Inferring Propagation Direction of Nonlinear Internal Waves in a Vertically Sheared Background Flow

Abstract

Internal waves heave the background flow through which they propagate. If the background flow is vertically sheared, the high-pass-filtered velocity field will thus contain signals of both the wave velocity and the heaved flow. Under conditions of large wave amplitude and large background shear-a common situation for nonlinear internal waves in coastal waters-the velocity fluctuations caused by wave heaving of the background flow can be comparable to the wave velocity itself. This complicates the inference of wave properties such as energy flux and propagation direction. The present study deals with methods to infer propagation direction in such situations. Attention is given to three methods that may be applied to acoustic Doppler current profiler measurements: a ''filtering'' method that estimates wave signals from high-pass-filtered time series, a ''beamwise'' method that infers wave direction from lagged correlations of echo intensity between the spatially separated acoustic beams of the profiler, and a ''modal'' method that separates background and wave signals by regressing the high-pass-filtered velocity field onto a normal-mode wave model. The methods are tested using synthetic datasets. The results suggest that the filtering method is biased by wave heaving of the background shear, while the beamwise and modal methods are resistant to heaving. The beamwise method provides accurate predictions of wave propagation angle for cases in which the measurements have high temporal resolution and the environment exhibits no depth-averaged background flow. The limitation on depth-averaged flow is relaxed for the modal method, but it requires the measurement of stratification. These issues are illustrated, and the applicability of these methods is explored with a series of sensitivity tests, and it is found that the different methods perform well under different circumstances.

Generation of Internal Solitary Waves by Lateral Circulation in a Stratified Estuary

“…The westward bottom velocity anomaly in the lower layer implies that the ISWs propagated westward. To determine the propagation direction u of ISWs more precisely, we use the filtering method described in Mirshak and Kelley (2009):…”

“…We use the velocities measured at the depth of 13.8 m where the wave-induced isopycnal displacements were small but the velocity anomalies were strongest. ADV measurements at 11.5 m depth (close to pycnocline) are not used because wave heaving of the background flow sometimes causes large biases in the estimate of u, as illustrated by Mirshak and Kelley (2009) and Xie et al (2015). Figure 3 shows the inferred wave propagation direction for the ISW observed between 26 September and 2 October, during which the ISW trains appeared roughly every 12 h at the M3 mooring site (see Fig.…”

Generation and propagation of internal tides and solitary waves at the shelf edge of the Bay of Biscay

“…The strong baroclinic tides may generate strong vertical shear, the approximation in (A1) may then lead to significant errors in estimating h of S1 and S2 [Chang et al, 2010;Mirshak and Kelley, 2009]. To further reduce the instrument error, the propagation direction of the packet is defined as h averaged over all available ISWs in a packet.…”

Shore-Based Video Observations of Nonlinear Internal Waves across the Inner Shelf *,+

“…Furthermore, the borelike internal wave shape found on the inner shelf creates ambiguity in separating wave velocities from the background velocity field, an important distinction before accurately deriving wave propagation speed and direction (e.g., Mirshak and Kelley 2009;Chang et al 2011). We attribute the scatter in propagation direction to the large difference in footprint size between the mooring and Argus estimates.…”

“…Wave direction and phase speed from the in situ moorings are determined by treating the four beams of each ADCP as a four-element wave-detection array following previous methods (Scotti et al 2005;Mirshak and Kelley 2009). As internal waves depress or elevate scattering layers within the water column, variations in echo intensity are measured by each ADCP transducer (see Fig.…”