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Stratified convection with multiple states
Authors:J A Whitehead
Institution:1. State Key Laboratory of Coal Combustion, School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan 430074, China;2. Faculty of Chemical Engineering, Universiti Teknologi MARA, Shah Alam 40450, Selangor, Malaysia;3. School of Material Science and Engineering, University of Jinan, Jinan 250022, China;4. China-EU Institute for Clean and Renewable Energy at Huazhong University of Science and Technology, Wuhan 430074, China;5. China Science and Technology Exchange Center, Beijing 10045, China;1. MEtRICs R&D Center, Department of Mechanical Engineering, School of Engineering, University of Minho, 4800-058 Guimarães, Portugal;2. ALGORITMI R&D Center, Department of Production and Systems, School of Engineering, University of Minho, 4800-058 Guimarães, Portugal;3. MEtRICs R&D Center, Department of Mechanical Engineering, School of Engineering, University of Minho, 4800-058 Guimarães, Portugal;1. Departamento de Ingeniería Hidráulica y Ambiental, Pontificia Universidad Católica de Chile, Av. Vicuña Mackenna 4860, 7820436, Santiago, Chile;2. Marine Energy Research & Innovation Center (MERIC), Av. Apoquindo 2827, 7550268, Santiago, Chile;3. Institute for Energy Systems, School of Engineering, The University of Edinburgh, Kings Buildings, Mayfield Rd, EH9 3JL, Edinburgh, United Kingdom
Abstract:A simplified box model of the cooling of a salt-stratified ocean is analyzed analytically and numerically. A large isothermal basin of salt water has a layer of fresh water at the surface. Beside this is a small basin, cooled from above and connected to the large basin by horizontal tubes at the top, middle and bottom. For small cooling rate, fresh water enters the small basin, is cooled and leaves through the middle tube. For greater cooling rate, the fresh water leaves the small basin through the middle and bottom tube. If the top tube is smaller than the deeper tubes and the fresh water layer is sufficiently shallow, flow in the middle tube reverses at a critical cooling rate. In this case, a mixture of salt and fresh water is cooled and leaves the bottom tube. Increased cooling produces much greater flow rate; consequentially temperature increases rather than decreases in the small basin. A relaxation heat flow condition results in multiple equilibria. One of the stable modes has fresh surface water descending in the small basin and flowing out through the middle and bottom tube. The other has a greater rate of flow of both fresh and salty water (through the middle tube) into the basin with the flow of mixed salty water out of the bottom tube. Implications for deep convection in the ocean are discussed.
Keywords:Mixing  Ocean convection  Salt balance  Water circulation  Ocean circulation  Water masses
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