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Increasing Reynolds #

Increasing Reynolds #. Turbulence characteristics. 3-dimensional rotational – carries vorticity (unlike linear surface waves) irregular, unpredictable (random) motion – described by probability density function diffusive – several orders of magnitude greater than molecular diffusion

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Increasing Reynolds #

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  1. Increasing Reynolds #

  2. Turbulence characteristics 3-dimensional rotational – carries vorticity (unlike linear surface waves) irregular, unpredictable (random) motion – described by probability density function diffusive – several orders of magnitude greater than molecular diffusion dissipative – K.E.→ heatrequires steady supply of energy

  3. Turbulence characteristics flow has large Reynolds #,(nonlinear) does not obey a dispersion relation (not wavelike) broad wavenumber spectrum generally anisotropic at larger scales is a function of the flow, not the fluid satisfies Navier-Stokes equations

  4. Dynamic Stability Concepts Figure from Thorpe Statically stable, dynamically unstable = forced convection (figure from Stull)

  5. Vertical turbulent transports What is a turbulent flux? Reynolds’ decomposition: <wT> = <w><T> + <w’T’> What determines the vertical distribution of turbulence? TKE equation: dTKE/dt = production – dissipation + advection How does turbulence determine the interfacial fluxes of heat, moisture and momentum? Near-surface gradients and TKE levels are related. How are vertical turbulent transports modeled? Flux profile relationships (Monin-Obukhov similarity theory) closure schemes (parameterizations) layered versus level models

  6. Turbulent Flux Definitions Reference Lecture 2 for bulk parameterizations of these

  7. Turbulence dissipation

  8. PBL TKE budget forced convection free convection • u* friction velocity • w* convective velocity scale • h boundary layer height • ε dissipation of TKE • S shear production of TKE • B buoyancy production/damping of TKE • T transport of TKE

  9. the flow is in steady state, i.e, • the boundary layer is horizontally homogeneous, i.e.,                      and • the boundary layer is statically neutral, i.e., • the boundary layer is barotropic, i.e., Ug and Vg are constant with height • there is no subsidence, i.e., W = 0 Ekman Flow assumptions

  10.                                                      (1) • How can we solve equation set (1)? • First, let's define the magnitude of the geostrophic wind, G by G = [U2g + V2g]0.5 • Let's also assume that the geostrophic wind is parallel to the X axis, thus: • G = Ug • V2g = 0 • Let's also use first-order local closure K-theory, assuming a constant Kmto eliminate the flux terms. • Hence:                                  (2) • Substituting (2) into (1) gives: •                                             (3) Ekman Flow

  11. Here we have a set of two partial differential equations...., how to solve????? • Well, we need to specify the boundary conditions: • U= 0 at z = 0 • V= 0 at z = 0 • U  --> G as z --> large (get above the boundary layer) • V --> 0 as z --> large (the geostrophic flow above the boundary layer is parallel to the X axis) • The solution to (3) using the above boundary conditions is: •                                                              (4)    • where Ekman Flow

  12. Ekman Flow

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