Resonance properties of a closed rotating rectangular basin subject to space- and time-dependent wind forcing

Abstract

We present an idealised process-based model to study the possibly resonant response of closed basins subject to periodic wind forcing. Two solution methods are adopted: a collocation technique (valid for arbitrary rotation) and an analytical expansion (assuming weak rotation). The spectral response, as obtained from our model, displays resonance peaks, which we explain by linking them to the spatial pattern of the wind forcing, the along-wind and cross-wind basin dimensions as well as the influence of rotation. Increasing bottom friction lowers the peaks. Finally, we illustrate how the spectral response is reflected in the time-dependent set-up due to a single wind event.

Response of large-scale coastal basins to wind forcing: influence of topography

“…To satisfy the closed boundary condition at x = L as well as the matching conditions between ramp-up zone and the rest of the inner region, we introduce two sets of M + 1 collocation points at x = L and x = L ramp , respectively. See Appendix C (and also Chen et al 2015). -A two-dimensional vertical (2DV) analytical solution can be found in the case without rotation (f = 0), with along-basin wind (θ = 0 • ), for the uniform depth or abrupt step topographies.…”

“…1). Note that Chen et al (2015) also considered a uniform depth, but in a closed rather than a semi-enclosed basin. -along-basin variations, such as a topographic step at…”

“…The colour plots show the amplification factor A for non-rotating basins of uniform depth (topography type 1), as a function of the dimensionless frequency and wind angle. Note that wind angle is important as the open boundary introduces an essential difference between along-basin dynamics and cross-basin dynamics (contrasting the closed basin study by Chen et al 2015). The response to along-basin wind has been obtained with the analytical 2DV solution, the response to cross-basin wind with the collocation solution (as outlined at the end of Section 3.3).…”

“…Hence, the basin's response to a wind event is contained in its so-called frequency response. Chen et al (2015) applied this principle to different wind events over closed basins. They demonstrated that strong oscillations ('sloshing') occurs whenever the spectral response contains resonant peaks at frequencies that are excited by the wind event.…”

“…Alternatively, Ponte (2010) investigated the response of large-scale, elongated closed basins with a parabolic cross-basin topography to alongbasin wind forcing. Recently, Chen et al (2015) extended this approach to closed basins with comparable length and width but restricted to uniform depth. Other studies focused on the eigenmodes of, e.g.…”