On the Coriolis Effect for Internal Ocean Waves

A derivation of the Ostrovsky equation for internal waves with methods of the Hamiltonian water wave dynamics is presented. The internal wave formed at a pycnocline or thermocline in the ocean is influenced by the Coriolis force of the Earth's rotation. The Ostrovsky equation arises in the long waves and small amplitude approximation and for certain geophysical scales of the physical variables.

Reduced order model approach for imaging with waves

We introduce a novel, computationally inexpensive approach for imaging with an active array of sensors, which probe an unknown medium with a pulse and measure the resulting waves. The imaging function uses a data driven estimate of the “internal wave” originating from the vicinity of the imaging point and propagating to the sensors through the unknown medium. We explain how this estimate can be obtained using a reduced order model (ROM) for the wave propagation. We analyze the imaging function, connect it to the time reversal process and describe how its resolution depends on the aperture of the array, the bandwidth of the probing pulse and the medium through which the waves propagate. We also show how the internal wave can be used for selective focusing of waves at points in the imaging region. This can be implemented experimentally and can be used for pixel scanning imaging. We assess the performance of the imaging methods with numerical simulations and compare them to the conventional reverse-time migration method and the “backprojection” method introduced recently as an application of the same ROM.

Tracking deep-sea internal wave propagation with a differential pressure gauge array

Temperature is used to trace ocean density variations, and reveals internal waves and turbulent motions in the deep ocean, called ‘internal motions.’ Ambient temperature detected by geophysical differential pressure gauges (DPGs) may provide year-long, complementary observations. Here, we use data from four DPGs fixed on the ocean bottom and a high-resolution temperature sensor (T-sensor) 13 m above the seafloor as a square-kilometer array deployed offshore ~ 50 km east of Taiwan facing the open Pacific Ocean to examine the impact of temperature on DPG signals related to internal motions. The DPG signals correlate with T-sensor temperature variations between 0.002 and 0.1 mHz, but have time shifts partially caused by slow thermal conduction from the ambient seafloor to the DPG chamber and partially by internal motion propagation time across the array. Applying beamforming-frequency-wavenumber analysis and linear regression to the arrayed T-sensor and DPG data, we estimate the propagating slowness of the internal motions to be between 0.5 and 7.4 s m−1 from the northwest and northeast quadrants of the array. The thermal relaxation time of the DPGs is within 103–104 s. This work shows that a systematic scan of DPG data at frequencies < 0.1 mHz may help shed light on patterns of internal wave propagation in the deep ocean, especially in multi-scale arrays.

The Close Relationship between Internal Wave and Ocean Free Surface Wave

A numerical model was used to simulate the propagation of internal waves (IW) along the surface layer. The results show that strong water exchange during IW propagation results in strong free surface flow and produces small but distinct free surface waves. We found a close relationship between the internal and ocean surface waves. Our intuitive reaction is that by training the relationship between the water surface wave height and the internal wave waveform, the internal wave waveform can be reversed from the water surface wave height value. This paper intends to validate our intuition. The artificial neural network (ANN) method was used to train the Fluent simulated results, and then the trained ANN model was used to predict the inner waves below by the free surface wave signal. In addition, two linear internal wave equations (I and II) were derived, one based on the Archimedes principle and the other based on the long wave and Boussinesq approximation. The prediction by equation (II) was superior to the prediction of equation (I), which is independent of depth. The predicted IW of the proposed ANN method was in good agreement with the simulated results, and the predicted quality was much better than the two linear wave formulas. The proposed simple method can help researchers infer the magnitude of IW from the free surface wave signal. In the future, the spatial distribution of IW below the sea surface might be obtained by the proposed method without costly field investigation.

Internal Bore Evolution Across the Shelf Near Pt. Sal CA interpreted as a Gravity Current

Off the central California coast near Pt. Sal, a large amplitude internal bore was observed for 20 h over 10 km cross-shore, or 100 m to 10 m water depth (D), and 30 km alongcoast by remote sensing, 39 in situ moorings, ship surveys, and drifters. The bore is associated with steep isotherm displacements representing a significant fraction of D. Observations were used to estimate bore arrival time tB, thickness h, and bore and non-bore (ambient) temperature difference ΔT, leading to reduced gravity g′. Bore speeds c, estimated from mapped tB, varied from 0.25 m s−1 to 0.1 m s−1 from D = 50 m to D = 10 m. The h varied from 5 to 35 m, generally decreased with D, and varied regionally alongisobath. The bore ΔT varied from 0.75 to 2.15 °C. Bore evolution was interpreted from the perspective of a two-layer gravity current. Gravity current speeds U, estimated from the local bore h and g− compared well to observed bore speeds throughout its cross-shore propagation. Linear internal wave speeds based on various stratification estimates result in larger errors. On average bore thickness h = D/2, with regional variation, suggesting energy saturation. From 50–10 m depths, observed bore speeds compared well to saturated gravity current speeds and energetics that depend only on water depth and shelf-wide mean g′. This suggests that this internal bore is the internal wave analogue to a saturated surfzone surface gravity bore. Alongcoast variations in pre-bore stratification explain variations in bore properties. Near Pt. Sal, bore Doppler shifting by barotropic currents is observed.

Impact of Wave-Vortical Interactions on Oceanic Submesoscale Lateral Dispersion

Submesoscale lateral transport of Lagrangian particles in pycnocline conditions is investigated by means of idealized numerical simulations with reduced-interaction models. Using a projection technique, the models are formulated in terms of wave-mode and vortical-mode nonlinear interactions, and they range in complexity from full Boussinesq to waves-only and vortical-modes-only (QG) models. We find that, on these scales, most of the dispersion is done by vortical motions, but waves cannot be discounted because they play an important, albeit indirect, role. In particular, we show that waves are instrumental in filling out the spectra of vortical-mode energy at smaller scales through non-resonant vortex-wave-wave triad interactions. We demonstrate that a richer spectrum of vortical modes in the presence of waves enhances the effective lateral diffusivity, compared to QG. Waves also transfer energy upscale to vertically sheared horizontal flows which are a key ingredient for internal-wave shear dispersion. In the waves-only model, the dispersion rate is an order of magnitude smaller and is attributed entirely to internal-wave shear dispersion.