Nearshore natural convection induced by a periodic thermal forcing at the water surface

Field observations reveal that under calm weather conditions, natural convection resulting from spatial variations in the temperature field plays a significant role in promoting exchanges and mixings in lakes and reservoirs. The present investigation is concerned with natural convection generated by a periodically varying surface temperature within a reservoir model consisting of a sloping nearshore section and a flat offshore section. Three approaches, including derivation of analytical solution, numerical simulation, and scaling analysis, are integrated to reveal the variation of flow response with the intensity of the thermal forcing. The analytical solution reveals that for a sinusoidally varying surface temperature, a cosinusoidally varying surface heat flux is imposed if the duration of the period is sufficiently long. Numerical results show dramatic differences in flow response between conduction-dominated and convection-dominated thermal flow. The former is in phase with the cosinusoidal variation of surface heat flux, whereas the latter is in phase with the sinusoidal variation of surface temperature. The thermal forcing for conduction-dominated and convection-dominated flow is prescribed by surface heat flux and surface temperature, respectively. An evident phase lag is observed shortly after the thermal forcing switches sign. For convection-dominated flow with a Rayleigh number of 2 × 107, the maximum velocity during the cooling phase is significantly larger than that during the heating phase owing to the occurrence of flow instability during the cooling phase, which agrees with field observations. The scales for flow velocity and phase lag are derived by scaling analysis and verified by the results of numerical simulations.