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    Re: New Moon, Perigee, and Solstice
    From: Rodney Myrvaagnes
    Date: 2003 Dec 24, 10:39 -0500

    On Tue, 23 Dec 2003 17:47:34 +0000, Trevor J. Kenchington wrote:
    >I have no intention of disputing what you say -- not least because I
    >don't understand it! I'm afraid that I have too little comprehension of
    >how electronic circuits really work for your analogy to aid my
    >almost-as-limited comprehension of the physics underlying tidal phenomena.
    Sorry. I am not trying to be obscure. Put another way, a driven
    harmonic oscillator is a driven harmonic oscillator. It stores,
    dissipates, and releases energy according to the same equations whether
    it is electrical, hydraulic, or mechanical. If you couple together a
    big bunch of such oscillators, of widely varying sizes, you still have
    a harmonic oscillator.
    The electrical analog is a convenient way of thinking about these
    things for those who are familiar with them. If you like springs and
    weights and dashpots instead, fine.
    The oceans of the world form an interconnected jumble of inertial,
    frictional, and gravitational elements. If you separate off a piece of
    the jumble, e.g. Minas Basin, you can then consider the activity at the
    mouth a forcing function for what happens inside. In principle, you
    could do the same for larger and more complex parts of the whole.
    In all these divisions, the general form of the differential equation
    would be the same. The number of terms and the numerical coefficients
    would be different. In each of them the forcing function is a boundary
    to a larger world. It is not something special, and cannot really be
    called a "cause" except in a local sense.
    >Let me try it this way:
    >Imagine a system with just the two tidal constituents, the semi-diurnal
    >lunar and semi-diurnal solar. Imagine also the Sun and Moon remaining
    >perpetually in phase (continuous Full Moon, for example). As I
    >understand it, the water in the various ocean basins would oscillate
    >with a semi-diurnal frequency, the range of the tide at a particular
    >place and the LHA of the Sun and Moon at the time of local high water
    >being determined by the particular pattern of local oscillation.
    >The gravitational pull of the two bodies would feed energy into the
    >tidal movement, while an exactly equal amount of energy would be lost
    >through friction. However, the amount of energy stored within the
    >resonant oscillation would be far greater (on most ocean basins) that
    >the half-daily addition and loss.
    >Now step up to a slightly more realistic model in which the Moon moves
    >around the celestial sphere, relative to the Sun. The tide generating
    >forces created by the two of them combine into something that closely
    >approximates the directional pattern of the forces created by the Moon
    >alone but those forces vary in magnitude on a spring/neap cycle.
    >Possibility #1: As the Sun and Moon come into phase and thus feed energy
    >into the tides at an increasing rate, the tides respond within a few
    >hours (reaching greater ranges and faster rates of drift), such that the
    >energy fed in each day is still essentially balanced by the losses to
    >friction in that day.
    >Possibility #2: The additional energy is partly stored within the
    >oscillating system, while the range and rate of drift (and hence the
    >loss of energy to friction) take some days to build up. Hence the
    >spring/neap cycle in the tides lags the cycle in the tide generating force.
    >Those two are different and #2 cannot be the cause of non-zero "ages" of
    >the tide if #1 is correct.
    A practical interface for this question would be tide tables for a
    mid-Pacific Island, such as Canton and Enderbury. That should give a
    good handle on the phase of the tidal bulge as it would be in a
    uniformly water-covered planet. I don't have such a tide table.
    But, an analogous situation does come to mind. Really big stone
    churches like St-Sulpice in Paris or Oratoire St-Joseph in Montreal
    have a striking effect on the sound of the organ. A held chord swells
    for several seconds before it fills all the possible modes of the air
    space at a level that balances the friction loss.
    In this case the sounding whistles represent the forcing function, and
    they have enough impedance that the influence is mostly (not entirely)
    from pipes to room, not vv.
    On this basis, I think #2 is closer.
    >In this second hypothetical model, the semi-diurnal lunar and solar
    >tides must have slightly different periods. Hence, they will tend to set
    >up somewhat different patterns of oscillations in various ocean basins.
    >LHA Sun at HW of the solar component of the tide and LHA Moon at HW of
    >the lunar component will be different (perhaps by a tiny amount, perhaps
    >by a great deal). According to the Admiralty Manual of Tides, on average
    >around the world, LHA Sun at HW of the solar component is larger than
    >LHA Moon at HW of the lunar component, though that is only an average
    >and particular ports can differ.
    >If the two LHAs at your port follow the global average, then HW of the
    >solar component will coincide with HW of the lunar component (producing
    >a spring tide) when LHA Sun is larger than LHA Moon, which clearly
    >occurs a few days after New Moon. (Since we are dealing with
    >semi-diurnal tides, this lag is repeated following Full Moon.) This
    >effect would produce non-zero "ages" of the tide even if Possibility #1
    >is correct.
    >I see no reason why both Possibility #2 and the different LHAs at HW
    >should not be true simultaneously but, even if they are, that would make
    >them two mechanisms contributing to the same outcome. It would not make
    >them the same outcome.
    >The only way I can rationalize your "You can't separate these things as
    >causes" would be to suppose that Possibility #2 is the physical cause of
    >  non-zero "ages" of the tide and that the difference between LHA Sun
    >and LHA Moon at their respective High Waters is just an artifact of
    >decomposing the spring/neap tidal record (including its non-zero "age")
    >into the M2 and S2 harmonics. That, however, would be contrary to the
    >Admiralty Manual's implication that the LHA difference is a _cause_ and
    >that, in the absence of the Moon, the tides really would oscillate in
    >time to the Sun's circuit with the appropriate LHA Sun at HW.
    To me, what is a "cause" is an aspect of the chosen boundary, and hence
    chosen driving function. To the extent that linear superposition holds
    in the ocean, separating the solution into two harmonic series based on
    the Sun and Moon is a correct view of the matter.
    Nonlinearities probably occur. One that comes to mind is an isthmus
    that covers during part of the tide cycle. But such things probably
    don't have a big influence over most of the world.
    >I dare say that there are plenty of errors in the above and I would
    >welcome having them pointed out -- particularly by anybody knowledgable
    >enough to provide authoritative answers.
    I don't find substantial errors, but I am not equipped with
    authoritative answers either.
    >On the effects of a tidal barrage at the head of Fundy: I'm not sure
    >that anyone really knows what it would do to amplitudes elsewhere.
    News accounts of the proposal stated that it was known (by whom??) that
    the mill would tune toward resonance. If you are engaged in active
    Fundy research you can probaly find the relevant papers faster than I
    could, if you are so inclined.
     I can
    >say that the marine geologists here have recently found active erosion
    >of the seabed in the Bay. One possible explanation is that the system is
    >gradually getting nearer to perfect resonance with the semi-diurnal
    >lunar tide (the likely cause being isostatic rebound, which is lifting
    >the New Brunswick side of the bay, while dipping the Atlantic coast
    >of Nova Scotia into the sea -- though the blockage of various tidal
    >rivers by road causeways might be contributing). The other possible
    >explanation is that the scallop draggers and groundfish trawlers are
    >breaking stony lag deposits on the bottom and exposing the underlying
    >glacial deposits to erosion by tides no stronger than they have been in
    >past centuries. I guess both could be simultaneously true.
    That is startling news to me. By "active erosion" do you mean
    noticeable depth changes year to year?
    >This week, I am trying to make sense of a data set which may provide a
    >bit more information on the effects of the fishing gear (though on the
    >seabed biota rather than the seabed itself). That won't answer any of
    >the above questions but may warn off anyone who wants to ask about gear
    >impacts -- I am liable to drown any inquiry in a torrent of unwanted,
    >and off-topic, information!
    I would be happy to receive your torrent off list, but only for
    curiosity, not scholarly interest.
    Rodney Myrvaagnes                                                              
                          Opinionated old geezer
     "It is, of course, quite true that no great amount of skill is required to 
    navigate a ship most of the time, and
    on those less frequent occasions when a higher level of competence is 
    desirable luck may suffice. If that runs out there is always insurance..." 
    __The late Captain Richard Cahill

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