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    "title": "Charney: why a vertically sheared current can grow weather-scale waves",
    "summary": "Charney added continuous vertical shear and latitude-dependent rotation to an idealized atmospheric model, deriving bounded long-wave stability and structure rather than treating all waves as stable barotropic motion.\n\nA wind can be faster higher in the atmosphere, with that shear tied to a horizontal temperature gradient. Charney studied how a small wave grows or travels in such a current. After excluding fast oscillations under stated inequalities, he reduced the vertical structure to an eigenvalue problem with ground and upper-air boundary conditions. Graphical calculations distinguish neutral waves from growing waves and relate the threshold to shear and wavelength. Near the onset of growth, the calculation produces thermal asymmetry and a westward tilt with height. The paper also identifies where the simplified upper atmosphere distorts the result, leaves the link to frontal disturbances unresolved and credits the theories it builds on.",
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        "description": "Small linear disturbances of an adiabatic compressible hydrostatic midlatitude zonal current; curvature neglected, meridional-independent perturbations with background coefficients evaluated at a mean latitude, prescribed lapse rate and continuous vertical shear. Ground impermeability, vanishing upper momentum and tropopause matching imposed. Slow-wave inequalities filter acoustic/shearing-gravity components and imply approximate meridional geostrophy. Further mean-temperature and continued-shear simplifications support graphical stability curves; unstable-wave speed/structure uses a near-critical expansion, not an unrestricted exact solution. Original 138–139/158 flags unrealistic upper-level extrema, unresolved frontal coupling, unfinished tropical extension and schematic values valid only in order of magnitude. Seasonal weather comparisons are not held-out forecast skill or proof for every real cyclone. exact equations, plotted curves and tables not independently certified/replayed. No nonlinear saturation, later Eady theory or numerical forecast implementation absorbed.",
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          "citation": "J.G.Charney, The Dynamics of Long Waves in a Baroclinic Westerly Current (1947), original135–162",
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      "statement": "# Charney: why a vertically sheared current can grow weather-scale waves\n\nCharney added continuous vertical shear and latitude-dependent rotation to an idealized atmospheric model, deriving bounded long-wave stability and structure rather than treating all waves as stable barotropic motion.\n\nA wind can be faster higher in the atmosphere, with that shear tied to a horizontal temperature gradient. Charney studied how a small wave grows or travels in such a current. After excluding fast oscillations under stated inequalities, he reduced the vertical structure to an eigenvalue problem with ground and upper-air boundary conditions. Graphical calculations distinguish neutral waves from growing waves and relate the threshold to shear and wavelength. Near the onset of growth, the calculation produces thermal asymmetry and a westward tilt with height. The paper also identifies where the simplified upper atmosphere distorts the result, leaves the link to frontal disturbances unresolved and credits the theories it builds on.\n\n## Scientific scope\n\nSmall linear disturbances of an adiabatic compressible hydrostatic midlatitude zonal current; curvature neglected, meridional-independent perturbations with background coefficients evaluated at a mean latitude, prescribed lapse rate and continuous vertical shear. Ground impermeability, vanishing upper momentum and tropopause matching imposed. Slow-wave inequalities filter acoustic/shearing-gravity components and imply approximate meridional geostrophy. Further mean-temperature and continued-shear simplifications support graphical stability curves; unstable-wave speed/structure uses a near-critical expansion, not an unrestricted exact solution. Original 138–139/158 flags unrealistic upper-level extrema, unresolved frontal coupling, unfinished tropical extension and schematic values valid only in order of magnitude. Seasonal weather comparisons are not held-out forecast skill or proof for every real cyclone. exact equations, plotted curves and tables not independently certified/replayed. No nonlinear saturation, later Eady theory or numerical forecast implementation absorbed.\n\n## People and systems\n\nJ. G. Charney\n\n\n\n## Original sources\n\n- [J.G.Charney, The Dynamics of Long Waves in a Baroclinic Westerly Current (1947), original135–162](https://empslocal.ex.ac.uk/people/staff/gv219/classics.d/Charney47.pdf)\n",
      "summary": "Charney added continuous vertical shear and latitude-dependent rotation to an idealized atmospheric model, deriving bounded long-wave stability and structure rather than treating all waves as stable barotropic motion.\n\nA wind can be faster higher in the atmosphere, with that shear tied to a horizontal temperature gradient. Charney studied how a small wave grows or travels in such a current. After excluding fast oscillations under stated inequalities, he reduced the vertical structure to an eigenvalue problem with ground and upper-air boundary conditions. Graphical calculations distinguish neutral waves from growing waves and relate the threshold to shear and wavelength. Near the onset of growth, the calculation produces thermal asymmetry and a westward tilt with height. The paper also identifies where the simplified upper atmosphere distorts the result, leaves the link to frontal disturbances unresolved and credits the theories it builds on.",
      "title": "Charney: why a vertically sheared current can grow weather-scale waves"
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    "title": "Charney: why a vertically sheared current can grow weather-scale waves",
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