Abstract
Abstract
Highlights
We present an analytical study of two-dimensional flow in a wedge driven by a time-dependent surface heat flux as a model problem to understand buoyancy-induced cross-shore flow
Excellent quantitative agreement is found for values of the Rayleigh number below a critical value at which the periodic solution undergoes a period-doubling bifurcation, leading to the establishment of thermal-instability cells that dominate the offshore flow dynamics, while the near-shore dynamics remains well described by the analytical solution
The analysis illustrates that a periodic heat input that leads to a vertically inhomogeneous temperature distribution can result in residual motion, net heat fluxes and persistent temperature structure in the cross-shore direction
Summary
The cross-shore exchange of heat, mass and momentum is a key problem in coastal oceanography and limnology. Considering an idealized wedge domain, relevant to many near-shore lake and coastal ocean settings, surface buoyancy fluxes across variable depth can set up cross-shore thermal variations with associated baroclinic pressure gradients. Molina et al (2014) described observations on a fore reef slope on Oahu, Hawai’i where strong along-shore flows provided high effective vertical mixing For this case, high turbulent transport distributes surface buoyancy fluxes vertically and an unsteady thermal response is observed, where the temperature is in quadrature with the surface buoyancy forcing. The same trapezoidal flow domain was employed in a subsequent numerical investigation (Bednarz, Lei & Patterson 2009), with the periodic heating/cooling introduced by harmonically varying the surface temperature. We explore a theoretical formulation for buoyancy-driven flow in a fluid wedge to show how cyclical thermal forcing may drive a harmonic flow response and a steady residual motion, with both components appearing in the leading-order solution for small bottom slopes. The occurrence of a steady residual flow is reasoned to be a more general feature for any harmonic wedge flow with a vertically non-uniform thermal response
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