Diurnal continental shelf waves with a permeable coastal boundary: Application to the shelf northwest of Norway

Jan Erik H Weber,Eli Børve

doi:10.1016/j.euromechflu.2021.05.003

Jan Erik H Weber, Eli Børve

Open Access

https://doi.org/10.1016/j.euromechflu.2021.05.003

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Abstract

Spatially damped continental shelf waves (CSWs) with diurnal tidal frequency outside Lofoten–Vesterålen in north-west Norway are studied theoretically for an idealized shelf topography. Wave damping is caused by the exchange of fluid on the shelf with an inner archipelago through a permeable coastline. This exchange is modelled by the application of a Robin condition at the coastal boundary. It is shown that CSWs with diurnal frequencies are possible in a small wave number range centred around zero group velocity. By calculating the nonlinear radiation stress components in the spatially damped CSWs, we find the time- and depth averaged Lagrangian mean drift current to second order along the coast. We show that the Lagrangian mean drift current is independent of the value of the damping coefficient, however small, as long as it is nonzero. This illustrates the singular behaviour of the Lagrangian wave drift problem for CSWs.

Highlights

We study sub-inertial wave motion over variable bottom topography
Having established that continental shelf waves (CSWs) with a diurnal frequency may form in the Lofoten–Vesterålen region, we proceed to investigate some non-linear properties of these waves
We realize that the system of Eqs. (29)–(31) has time dependent free solutions in the form of CSWs

Summary

Introduction

We study sub-inertial wave motion over variable bottom topography. Longuet-Higgins [1,2] has described how such waves can propagate along a sloping bottom. The focus here is on wave motion along a continental shelf that is limited laterally by a coastal boundary; see e.g. Buchwald and Adams [3]. Wind systems hitting the southwestern part of Norway has a storm track with an oblique angle to the coast This generates CSWs that propagate northward along the Norwegian continental shelf, see e.g. This will remove energy from the CSW, and lead to spatial damping as the wave propagates along the shelf slope. The sloping shelf region is taken to be inviscid This simplifies the calculation of the Lagrangian mean drift current, which is discussed for parameters that are typical for the shelf outside Lofoten

Linear analysis for idealized bottom profiles and an impermeable coastal wall

Linear waves with a robin condition at the coast

The nonlinear drift problem

Hydrographic conditions west of Norway

Discussion and concluding remarks