# 2.DYNAMICS - ES8007 Climate and Climate Change ES1007...

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y.sg ES8007 Climate and Climate Change ES1007 Oceans, Atmosphere and Climate © NEA-MSS Dynamics- Part II Asst. Prof. WANG Xianfeng Asian School of the Environment Nanyang Technological University 26 January, 2016

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y.sg ES8007 Climate and Climate Change ES1007 Oceans, Atmosphere and Climate © NEA-MSS Dynamics- Part I Asst. Prof. WANG Xianfeng Asian School of the Environment Nanyang Technological University 19 January, 2016
y.sg Pressure and Ideal Gas Law 19 January, 2016 Pressure is the force exerted per unit area perpendicular to the force . In a fluid, the pressure at a location is the same from all directions. In our atmosphere, the pressure p is well described by the ideal gas law , which states that where ρ is the density, T is the temperature (in K) and R is the specific gas constant (287 J K -1 kg -1 for air). So the pressure of air increases with increasing density if temperature is kept constant increases with increasing temperature if density is kept constant. p RT

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y.sg Hydrostatic Balance 19 January, 2016 Consider a thin slab of fluid of density ρ , area A and thickness Δz located at height z . Weight of the slab = ρ A Δz g where g is the gravity field strength (9.8 N kg -1 or 9.8 m s -2 ) Pressure force acting upward on the slab = p ( z ) A Pressure force acting downward on the slab = p ( z+ Δz ) A weight of the slab of fluid pressure p ( z ) at z pressure p ( z+Δz ) at z + Δ z z z+ Δz mass of the slab
y.sg Hydrostatic Balance 19 January, 2016 For the slab of fluid to remain at the same height z , there must be no net resultant force acting on it. Hydrostatic balance is the equilibrium that exists between the force due to vertical pressure gradient and the weight of a fluid such that the fluid remains at rest in the vertical direction. This is a very good approximation for the atmosphere and the oceans because vertical motion is generally weak. Since the right-hand-side of the equation is negative, pressure must decrease upwards for the fluid to support its own weight. Exercise: How does pressure vary for the ocean, assuming that water is incompressible? (i.e. assume the density is constant.) Hint: the gradient is constant ( ) ( ) ( ) ( ) g A z p z z A p z A p z z p z g z p dp g z dz          

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y.sg Atmospheric Mass Distribution 19 January, 2016 Pressure in the atmosphere falls roughly exponentially with height. From the ideal gas law, the atmospheric density also falls roughly exponentially with height (for temperature is roughly constant). Pressure and density falls roughly by a factor of e ≈ 2.718 for every ascent of H in height in the atmosphere.
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• Spring '16
• Tropical cyclone, Atlantic Ocean, Kelvin, Equator, non-zero temperature

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