WATER MOVEMENTS


I. Why would a biological limnologist be interested in water movements?
     -Distribution of organisms
     -Distribution of dissolved gases and nutrients
     -Distribution of temperature

    We will deal with 5 basic categories of physical factors that describe water motion or the movement of substances in water :
         SIMPLE DIFFUSION
         TURBULENT VERSUS LAMINAR FLOW
         CONVECTION / ADVECTION
         CURRENTS
         WAVES
         MORE COMPLEX COMBINATIONS OF CURRENTS AND WAVES

II. Diffusion – molecular movement of substances in water, but not movement of water itself

    Fick's first law of diffusion:
Fick's first law of diffusion

    Where flux equals bulk movement – the amount that can pass through a given area
         in a given time
         Ks = diffusivity coefficient;units for Ks
         dS = change in [solute];units for dS

         dx = change in distance; cm
    Always check to make sure that the units cancel out!

unit check

    Heat diffusion
        KT is thermal diffusivity – Fourier’s Law
         KT (heat) for water is 1.5 X 10-3 cm2 sec-1
        Ks most dissolved substances is ~1 X 10-5 cm2 sec-1

III. Laminar Flow versus Turbulent Flow

    A. Laminar flow

    B. Turbulent Flow

        Particles move in highly irregular manner, even though the bulk fluid is traveling on average in one direction – this is
            the ‘statistical’ nature of turbulence

        Similar for heat and dissolved substances (whole water parcels exchanged) – unlike diffusive processes

    C. How do you predict whether laminar or turbulent flow will occur?

        Reynold's number (dimensionless)

Reynolds # equation

            where velocity symbol = mean velocity (cm s-1)
                     r  = density (g cm-3)
                     m  = viscosity (gm cm-1 sec-1)
 


Reynolds number breakpoints for laminar and turbulent flow

                  most flow generates turbulence
                  important for small organisms

         Viscosity and Temperature


IV. Convection -- – flow arising from density differences (independent of externally supplied velocity gradients)

            Advection – bulk movement of water and its contents

         1. Heat source
         2. Evaporation
         3. Cooling
         4. Salinity

V. Eddy diffusion

    Measure of rate of exchange or intensity of mixing across a density layer (thermal or salt)
    Result of molecular diffusion + turbulent flow + advection

    Disorganized flow of water on different spatial scales
    “Big whirls have lesser whirls that feed on their velocity and lesser whirls have smaller whirls and so on ‘til viscosity”

    Richardson’s number (see mixing section)
    Ri = (g x dr/dz) / (r x du/dz)2

VI. Waves - periodic movement, but not much unidirectional flow

 A. Surface traveling waves
Surface wave showing height and length
 

        h = height that a water molecule moves
        h is halved for each wavelength/9 of depth in the water column

      1. wave velocity   Cw = l / T;  T= period
      2. particle velocity wave particle equation
      3. Stokes limit

        Stoke's equation

        Stoke's limit, then waves will tend to break up (Stokes Limit)
      4. potential versus kinetic energy
         Energy in deep water is mostly potential
         Nearshore it is converted to kinetic, can get damage

      5. capillary waves – capillarity is a calming force.  At higher windspeeds
           you get gravity waves (>1.75 cm in height or 6.28 cm in length)
                where gravity is a calming force.

    B. Standing Waves

        1. Surface seiche

<>            pressure of wind pushes water to one side
            when wind stops, oscillation begins     (also earthquakes and pressure systems)

                                   period of seiche Seiche period equation
                                       where l = length of basin
                                               n = number of nodes
                                               g = gravity
                                               z = mean depth
                                  setup of surface seiches Sh=3.2X10-6*l*[u2]/(g*zmax)

      2. Internal seiche
If the wind causes a 1 cm set-up at the surface, the pressure at depth will increase by rgh.  To get an equivalent pressure difference, the slope of the thermocline would have to be 1000X greater (you have displaced air with water), so a 1 cm setup leads to a ~10 m internal seiche!

           i. set-up
                a. winds
                b. pressure differences
                c. rain, river inputs, landslides
           ii. amplitude
                Internal seiches have amplitudes much larger than surface seiches, and the period is much longer
                 internal seiches (Ai=Sh*(rh/(rh-re)))

                Will get floating organisms piling up on the end toward which the wind is blowing
           iii. period

Equation for formula of a seiche
                        l = length of basin
                        rh = density of hypolimnion
                        re = density of epilimnion
                        zh = thickness of hypolimnion
                        ze = thickness of epilimnion

                            Characteristics of internal seiches are strongly dependent on basin morphology, and so there is more than
                            one formula to calculate the period of a seiche.
             Upwelling

                Can get internal waves along thermocline

VII. Currents -- non-periodic movements generated by external forces (but do have flow in one direction, unlike waves)

    A. Coriolis force

                Coriolis accelerationCoriolus acceleration

                Tendency to drift to right of wind or velocity direction in Northern hemisphere

                Not a true force

                Usually small in lakes
 

     B Ekman spirals
Ekman Spiral

    C. Langmuir circulation

Langmuir Circulation

        Very common: form of organized advection, controls distribution of organisms as well as mixes
        Streak of convergence – floating matter (flotsam); wind rows
        Divergence – things that sink – algae, zooplankton (upwelling)
        Can think of the cells as rotation of gears.  Each of the rotating circles is known as a Langmuir Cell
 

VIII. Combination of waves and currents

     Kelvin and Poincaré waves

      Interaction of internal waves and Coriolis effect

        Kelvin waves – currents along a line parallel to the shore; decrease in amplitude away from shore
        Poincaré waves – in large lakes where long waves travel without influence of shore and make a standing
            wave pattern across the basin, rotating clockwise once a wave cycle; continue away from shore
 
 

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