Studies of the Thermal State of the Earth. The 14th Paper : A Theory of Non-Steady mantle Convection

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Rotational motion of a rigid sphere placed in gravity and temperature fields is studied in the hope of getting some clue as to time-dependent mantle convection. The estimate of mechanical couple exerted to the sphere due to thermal expansion leads to an equation of motion which is given in a form of non-linear integral equation provided proper account is taken of heat conduction. Solving numerically the integral equation thus obtained, it is found that the sphere overturns in a way studied by Griggs. For cells having radii of 100 and 1000 km, the rapidly accelerating period is estimated to last some 108 and 106yrs respectively. The effect of heat conduction is serious for a small cell of which the radius is of the order of 100 km, while it can be ignored for a cell having a radius of 1000 km or more.温度勾配のある重力場中に置かれた剛体球の力学的不安定を,熱伝導を考慮した上で,吟味した.このモデルはマントル熱対流に関するGriggsの理論を数式によつて定量化したものである.
1963-07-30