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    Re: New Moon, Perigee, and Solstice
    From: Trevor Kenchington
    Date: 2003 Dec 23, 17:47 +0000

    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.
    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.
    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.
    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.
    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. 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.
    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!
    Trevor Kenchington
    Rodney Myrvaagnes wrote:
    > On Mon, 22 Dec 2003 21:02:22 +0000, Trevor J. Kenchington wrote:
    >>Which I think is the same as your explanation albeit in different words.
    >>However, the Manual continues:
    >>"It is possible that this phenomenon [meaning the greater lag of the
    >>solar tides, not the Age of the Tide directly] is due to dissipation of
    >>energy in the coastal fringes."
    >>Which approaches my supposed explanation, without being quite the same.
    >>However, the Manual is over 60 years old now and there must have been a
    >>lot of relevant research in that time. Can you suggest somewhere I could
    >>go for a fuller account of the cause(s) of the Age of the Tide?
    > You can't separate these things as causes. Someone earlier referred to
    > the "Q" of electrical tank (RLC) circuits. [snip]
    > For example, it is apparently known well enough to say that adding some
    > R at the top of the Bay, by putting a tide mill there, would tune the
    > bay toward resonance, rather than away. Hence the phrase "Canada's
    > answer to acid rain," referring to the Maine real estate that would be
    > lost to a higher tide line. [snip]
    Trevor J. Kenchington PhD                         Gadus{at}iStar.ca
    Gadus Associates,                                 Office(902) 889-9250
    R.R.#1, Musquodoboit Harbour,                     Fax   (902) 889-9251
    Nova Scotia  B0J 2L0, CANADA                      Home  (902) 889-3555
                         Science Serving the Fisheries

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