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| This is called a wave group |
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Definition
| Atmospheric waves consist of many single waves |
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| Phase Speed C depends on K |
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| This waves shape changes with time |
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| This wave doesn't change shape as it propagates |
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| The velocity at which the wave group energy propagates |
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| non dispersive (for Cp and Cg) |
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| Phase prop. faster than energy (For Cp and Cg) |
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| Phase prop. slower (For Cp and Cg) |
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| phase dispersion relationship |
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| Wi > 0 = growing wave (amplifying) Unstable..Ci > 0 |
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| This is when we have a growing wave (wi or ci) |
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| Wi < 0 = Decaying wave (Damping) Unstable.... Ci < 0 |
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| This is when we have a decaying wave (wi or ci) |
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| wi = 0...A = A = Const --> stable, neutral |
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simplest
barotropic shearing flow
Baroclinic shearing flow
studying interactions between perturb and basic state |
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Definition
((U))=const
((U))=((U(Y)))
((U))=((U(Y,Z)))
((U))=((U(Y,Z,t))) |
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| Linear perturbation eqn can be solved |
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| If given the basic state... |
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Eqns become linear
Can be solved easily
Linearized eqns can describe properties of the w/x disturbance at the initial development period |
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| Advantages of linear perturb |
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Only accurate from initial period
Only reflect the effect of background flow (basic state) on the perturb, not the other direction
unstable waves develop w/o constrains |
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| Disadvantages of linear perturb eqn |
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| Example of horizontal tranverse wave |
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1. Identify state variables
2. find eqns
3. try to reduce the number of eqns
4. Linearize the eqn (only keep first order term)
5. Substitute wave solution
6. Find wave properties
7. Obtain wave solution for all variables |
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| How do you filter sound waves |
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| restoring forces are adiabatic compression and expansion |
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| Sound waves restoring forces are what? |
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| studying simple barotropic atmosphere |
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| what is shallow water model useful for |
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| Assume incompressible & homogenous |
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| What are you assuming for Shallow water gravity waves? |
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| they exist on a free surface or internal density discontinuity |
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| Shallow water waves exist on what? |
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Cg = dw/dk = u (+/-) SQRT (GH)
C = w/k = u (+/-) SQRT (GH)
Thus Cg = C |
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Show that this is non dispersive (Find phase speed and group velocity)
w = ku (+/-) kSqrt(gH) |
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| example of a shallow water wave |
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| is shallow water wave dispersive or non dispersive? |
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| restoring force for shallow water wave |
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| Shallow water wave is generated by what? |
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horizontal non-divergent (du/dx = 0)
2D (du/dx + dv/dy = 0) |
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| filtering method for shallow water gravity waves |
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| they exist on a stably stratified atmosphere |
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| internal gravity waves exist on what kind of atmosphere? |
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| to the middle of the atmosphere |
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| Internal gravity waves transport energy/momentum where? |
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| What is the source of CAT (Clear air Turbulence) |
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Ignore coriolis force
assume 2D (X,Z) wave propogates in both directions
Boussinesq approximation ro=ro_o=constant, except in the buoyancy term in the vertical momentum eq.
Incompressible |
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| For pure internal gravity waves what are we assuming/Ignoring? |
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| they don't propagate, they are stationary |
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| what direction do topographic waves propagate? |
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| the amplification decreases along a direction |
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| what happens with amplification with a trapped wave |
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| what is Cp for stationary waves? |
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assume 1) no basic state flow (no background flow)
2) no pressure pert. |
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| what are u assuming for Pure inertial Oscillation (Gravity waves modified by rotation) |
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basic state motionless, hydrostatic
f=const
both basic state and perturb. are hydrostatic |
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| what are you assuming for inertial-gravity waves? |
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