Abstract
We present a theoretical model of the temperature distribution in the boundary layer region close to the seabed. Using a perturbation expansion, multiple scales and similarity variables, we show how free-surface waves enhance heat transfer between seawater and a seabed with a solid, horizontal, smooth surface. Maximum heat exchange occurs at a fixed frequency depending on ocean depth, and does not increase monotonically with the length and phase speed of propagating free-surface waves. Close agreement is found between predictions by the analytical model and a finite-difference scheme. It is found that free-surface waves can substantially affect the spatial evolution of temperature in the seabed boundary layer. This suggests a need to extend existing models that neglect the effects of a wave field, especially in view of practical applications in engineering and oceanography.
Highlights
The present manuscript investigates how surface water waves impact temperature transport at the seabed
We have investigated the mechanism of heat transfer in the boundary-layer region at the seabed
Given the small thermometric conductivity of water, large temperature gradients occur in the region close to the ocean bed
Summary
The present manuscript investigates how surface water waves impact temperature transport at the seabed. It is often possible to adopt the simplifying assumption that the flow is independent of temperature When it comes to the oceanic environment, temperature transport has been studied at large as well as small scales. Whereas the motion associated with surface waves decreases with depth, in intermediate depths (relative to the length scale of the waves) this motion extends all the way down the water column This is an important driver of seabed mass transport (Mei & Chian 1994), as well as the transport of solutes and contaminants (Winckler, Liu & Mei 2013). The second-order wave-induced motion is determined by an approach analogous to that used in investigating mass transport by Mei, Stiassnie & Yue (2005, Chapter 10) This motion drives flow in the boundary layer, and results in a convection–diffusion equation for the temperature. Our results suggest that the effect of free-surface waves should be included in existing models to ensure proper estimation of the temperature field near the seabed, especially when such models are applied in practice
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