Unsteady natural convection in near-shore waters

Mao, Yadan (2009) Unsteady natural convection in near-shore waters. PhD thesis, James Cook University.

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Abstract

In the near-shore waters of natural water bodies, an increasing depth in the offshore direction is a geometric factor which results in differential heating or cooling across the shore. Exposed to daylight radiation, the volumetric heating rate in the shallow region is greater than in the deep region, generating a warm surface layer flowing offshore. At night, a circulation in the opposite direction is induced by differential cooling owing to heat loss from the water to the atmosphere. Field experiments demonstrate that this natural convection in calm near-shore waters plays a significant role in cross-shore exchanges with significant biological and environmental implications. This thesis aims to provide detailed quantification of this thermal flow for various thermal forcing conditions.

Based on a wedge model, an improved scaling analysis is proposed in the present study to reveal more detailed features of the flow than the previous scaling analysis, especially the dependency of flow properties on offshore distance. Four different types of thermal forcing (radiative heating, isoflux cooling, constant and ramped isothermal heating) are considered in the scaling analysis, and the scaling results are verified by the corresponding numerical simulations.

For heating induced by absorption of radiation, two critical functions of the Rayleigh number with respect to offshore distance are derived from scaling analysis to identify the distinctness and stability of the thermal boundary layer at any local position. These two functions reveal four possible flow scenarios, depending on the bottom slope and the maximum water depth. For each flow scenario, the flow domain may be composed of multiple subregions with distinct thermal and flow features, depending on the Rayleigh number. The dividing positions between neighboring subregions and the flow properties in each subregion are quantified by scaling. The scenario of relatively large bottom slope and shallow water is examined in detail and classified into three flow regimes based on the Rayleigh number. For the unstable flow regime, the entire flow domain is composed of three subregions, with the dominant mode of heat transfer changing from conduction to stable convection and finally to unstable convection as offshore distance increases. Characteristics of instability are investigated through a comprehensive spectral analysis which reveals the dependency of spectral properties on water depth, offshore distance and the Rayleigh number.

For isoflux cooling on the water surface, flow scenarios revealed by scaling analysis share similarity with that of the radiation heating, although the mechanisms of these two cases are significantly different. The distinctness and stability of the thermal boundary layer are identified by two critical Rayleigh number functions, a comparison between which reveals two possible flow scenarios depending on the bottom slope. The scenario with relatively large bottom slopes is examined in detail and further classified into three possible flow regimes depending on the Rayleigh number.

For constant and ramped (increasing linearly with time) isothermal heating at the water surface, a hybrid of approximate analytical solutions and scaling analysis is used to quantify the flow in the conductive region and scaling analysis is developed for the convective region. For the conductive region, the problem is simplified into a one dimensional conduction problem with a variable local water depth. The analytical solutions of the simplified problem agree well with the numerical results obtained by solving the full Navier-Stokes equations. It is revealed that for the conductive region, when the thermal boundary layer reaches the local bottom at time tsp, the local velocity reaches a maximum value for constant heating, and for ramp heating, the flow becomes steady at time tsp if the ramp duration is larger than tsp. For both constant and ramped heating, flow in the conductive region eventually becomes isothermal and stationary. The dependency of the maximum velocity and steady state velocity on various flow parameters is quantified by scaling. For the convective region, a comparison between the ramp duration P and the time it takes for convection to balance conduction reveals two scenarios: if the ramp finishes before the balance, no steady state is reached within the ramp duration, and after the ramp finishes, the flow velocity continues to increase and gradually becomes steady, whereas if the ramp finishes after the balance, a quasi-steady state is reached within the ramp duration, and the flow becomes steady soon after the ramp finishes. For both scenarios, the flow reaches the same steady state velocity as the corresponding constant heating case.

Item ID: 10962
Item Type: Thesis (PhD)
Keywords: natural convection, coastal waters, near shore, thermal flow, hydrothermal circulation, thermal boundary layer, heat transfer, thermally stimulated currents, thermal transfer
Date Deposited: 27 May 2010 00:01
FoR Codes: 02 PHYSICAL SCIENCES > 0203 Classical Physics > 020303 Fluid Physics @ 33%
04 EARTH SCIENCES > 0404 Geophysics > 040403 Geophysical Fluid Dynamics @ 33%
09 ENGINEERING > 0915 Interdisciplinary Engineering > 091501 Computational Fluid Dynamics @ 34%
SEO Codes: 96 ENVIRONMENT > 9611 Physical and Chemical Conditions of Water > 961102 Physical and Chemical Conditions of Water in Coastal and Estuarine Environments @ 33%
97 EXPANDING KNOWLEDGE > 970102 Expanding Knowledge in the Physical Sciences @ 34%
97 EXPANDING KNOWLEDGE > 970101 Expanding Knowledge in the Mathematical Sciences @ 33%
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