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Phenomenological Coefficients of Water

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Physics of Lakes

Abstract

This chapter is based on the work done by Hutter and Trösch [35] and extensions of it. We shall list the phenomenological coefficients which describe water as a heat-conducting viscous fluid.

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Notes

  1. 1.

    We shall use ‘ppt’ as the standard symbol for ‘parts per thousand’. So \(1\,\mathrm{ppt} =0.001\).

  2. 2.

    In all subsequent formulae it is understood that the temperature is given in degree Celsius.

  3. 3.

    1 millipoise equals \(10^{-3}\) poise. \(1\, [\mathrm{poise}] = 0.1\, [\mathrm{kg}\,\mathrm{m}^{-1}\,\mathrm{s}^{-1}]\).

  4. 4.

    Formula (10.31) shows that the orientation distribution of the ellipsoids is statistically homogeneous, as the bulk viscosity is isotropic.

  5. 5.

    The heat conductivity and thermal diffusivity are defined by the equations:

    $$\rho c_p\frac{\mathrm{d}T}{\mathrm{d}t}=\kappa\nabla ^2T+\cdots$$

    and

    $$\frac{\mathrm{d}T}{\mathrm{d}t}=\chi\nabla ^2T+\cdots ,$$

    respectively. Note that the transformation \(\chi=\kappa/(\rho c_\mathrm{p})\) only conforms with these equations for constant κ and c p.

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Authors and Affiliations

  1. ETH Zürich, c/o Versuchsanstalt für Wasserbau Hydrologie und Glaziologie, Gloriastr. 37/39, 8092, Zürich, ETH-Zentrum, Switzerland

    Prof. Dr. Kolumban Hutter

  2. Department of Mechanical Engineering, Darmstadt University of Technology, Petersenstr. 30, 64287, Darmstadt, Germany

    PD. Dr. Yongqi Wang (Chair of Fluid Dynamics)

  3. Russian Academy of Sciences, P.P. Shirshov Institute of Oceanology, prospect Mira 1, 236000, Kaliningrad, Russia

    Dr. Irina P. Chubarenko

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  1. Prof. Dr. Kolumban Hutter
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  2. PD. Dr. Yongqi Wang
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  3. Dr. Irina P. Chubarenko
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Correspondence to Kolumban Hutter .

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Hutter, K., Wang, Y., Chubarenko, I.P. (2011). Phenomenological Coefficients of Water. In: Physics of Lakes. Advances in Geophysical and Environmental Mechanics and Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15178-1_10

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