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9 de setembro de 2010 LNCC From observation to modeling: Lessons and regrets from 36 years in the field. David Fitzjarrald Atmospheric Sciences Research Center University at Albany, SUNY Albany, New York USA

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Experimentos do campo faz-se envelhecer 1989

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Observações Teoria/modelos simples Modelos mais complexos (DNS, LES, meso) Resultados: C = + C’ Ya conheciamos (o ‘obvio’) Inovação (merece publicar) conhecimento

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A região de Xalapa, Veracruz, México 20°N 19°N 96°W97°W a cidade de Xalapa fica alredor de un volcán Um projeto simple, 1980-81.

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Experimento do campo julho 1980 & fevereiro 1981 Balão cativo

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Vento catabático na presença no fluxo em oposição Julho 1980 Los alisios uphill downhill

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Fevereiro 1981 sem alisios, vento descendente depois a inversão pasa abaixo

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Vento catabático sem oposição

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First simplification: 1D momentum equation along a slope: [1] [2] [3] [4] [5] [1] acceleration[3] stress divergence [2] advection of momentum[4] buoyant forcing [5] pressure forcing x3x3 x1x1 h

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The Prandtl katabatic wind solution (1940’s) Prandtl assumed that the steady downslope momentum balance is made between “vertical” (perpendicular to the slope, called z here) turbulent flux of momentum (Fm ) and the “buoyancy force” (Archimedean acceleration): Turbulent flux divergence buoyancy force along slope Momentum (steady) : 0 = -∂Fm/∂z + [b q’ sin ] a [Here q’ is the deviation of the potential temperature from a base state and b is the buoyancy parameter g/ v.] The whole analysis works because the base state is assumed to have a (z’) that changes only in the true vertical, not perpendicular to the slope (n). The thermal balance is assumed to be between along-slope (labeled s) heat advection and turbulent flux divergence: horizontal thermal advection vertical turbulent heat flux divergence: U∂ /∂s ≈ U[g sin ] = -∂F /∂n, [ where g is the base state potential temperature gradient, ∂ /∂z’, where z’ is the true vertical. ]

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Prandtl (1953)

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Prandtl’s analytic solution Maximum wind speed independent of slope angle

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Most results can be obtained through dimensional analysis alone! (Comes from the simplification.) notes from USP IAG June1984

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Prandtl July 1980 February 1981 Xalapa data revisited, scaled by height of wind speed maximum Effects of entrainment larger than Prandtl can predict

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Fedorovich & Shapiro (2009) Redoing this problem using DNS & (inevitably) LES

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Fedorovich & Shapiro (2009)Fedorovich & Shapiro (2009) DNS simulation: confirms that maximum wind ≠ f(slope)

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A 2 nd simple model approach: By integrating equations in the vertical, we form an analogy with open channel hydraulics

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The hydraulic jump Supercritical “shooting” Subcritical “tranquil”

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Modelo integrado no vertical Manins & Sawford (1979)

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Uh = integral mass transport Manins & Sawford (1979)

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‘shooting’ (supercritical) flows vs. ‘tranquil’ (subcritical) Manins & Sawford (1979)

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Entrainment assumptions Manins & Sawford (1979)

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Uh U Ri U

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Conditions on Ri for steady state

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Fitzjarrald (1984)

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Dimensionless equation set; u a is the ambient wind.

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Changes in time

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Stability of models Solutions in time

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Steady solutions

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shooting tranquil Fitzjarrald, 1984 downhilluphill

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Some thoughts in 2010: Prandtl solution gave good insight. When do we know that we are publishing new information? Question of shooting vs tranquil flows (from the bulk models) observationally unresolved. Oscillations simulated with DNS, but no observations yet

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Reynolds Analogy It can be shown that, under specific conditions (no external pressure gradient and Prandtle number equals to one), the momentum and heat.

Reynolds Analogy It can be shown that, under specific conditions (no external pressure gradient and Prandtle number equals to one), the momentum and heat.

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