أثر كوريوليس

Figure 1: In the inertial frame of reference (upper part of the picture), the black object moves in a straight line. However, the observer (red dot) who is standing in the rotating frame of reference (lower part of the picture) sees the object as following a curved path.

أثر كوريوليس هو ميل أو انحراف جسم متحرك بتأثير من دوران الكرة الأرضية فالحركة الأفقية تميل إلى اليمين في نصف الكرة الشمالي وتميل الى اليسار في نصف الكرة الجنوبي. وأثر كوريوليس نسبة الى العالم الفرنسي گاسپار-گوستاڤ كوريوليس الذى أثبت رياضيا سنة 1835م تأثير دوران الكرة الأرضية على الأجسام المتحركة فوق سطحها، مع أن الرياضيات التي ظهرت في المعادلات المدية tidal equations من قبل پيير-سيمون لاپلاس منذ عام 1778. يحدث تأثير كوريوليس نتيجة ما يدعى بقوة كوريوليس، التي تظهر في معادلة الحركة لجسم ما ضمن إطار مرجعي دوراني. قوة كوريوليس تعتبر مثالا عن القوى التخيلية fictitious force (أو القوى الكاذبة pseudo force) ، لأنها لا تظهر عندما يتم التعبير عن نفس الحركة ضمن إطار مرجعي عطالي inertial frame of reference .، حيث يتم شرح حركة الجسم عن طريق القوى الحقيقية المطبقة دون الحاجة لقوة تخيلية، طبعا مع مفهوم العطالة. أما في إطار مرجعي دوراني ، فإن قوى كوريوليس تعتمد على السرعة للجسم المتحرك ، و القوة النابذة، التي لاتعتمد على سرعة الأجسام المتحركة. كلا القوتين لازمتين لوصف الحركة بشكل دقيق.

ربما تكون الإطار المرجعي الدوراني الأكثر أهمية هو الأرض. فالأجسام المتحركة بحرية على سطح الأرض تتعرض لقوة كوريوليس، و يظهر ذلك في ميلان حركتها نحو اليمين في نصف الكرة الشمالي، و نحو اليسار في نصف الكرة الجنوبي. حركة الهواء و الرياح في الغلاف الأرضي و المياه في المحيطات هي أمثلة واضحة لهذا السلوك. فبدلا من التوجه مباشرة من مناطق الضغط المرتفع لمناطق الضغط المنخفض كما يجب أن يحدث في كوكب غير دائر ، نجد أن اتجاه الحركة ينحرف قليلا إلى اليمين من منطقة الضغط المنخفض في النصف الشمالي، و بالعكس إلى اليسار في النصف الجنوبي.

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 تطبيقه على الأرض

 كرة دوارة

Figure 2: Coordinate system at latitude φ with x-axis east, y-axis north and z-axis upward (that is, radially outward from center of sphere).

 الشمس والنجوم البعيدة

The motion of the Sun as seen from Earth is dominated by the Coriolis and centrifugal forces. For ease of explanation consider the situation of a distant star (with mass m) located over the equator, at position ${\boldsymbol {r}}$, perpendicular to the rotation vector ${\boldsymbol {\Omega }}$ so ${\boldsymbol {\Omega \cdot r}}=0$. It is observed to rotate in the opposite direction as the Earth's rotation once a day, making its velocity ${\boldsymbol {v}}=-{\boldsymbol {\Omega }}\times {\boldsymbol {r}}$. The fictitious force consisting of Coriolis and centrifugal forces is:

${\boldsymbol {F_{f}}}=-2\,m\,{\boldsymbol {\Omega \times v}}-m\,{\boldsymbol {\Omega \times {(\Omega \times r)}}}$

$=+2\,m\,{\boldsymbol {\Omega \times (\Omega \times r)}}-m\,{\boldsymbol {\Omega \times {(\Omega \times r)}}}$

$=m\,{\boldsymbol {\Omega \times (\Omega \times r)}}$

$=m\,({\boldsymbol {\Omega (\Omega \cdot r)-r(\Omega \cdot \Omega ))}}$

$=-m\,\Omega ^{2}\,{\boldsymbol {r}}$

This can be recognised as the centripetal force that will keep the star in a circular movement around the observer.

 علم الأرصاد الجوية

Figure 12: This low pressure system over Iceland spins counter-clockwise due to balance between the Coriolis force and the pressure gradient force.

Figure 13: Schematic representation of flow around a low-pressure area in the Northern hemisphere. The Rossby number is low, so the centrifugal force is negligible. The pressure-gradient force is represented by blue arrows, the Coriolis acceleration (always perpendicular to the velocity) by red arrows

Figure 14: Schematic representation of inertial circles of air masses in the absence of other forces, calculated for a wind speed of approximately 50 to 70 m/s. Note that the rotation is exactly opposite of that normally experienced with air masses in weather systems around depressions.

 الحالات الخاصة

 مدفع على قرص دوار

انظر أيضاً: قوة خيالية § عبور كاروسل

Figure 3: Cannon at the center of a rotating turntable. To hit the target located at position 1 on the perimeter at time t = 0s, the cannon must be aimed ahead of the target at angle θ. That way, by the time the cannonball reaches position 3 on the periphery, the target also will be at that position. In an inertial frame of reference, the cannonball travels a straight radial path to the target (curve y_A). However, in the frame of the turntable, the path is arched (curve y_B), as also shown in the figure.

Figure 4: Successful trajectory of cannonball as seen from the turntable for three angles of launch θ. Plotted points are for the same equally spaced times steps on each curve. Cannonball speed v is held constant and angular rate of rotation ω is varied to achieve a successful "hit" for selected θ. For example, for a radius of 1 m and a cannonball speed of 1 m/s, the time of flight t_f = 1 s, and ωt_f = θ → ω and θ have the same numerical value if θ is expressed in radians. The wider spacing of the plotted points as the target is approached show the speed of the cannonball is accelerating as seen on the turntable, due to fictitious Coriolis and centrifugal forces.

Figure 5: Acceleration components at an earlier time (top) and at arrival time at the target (bottom)

Figure 6: Coriolis acceleration, centrifugal acceleration and net acceleration vectors at three selected points on the trajectory as seen on the turntable.

 كرة ملقاة على كاروسل دوار

Figure 7: A carousel is rotating counterclockwise. Left panel: a ball is tossed by a thrower at 12:00 o'clock and travels in a straight line to the center of the carousel. While it travels, the thrower circles in a counterclockwise direction. Right panel: The ball's motion as seen by the thrower, who now remains at 12:00 o'clock, because there is no rotation from their viewpoint.

 كرة مرتدة

Figure 8: Bird's-eye view of carousel. The carousel rotates clockwise. Two viewpoints are illustrated: that of the camera at the center of rotation rotating with the carousel (left panel) and that of the inertial (stationary) observer (right panel). Both observers agree at any given time just how far the ball is from the center of the carousel, but not on its orientation. Time intervals are 1/10 of time from launch to bounce.

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 شرح تصويري لتأثير كوريوليس

Figure 9: A fluid assuming a parabolic shape as it is rotating

Figure 10: The forces at play in the case of a curved surface.
Red: gravity
Green: the normal force
Blue: the resultant centripetal force.

 تأثيرات كوريوليس في مجالات أخرى

 مقياس كوريوليس للسريان

Figure 11: Object moving frictionlessly over the surface of a very shallow parabolic dish. The object has been released in such a way that it follows an ellipse-shaped trajectory.
Left: The inertial point of view.
Right: The co-rotating point of view.

 انظر أيضا

• ميكانيكا تحليلية
• ميكانيكا تطبيقية
• Centrifugal force (rotating reference frame)
• Centripetal force
• ميكانيكا كلاسيكية
• ديناميكا (فيزياء)
• دوران الأرض
• Frenet-Serret formulas
• Geostrophic wind

• Gyroscope
• Kinetics (physics)
• Mass flow meter
• ميكانيكا حركة الجسيمات المستوية
• Reactive centrifugal force
• Secondary flow
• استاتيكا
• Uniform circular motion

 المصادر

• مؤمن, عبد الأمير (2006). قاموس دار العلم الفلكي. بيروت، لبنان: دار العلم للملايين. {{cite book}}: Cite has empty unknown parameter: |طبعة أولى coauthors= (help)

 مزيد من القراءة

• Coriolis, G.G., 1832: Mémoire sur le principe des forces vives dans les mouvements relatifs des machines. Journal de l'école Polytechnique, Vol 13, 268–302.
  (Original article [in French], PDF-file, 1.6 MB, scanned images of complete pages.)
• Coriolis, G.G., 1835: Mémoire sur les équations du mouvement relatif des systèmes de corps. Journal de l'école Polytechnique, Vol 15, 142–154
  (Original article [in French] PDF-file, 400 KB, scanned images of complete pages.)
• Gill, AE Atmosphere-Ocean dynamics, Academic Press, 1982.
• Robert Ehrlich (1990). Turning the World Inside Out and 174 Other Simple Physics Demonstrations. Princeton University Press. p. Rolling a ball on a rotating turntable; p. 80 ff. ISBN 0691023956.
• Durran, D. R., 1993: Is the Coriolis force really responsible for the inertial oscillation?, Bull. Amer. Meteor. Soc., 74, 2179–2184; Corrigenda. Bulletin of the American Meteorological Society, 75, 261

• Durran, D. R., and S. K. Domonkos, 1996: An apparatus for demonstrating the inertial oscillation, Bulletin of the American Meteorological Society, 77, 557–559.
• Marion, Jerry B. 1970, Classical Dynamics of Particles and Systems, Academic Press.
• Persson, A., 1998 How do we Understand the Coriolis Force? Bulletin of the American Meteorological Society 79, 1373–1385.
• Symon, Keith. 1971, Mechanics, Addison-Wesley
• Phillips, Norman A., 2000 An Explication of the Coriolis Effect, Bulletin of the American Meteorological Society: Vol. 81, No. 2, pp. 299–303.
• Akira Kageyama & Mamoru Hyodo: Eulerian derivation of the Coriolis force
• James F. Price: A Coriolis tutorial Woods Hole Oceanographic Institute (2003)
• MIT essays by James F. Price, Woods Hole Oceanographic Institution (2006)

 قراءات اخرى

• Grattan-Guinness, I., Ed., 1994: Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences. Vols. I and II. Routledge, 1840 pp.
  1997: The Fontana History of the Mathematical Sciences. Fontana, 817 pp. 710 pp.
• Khrgian, A., 1970: Meteorology—A Historical Survey. Vol. 1. Keter Press, 387 pp.

• Kuhn, T. S., 1977: Energy conservation as an example of simultaneous discovery. The Essential Tension, Selected Studies in Scientific Tradition and Change, University of Chicago Press, 66–104.
• Kutzbach, G., 1979: The Thermal Theory of Cyclones. A History of Meteorological Thought in the Nineteenth Century. Amer. Meteor. Soc., 254 pp.

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 وصلات خارجية

• The definition of the Coriolis effect from the Glossary of Meteorology
• The Coriolis Effect PDF-file. 17 pages. A general discussion by Anders Persson of various aspects of the coriolis effect, including Foucault's Pendulum and Taylor columns.
• Anders Persson The Coriolis Effect: Four centuries of conflict between common sense and mathematics, Part I: A history to 1885 History of Meteorology 2 (2005)
• 10 Coriolis Effect Videos and Games- from the About.com Weather Page
• Coriolis Force - from ScienceWorld
• Coriolis Effect and Drains An article from the NEWTON web site hosted by the Argonne National Laboratory.
• Catalog of Coriolis videos
• Do bathtubs drain counterclockwise in the Northern Hemisphere? by Cecil Adams.

• Bad Coriolis. An article uncovering misinformation about the Coriolis effect. By Alistair B. Fraser, Emeritus Professor of Meteorology at Pennsylvania State University
• The Coriolis Effect: A (Fairly) Simple Explanation, an explanation for the layperson
• Observe an animation of the Coriolis effect over Earth's surface
• Animation clip showing scenes as viewed from both an inertial frame and a rotating frame of reference, visualizing the Coriolis and centrifugal forces.
• Vincent Mallette The Coriolis Force @ INWIT
• NASA notes