Application of Classical Coastal Trapped Wave Theory to High-Scattering Regions

Abstract

Since the 1970s, analytical models of coastal trapped waves (CTWs) have been developed using a first-order wave equation in the long-wave limit. Formulations of this kind require assumptions of a straight coastline with similar shelf bathymetry. These assumptions prevent the models from capturing the scattering and backscattering behavior of propagating CTWs that encounter changing coastlines, bathymetry, or shelf width. CTW modes from two different analytical models, one of which includes friction and stratification, are compared with CTW observations of velocity and pressure from a study region near the Outer Banks off the North Carolina coast in the United States. The coastline in the study region is relatively straight locally but is bounded by an estuary to the north and shelf narrowing to the south, both of which induce scattering. The models suggest that the CTWs in this region are insensitive to changes in stratification, implying that observed seasonal differences in wave magnitude are due to seasonal wind forcing. Furthermore, friction is found to be important, particularly for mode-1 propagation, but higher-order modes are prevalent despite the importance of friction. There is very poor agreement between the observed and modeled free and forced CTWs because of scattering. This lack of agreement indicates that this is not a globally applicable theoretical formulation because many global coastlines violate the basic assumptions.

Alongshore Propagation of Subtidal Sea Level Fluctuations Around the Korean Peninsula Over Varying Stratification and Shelf Topography

“…Increasing stratification in summer and fall with the faster propagation of the CTWs is related to decreasing a 11 , because the increased stratification mitigates the effect of bottom friction and wave damping (Brink, 1982(Brink, , 1991. Although higher MPSs (c 1 ) were found with more stratified conditions, yielding a large D and M and small a 11 , as suggested by previous studies (Wang and Mooers, 1976;Brink, 1991;Brunner et al, 2019), the greatest seasonal variations in the OPS could not be explained by the CTW dynamics (Tables 1, 2 and Figures 5A,C). However, the low C of the OPS in Segs.…”

“…Density stratification, characterized by the vertical mean buoyancy frequency squared, M, and the density difference between the bottom and the lower boundary of the seasonal thermocline (d th , 70 m), D, affects the MPS following mode-1 CTW dynamics; in other words, higher speeds with the stronger density stratification with larger D and M, but their effect on OPS was partial. This faster propagation of the CTWs by stronger seasonal stratification has been simulated in many studies, but has not yet been well observed (Wang and Mooers, 1976;Battisti and Hickey, 1984;Schumann and Brink, 1990;Brunner et al, 2019). Increasing stratification in summer and fall with the faster propagation of the CTWs is related to decreasing a 11 , because the increased stratification mitigates the effect of bottom friction and wave damping (Brink, 1982(Brink, , 1991.…”

“…However, owing to the assumptions of classical CTW theory, namely a straight coastline or limited consideration for external forcing (e.g., only alongshore wind forcing is considered), the CTW model often results in sea level fluctuations that are significantly different from the observations (Cho et al, 2014;Brunner et al, 2019). Recent studies have pointed out that the classic CTW model is not universally applicable to most coastlines that do not meet the required assumptions of a straight coastline with similar shelf topography (Brunner et al, 2019). The coastal areas around the Korean Peninsula (KP) are one such region where the assumptions for the CTW model cannot be optimally satisfied (Figure 1).…”

Anatomy of Subinertial Waves Along the Patagonian Shelf Break in a 1/12° Global Operational Model

“…10.1029/2020JC016549 Although Brink's model is too idealistic (e.g., Brunner et al, 2019) and requires several assumptions such as a straight coastline with similar slope bathymetry, which are not fulfilled along the Patagonian shelf break, it provided guidance to the interpretation of those waves. Their phase speed and their spatial structure across the slope corresponded to modes 2-4 in Brink's model (Figures 7-9 stage featured increased northward along-slope velocity (5-20 cm/s) associated with inshore cross-slope velocities (1-2 cm/s).…”

Influence of intraseasonal eastern boundary circulation variability on hydrography and biogeochemistry off Peru

“…Because microbial storage of nitrate and nitrite by microorganisms in the sediment can sustain vigorous N turnover even in the absence of bottom water nitrate and nitrite (Dale et al, 2016;Sommer et al, 2016), episodic events of nitrogen supply can be associated with continuous benthic nitrogen cycling. The absence of nitrate supply due to the absence of CTWs over longer time periods favours the depletion of nitrate in the water column as observed by Sommer et al (2016) and may lead ultimately to the development of sulfidic events (Schunck et al, 2013;Dale et al, 2016;Callbeck et al, 2018).…”