is entropy production due to internal dissipation,
is entropy flux and generation due to heat transport, including entropy fluxes through the air-sea interface and internal entropy generation through thermal mixing. In order to analyze this term we divide the ocean into two layers: an upper layer (about 10-15 m, denoted as Vi) and a lower layer (denoted as V2) (Fig. 3.53).
On the sea surface, there are five heat fluxes: net short-wave radiation qsw, net long-wave radiation qlw, latent heat qlh, sensible heat qsh, and additional heat flux qadd = qgeo + qdis (geothermal heat qgeo plus dissipation heat associated with the external mechanical energy qdis). Ignoring the horizontal heat flux within the upper layer, there are two heat fluxes across the interface between the upper and lower layers: \qnet | = qnet = qsw + qlw + qlh + qsh and \qadd \ = qadd .Thus, Eqn. (3.183c) is reduced to
Hthermal = —^ | • nds + ^ ^ • nds + H^ + Hv2 +JJJy ^J^dV (3.184)
where HV1 = ff fViq • V^dv is entropy production within the upper layer, which is where the short-wave radiation is absorbed and turned into the internal energy of the water. As the equivalent temperature drops from TSun — 5.777K to Ts = 291.3K, there is a huge
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60.8PW 35PW 21.2PW
production of entropy in this thin layer. Because such entropy production is not directly related to the oceanic general circulation, the corresponding negative entropy flux through the air-sea interface will be called a non-active (negative) entropy flux. The details of this layer remain unclear at this time.
H-v2 = fffy2qadd • VT dv is the entropy production associated with additional heat flux in the ocean. The calculation of this term requires detailed information about the circulation, and hence is left for further study. The last term in Eqn. (3.184) represents the entropy production due to the internal heat transport and mixing, which remains unclear because its value depends on the detailed information of V • qnet, which is not available from observations at this time.
We will therefore focus on the first two terms in (3.184). Since the contribution due to geothermal heat flux is unknown, this small term will be omitted. There is no lateral flux term due to periodic condition. Thus, the surface heat flux term is reduced to the flux on the sea surface (SS) Hsurf .heat = — jjSS (q/T) • nds and entropy production through heat transport in the oceanic interior Hheat mixing = (j^, (qnet/T) •nds ~ — /fSS qnet/Tsds.
Entropy fluxes through the air-sea interface The global sum of the air-sea heat flux includes the following four terms: Qsw (net shortwave radiation), Qlw (net long-wave radiation), Qlh (latent heat), and Qsh (sensible heat). Here heat flux received by the ocean is defined as positive. Entropy flux associated with radiation is different from that of ordinary heat flux. According to the laws of Planck and Stefan-Boltzmann (Kittel and Knoemer, 1980; Yan et al., 2004) energy and entropy flux associated with black body radiation obey
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