Coastal Upwelling and Kelvin Waves with Small Longshore Topography

Abstract

A simple, uniformly stratified, linear model is developed to examine the effects on upwelling and internal Kelvin wave propagation of small, slow, longshore varying topography and coastline. The condition of no normal flow at the bottom yields correction terms with responses that propagate as Kelvin waves. For the first problem considered, a uniform wind stress is turned on abruptly. The response is fully three-dimensional with a zone of upwelling (downwelling) to the south of a ridge (canyon) near the shore. As time passes, the zone moves poleward and becomes centered over the topography. A complicated cyclonic and anticyclonic circulation is associated with a shoreward (seaward) flow over the ridge (canyon). If the basic state (i.e., the flow in the absence of topography) had no poleward undercurrent, the sign of the response is altered. The second problem considered the modification of an internal Kelvin wave by isolated topography. Energy is scattered into all vertical modes (i.e., the natural decomposition of the flat-bottom response with respect to the vertical). Most energy goes into neighboring modes. The response consists of a steady contribution over the topography and a traveling, free Kelvin wave. For high incoming modes (those with many zero crossings in the vertical), little energy is scattered., most of what is scattered goes into the steady contribution. For low incoming modes, much energy is lost, divided about equally between steady and traveling responses. Although this problem can only be thought of as a first attempt at understanding scattering of baroclinic coastal waves by topography, it may help to explain why only low-mode Kelvin waves are observed.