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Physics of Lakes pp 251–286Cite as

Higher-Order Baroclinicity (II)Interpretation of Lake Data with Rotating and Non-rotating Models

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Part of the book series: Advances in Geophysical and Environmental Mechanics and Mathematics ((AGEM,volume 2))

Abstract

In parts A and B of the last chapter, two sources of higher order baroclinicity were looked at (1) a two-layer fluid system with a diffusive interface and (2) a three-layer configuration with two sharp interfaces due to the presence of a thermocline and a chemocline. In this chapter we give further field evidences of higher order baroclinicity. Both cases are to a certain extent idealized; in a realistic situation, density changes are generally less abrupt and should be represented by using a thermal equation of state ρ = ρ(T, s) from measured temperature and electrical conductivity profiles. If this argument is consistently adopted, this would, strictly, mean that a numerical model for a stratified lake should be based on a multi-layer model, e.g. with linear density variation across each layer. For reasons of accurate determination of the phase speeds of the higher baroclinic seiche, this should be done so, even if only fundamental (V1) and first higher order (V2) modes are of interest.

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Notes

  1. 1.

    V1 and V2, etc., stand for vertical mode 1, mode 2, etc.; similarly, H1, H2, etc., stand for horizontal mode 1, mode 2, etc.

  2. 2.

    The authors present the analysis, which was already given by Longuet–Higgins in Mortimer [36] and by Heaps [17].

  3. 3.

    The authors do not specify in their paper how these profiles were determined from the measured temperature time series of the thermistors in the thermistor chains during the June/July 1992 summer campaign.

  4. 4.

    By varying the profiles slightly, they found \({T}_{1,1} \in (7.7\mbox{ \textendash }8.8)\) h and \({T}_{1,2} \in (22.2\mbox{ \textendash }25.7)\) h and conclude that their results corroborate their physical interpretation.

  5. 5.

    Saggio and Imberger [46], Antenucci et al. [3], Antenucci and Imberger [1,  2], Boegman et al. [11,  12], Appt et al. [4], Shimizu et al. [50], Shimizu and Imberger [51,  52].

  6. 6.

    The model was also used with the actual bathymetry of Lake Biwa and the measured winds during the experiment in 1993. The corresponding analysis is not reported by Saggio and Imberger [46] but was presented in a Ph.D. dissertation by Ogihara [42]. It is claimed also elsewhere in the manuscript that inferences from these results are less convincing. We have not had access to this work.

  7. 7.

    Figure 16.14 shows the spectra for the 13 and 19 ∘ C isotherm depths at BN50 obtained with the model, and representative for the centre of the metalimnion and the hypolimnion, respectively. Peaks (i) and (ii) are reminiscent of V2 and V1 Kelvin-type behaviour, whilst (iii)–(v) are likely HmV1 (m = 2, 3, 4) responses. These interpretations are likely, because at peak (i) vertical velocities (displacements) in the centre of the metalimnion are small, but large at peak (ii).

  8. 8.

    Saggio and Imberger call Kelvin and Poincaré behaviour what we call Kelvin-type and Poincaré-type behaviour.

  9. 9.

    We interpret the claims of Antenucci and Imberger [1] and Boegman et al. [11] for Lake Biwa and Kinneret as (perhaps strong) indications, but not as proofs of their existence. The vertical resolution from temperature–time series of thermistor chains with much denser distribution of the thermistors with depth are necessary, to claim with certainty that V n -modes with n > 2 can be isolated.

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Authors and Affiliations

  1. c/o Versuchsanstalt für Wasserbau Hydrologie und Glaziologie ETH-Zentrum, ETH Zürich, Gloriastr. 37/39, 8092, Zürich, 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. P.P. Shirshov Institute of Oceanology, Russian Academy of Sciences, 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). Higher-Order Baroclinicity (II)Interpretation of Lake Data with Rotating and Non-rotating Models. In: Physics of Lakes. Advances in Geophysical and Environmental Mechanics and Mathematics, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19112-1_16

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