skip to main content


The NSF Public Access Repository (NSF-PAR) system and access will be unavailable from 11:00 PM ET on Thursday, June 13 until 2:00 AM ET on Friday, June 14 due to maintenance. We apologize for the inconvenience.

Title: Generation and Evolution of Internal Solitary Waves in a Coastal Plain Estuary

Large-amplitude internal solitary waves were recently observed in a coastal plain estuary and were hypothesized to evolve from an internal lee wave generated at the channel–shoal interface. To test this mechanism, a 3D nonhydrostatic model with nested domains and adaptive grids was used to investigate the generation of the internal solitary waves and their subsequent nonlinear evolution. A complex sequence of wave propagation and transformation was documented and interpreted using the nonlinear wave theory based on the Korteweg–de Vries equation. During the ebb tide a mode-2 internal lee wave is generated by the interaction between lateral flows and channel–shoal topography. This mode-2 lee wave subsequently propagates onto the shallow shoal and transforms into a mode-1 wave of elevation as strong mixing on the flood tide erases stratification in the bottom boundary layer and the lower branch of the mode-2 wave. The mode-1 wave of elevation evolves into an internal solitary wave due to nonlinear steepening and spatial changes in the wave phase speed. As the solitary wave of elevation continues to propagate over the shoaling bottom, the leading edge moves ahead as a rarefaction wave while the trailing edge steepens and disintegrates into a train of rank-ordered internal solitary waves, due to the combined effects of shoaling and dispersion. Strong turbulence in the bottom boundary layer dissipates wave energy and causes the eventual destruction of the solitary waves. In the meantime, the internal solitary waves can generate elevated shear and dissipation rate in local regions.

Significance Statement

In the coastal ocean nonlinear internal solitary waves are widely recognized to play an important role in generating turbulent mixing, modulating short-term variability of nearshore ecosystem, and transporting sediment and biochemical materials. However, their effects on shallow and stratified estuaries are poorly known and have been rarely studied. The nonhydrostatic model simulations presented in this paper shed new light into the generation, propagation, and transformation of the internal solitary waves in a coastal plain estuary.

more » « less
Author(s) / Creator(s):
Publisher / Repository:
American Meteorological Society
Date Published:
Journal Name:
Journal of Physical Oceanography
Medium: X Size: p. 641-652
["p. 641-652"]
Sponsoring Org:
National Science Foundation
More Like this
  1. Recent mooring observations at a cross-channel section in Chesapeake Bay showed that internal solitary waves regularly appeared during certain phases of a tidal cycle and propagated from the deep channel to the shallow shoal. It was hypothesized that these waves resulted from the nonlinear steepening of internal lee waves generated by lateral currents over channel-shoal topography. In this study numerical modeling is conducted to investigate the interaction between lateral circulation and cross-channel topography and discern the generation mechanism of the internal lee waves. During ebb tides, lateral bottom Ekman forcing drives a counterclockwise (looking into estuary) lateral circulation, with strong currents advecting stratified water over the western flank of the deep channel and producing large isopycnal displacements. When the lateral flow becomes supercritical with respect to mode-2 internal waves, a mode-2 internal lee wave is generated on the flank of the deep channel and subsequently propagates onto the western shoal. When the bottom lateral flow becomes near-critical or supercritical with respect to mode-1 internal waves, the lee wave evolves into an internal hydraulic jump. On the shallow shoal, the lee waves or jumps evolve into internal bores of elevation.

    more » « less
  2. Abstract

    Large-amplitude internal solitary wave (ISW) shoaling, breaking, and run-up was tracked continuously by a dense and rapidly sampling array spanning depths from 500 m to shore near Dongsha Atoll in the South China Sea. Incident ISW amplitudes ranged between 78 and 146 m with propagation speeds between 1.40 and 2.38 m s−1. The ratio between wave amplitude and a critical amplitudeA0controlled breaking type and was related to wave speedcpand depth. Fissioning ISWs generated larger trailing elevation waves when the thermocline was deep and evolved into onshore propagating bores in depths near 100 m. Collapsing ISWs contained significant mixing and little upslope bore propagation. Bores contained significant onshore near-bottom kinetic and potential energy flux and significant offshore rundown and relaxation phases before and after the bore front passage, respectively. Bores on the shallow forereef drove bottom temperature variation in excess of 10°C and near-bottom cross-shore currents in excess of 0.4 m s−1. Bores decelerated upslope, consistent with upslope two-layer gravity current theory, though run-up extentXrwas offshore of the predicted gravity current location. Background stratification affected the bore run-up, withXrfarther offshore when the Korteweg–de Vries nonlinearity coefficientαwas negative. Fronts associated with the shoaling local internal tide, but equal in magnitude to the soliton-generated bores, were observed onshore of 20-m depth.

    more » « less
  3. 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 Δ h scaling approximately with , where V is the maximum lateral flow velocity and is the buoyancy frequency. The model results are summarized using the estuarine classification diagram based on the freshwater Froude number Fr f and the mixing parameter M . The Δ h decreases with increasing Fr f as stronger stratification suppresses waves, and no internal waves are generated at large Fr f . The Δ h 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. 
    more » « less
  4. Abstract

    Enhanced diapycnal mixing induced by the near-bottom breaking of internal waves is an essential component of the lower meridional overturning circulation. Despite its crucial role in the ocean circulation, tidally driven internal wave breaking is challenging to observe due to its inherently short spatial and temporal scales. We present detailed moored and shipboard observations that resolve the spatiotemporal variability of the tidal response over a small-scale bump embedded in the continental slope of Tasmania. Cross-shore tidal currents drive a nonlinear trapped response over the steep bottom around the bump. The observations are roughly consistent with two-dimensional high-mode tidal lee-wave theory. However, the alongshore tidal velocities are large, suggesting that the alongshore bathymetric variability modulates the tidal response driven by the cross-shore tidal flow. The semidiurnal tide and energy dissipation rate are correlated at subtidal time scales, but with complex temporal variability. Energy dissipation from a simple scattering model shows that the elevated near-bottom turbulence can be sustained by the impinging mode-1 internal tide, where the dissipation over the bump isO(1%) of the incident depth-integrated energy flux. Despite this small fraction, tidal dissipation is enhanced over the bump due to steep topography at a horizontal scale ofO(1) km and may locally drive significant diapycnal mixing.

    Significance Statement

    Near-bottom turbulent mixing is a key element of the global abyssal circulation. We present observations of the spatiotemporal variability of tidally driven turbulent processes over a small-scale topographic bump off Tasmania. The semidiurnal tide generates large-amplitude transient lee waves and hydraulic jumps that are unstable and dissipate the tidal energy. These processes are consistent with the scattering of the incident low-mode internal tide on the continental slope of Tasmania. Despite elevated turbulence over the bump, near-bottom energy dissipation is small relative to the incident wave energy flux.

    more » « less
  5. Abstract

    Although typically used to measure dynamic strain from seismic and acoustic waves, Rayleigh‐based distributed acoustic sensing (DAS) is also sensitive to temperature, offering longer range and higher sensitivity to small temperature perturbations than conventional Raman‐based distributed temperature sensing. Here, we demonstrate that ocean‐bottom DAS can be employed to study internal wave and tide dynamics in the bottom boundary layer, a region of enhanced ocean mixing but scarce observations. First, we show temperature transients up to about 4 K from a power cable in the Strait of Gibraltar south of Spain, associated with passing trains of internal solitary waves in water depth <200 m. Second, we show the propagation of thermal fronts associated with the nonlinear internal tide on the near‐critical slope of the island of Gran Canaria, off the coast of West Africa, with perturbations up to about 2 K at 1‐km depth and 0.2 K at 2.5‐km depth. With spatial averaging, we also recover a signal proportional to the barotropic tidal pressure, including the lunar fortnightly variation. In addition to applications in observational physical oceanography, our results suggest that contemporary chirped‐pulse DAS possesses sufficient long‐period sensitivity for seafloor geodesy and tsunami monitoring if ocean temperature variations can be separated.

    more » « less