On modeling of wave-induced vertical mixing

Abstract

A theoretical approach is applied to investigate wave-induced mixing. The problem is formulated to describe evolution of temperature in a layer of fluid and is solved by applying eigenfunction expansions. The derived semi-analytical solution is applied to predict temperature changes and evolution of temperature profiles due to mechanically generated waves in a closed flume. The results show that water waves modify the temperature distribution in space and time. The analysis shows that the changes occur in the whole layer of fluid. The results indicate that time is a more important factor in a process of wave-induced mixing than expected. Mixing processes depend on a wave height. The rate of change of temperature distribution is more pronounced for higher waves. Another important parameter in mixing processes is the wavelength. The mixing effects are more distinct for deep water waves. The sensitivity analysis implies a need to conduct more theoretical studies and experimental investigations on wave-induced mixing. the model is verified in the course of the original laboratory experiments that were conducted in the insulated flume. A reasonable agreement between predicted and measured temperature profiles proves the applicability of the present approach even for relatively high gradients of temperature distribution over water depth.