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

Abstract

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.