email: rli@umces.edu.

Abstract

Using an idealized channel representative of a coastal plain estuary, we conducted numerical simulations to investigate the generation of internal lee waves by lateral circulation. It is shown that the lee waves can be generated across all salinity regimes in an estuary. Since the lateral currents are usually subcritical with respect to the lowest mode, mode-2 lee waves are most prevalent but a hydraulic jump may develop during the transition to subcritical flows in the deep channel, producing high energy dissipation and strong mixing. Unlike flows over a sill, stratified water in the deep channel may become stagnant such that a mode-1 depression wave can form higher up in the water column. With the lee wave Froude number above 1 and the intrinsic wave frequency between the inertial and buoyancy frequency, the lee waves generated in coastal plain estuaries are nonlinear waves with the wave amplitude scaling approximately with 𝑉/N¯ where V is the maximum lateral flow velocity and N¯ is the buoyancy frequency. The model results are summarized using the estuarine classification diagram based on the freshwater Froude number Frf and the mixing parameter M. Δh decreases with increasing Frf as stronger stratification suppresses waves, and no internal waves are generated at large Frf. Δh initially increases with increasing M as the lateral flows become stronger with stronger tidal currents, but decreases or saturates to a certain amplitude as M further increases. This modeling study suggests that lee waves can be generated over a wide range of estuarine conditions.

Corresponding author: Renjian Li, Horn Point Lab., University of Maryland Center for Environmental Science, 2020 Horns Point Road, Cambridge, MD 21613, U.S.A. Email: rli@umces.edu.
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