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<h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Gradientwind</span></h1>
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<div id="mw-content-text" class="mw-body-content mw-content-ltr" lang="de" dir="ltr"><div class="mw-content-ltr mw-parser-output" lang="de" dir="ltr"><p>Der <b>Gradientwind</b> bezeichnet in der <a href="Meteorologie" title="Meteorologie">Meteorologie</a> ein <a href="Wind" title="Wind">Wind</a>-Modell, bei dem sich
</p>
<ul><li>die <a href="Gradientkraft" title="Gradientkraft">Druckgradientkraft</a> (infolge der <a href="Druckgradient" class="mw-redirect" title="Druckgradient">Druckunterschiede</a> zwischen einem <a href="Hochdruckgebiet" title="Hochdruckgebiet">Hoch-</a> und einem <a href="Tiefdruckgebiet" title="Tiefdruckgebiet">Tiefdruckgebiet</a>),</li>
<li>die <a href="Corioliskraft" title="Corioliskraft">Corioliskraft</a> (infolge der <a href="Erddrehung" class="mw-redirect" title="Erddrehung">Erddrehung</a>) sowie</li>
<li>die <a href="Zentrifugalkraft" title="Zentrifugalkraft">Zentrifugalkraft</a> (infolge der Eigendrehung eines Hoch- oder Tiefdruckgebietes)</li></ul>
<p>im <a href="Kr%C3%A4ftegleichgewicht" class="mw-redirect" title="Kräftegleichgewicht">Kräftegleichgewicht</a> befinden. Lokale Effekte, beispielsweise durch Gebirge oder Boden<a href="Reibung" title="Reibung">reibung</a>, werden nicht berücksichtigt.
</p><p>Der Gradientwind ist eine Erweiterung des <a href="Geostrophischer_Wind" title="Geostrophischer Wind">geostrophischen Windes</a> sowie des <a href="Zyklostrophischer_Wind" title="Zyklostrophischer Wind">zyklostrophischen Windes</a>, sodass auch der Begriff <b>geostrophisch-zyklostrophischer Wind</b> benutzt wird. Er stellt die beste Näherung an den realen Wind dar, die aus <a href="Wetterkarte" title="Wetterkarte">Wetterkarten</a> und <a href="H%C3%B6henwind" class="mw-redirect" title="Höhenwind">Höhenwindmessungen</a> noch relativ genau vorhergesagt werden kann.<sup id="cite_ref-:0_1-0" class="reference"><a href="#cite_note-:0-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>
</p>

<div class="mw-heading mw-heading2"><h2 id="Geschwindigkeit_des_Gradientwindes">Geschwindigkeit des Gradientwindes</h2></div>
<p>Die <a href="Geschwindigkeit" title="Geschwindigkeit">Geschwindigkeit</a> des Gradientwindes ist abhängig von der ihm aufgezwungenen Bahn:
</p>
<div class="mw-heading mw-heading3"><h3 id="Zyklonal">Zyklonal</h3></div>
<p>Bei einer <a href="Zyklonale_Rotation" title="Zyklonale Rotation">zyklonalen</a> Bewegung dreht sich die Luft um ein <a href="Tiefdruckgebiet" title="Tiefdruckgebiet">Tiefdruckgebiet</a>. Die <a href="Corioliskraft" title="Corioliskraft">Corioliskraft</a> <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{\mathrm {C} }}">
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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/c099296fe1e34c029270715fd5fc2ebf2b996baf.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.913ex; height:2.509ex;" alt="{\displaystyle F_{\mathrm {C} }}" loading="lazy"></span> zeigt dabei zusammen mit der <a href="Zentrifugalkraft" title="Zentrifugalkraft">Zentrifugalkraft</a> <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{\mathrm {Z} }}">
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<annotation encoding="application/x-tex">{\displaystyle F_{\mathrm {Z} }}</annotation>
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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/ae017f90c59400bb1dfaa9eb40139d0078e0b62b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.731ex; height:2.509ex;" alt="{\displaystyle F_{\mathrm {Z} }}" loading="lazy"></span> weg vom Zentrum, die <a href="Gradientkraft" title="Gradientkraft">Druckgradientkraft</a> <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{\mathrm {D} }}">
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<annotation encoding="application/x-tex">{\displaystyle F_{\mathrm {D} }}</annotation>
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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/332a0a0c700414dc34bab466aa7585a254c9c017.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.982ex; height:2.509ex;" alt="{\displaystyle F_{\mathrm {D} }}" loading="lazy"></span> zeigt zum Zentrum. Es gilt folglich
</p><dl><dd><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{\mathrm {C} }+F_{\mathrm {Z} }=F_{\mathrm {D} }\quad \Leftrightarrow \quad f_{\mathrm {c} }v+{\frac {v^{2}}{R}}=-{\frac {1}{\rho }}{\frac {\partial p}{\partial n}}}">
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<annotation encoding="application/x-tex">{\displaystyle F_{\mathrm {C} }+F_{\mathrm {Z} }=F_{\mathrm {D} }\quad \Leftrightarrow \quad f_{\mathrm {c} }v+{\frac {v^{2}}{R}}=-{\frac {1}{\rho }}{\frac {\partial p}{\partial n}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/9987feafdabc7c3060ede91d36569ebfa7e564fc.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:42.406ex; height:6.176ex;" alt="{\displaystyle F_{\mathrm {C} }+F_{\mathrm {Z} }=F_{\mathrm {D} }\quad \Leftrightarrow \quad f_{\mathrm {c} }v+{\frac {v^{2}}{R}}=-{\frac {1}{\rho }}{\frac {\partial p}{\partial n}}}" loading="lazy"></span></dd></dl>
<p>Nach Auflösen nach der Geschwindigkeit <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v}">
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<mi>v</mi>
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<annotation encoding="application/x-tex">{\displaystyle v}</annotation>
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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/e07b00e7fc0847fbd16391c778d65bc25c452597.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.128ex; height:1.676ex;" alt="{\displaystyle v}" loading="lazy"></span> ergibt sich
</p>
<dl><dd><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v=-{\frac {Rf_{\mathrm {c} }}{2}}\pm {\sqrt {\left({\frac {Rf_{\mathrm {c} }}{2}}\right)^{2}-{\frac {R}{\rho }}{\frac {\partial p}{\partial n}}}}}">
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<annotation encoding="application/x-tex">{\displaystyle v=-{\frac {Rf_{\mathrm {c} }}{2}}\pm {\sqrt {\left({\frac {Rf_{\mathrm {c} }}{2}}\right)^{2}-{\frac {R}{\rho }}{\frac {\partial p}{\partial n}}}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/436738eae8d527d2224114fc6376b2e4541a1091.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:34.067ex; height:7.676ex;" alt="{\displaystyle v=-{\frac {Rf_{\mathrm {c} }}{2}}\pm {\sqrt {\left({\frac {Rf_{\mathrm {c} }}{2}}\right)^{2}-{\frac {R}{\rho }}{\frac {\partial p}{\partial n}}}}}" loading="lazy"></span></dd></dl>
<p>Weil die <a href="Quadratische_Gleichung" title="Quadratische Gleichung">Gleichung quadratisch</a> ist, gibt es zwei theoretisch mögliche Lösungen. Die negative erfordert aber höhere Windgeschwindigkeiten und stellt sich deshalb in der Realität nie ein. Für die tatsächliche Geschwindigkeit gilt deshalb
</p>
<dl><dd><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v=-{\frac {Rf_{\mathrm {c} }}{2}}+{\sqrt {\left({\frac {Rf_{\mathrm {c} }}{2}}\right)^{2}-{\frac {R}{\rho }}{\frac {\partial p}{\partial n}}}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
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<annotation encoding="application/x-tex">{\displaystyle v=-{\frac {Rf_{\mathrm {c} }}{2}}+{\sqrt {\left({\frac {Rf_{\mathrm {c} }}{2}}\right)^{2}-{\frac {R}{\rho }}{\frac {\partial p}{\partial n}}}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/734bec0e7058e1031c53ac47b526da53382f0945.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:34.067ex; height:7.676ex;" alt="{\displaystyle v=-{\frac {Rf_{\mathrm {c} }}{2}}+{\sqrt {\left({\frac {Rf_{\mathrm {c} }}{2}}\right)^{2}-{\frac {R}{\rho }}{\frac {\partial p}{\partial n}}}}}" loading="lazy"></span></dd></dl>
<p>Dabei ist
</p>
<dl><dd><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R}">
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<annotation encoding="application/x-tex">{\displaystyle R}</annotation>
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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4b0bfb3769bf24d80e15374dc37b0441e2616e33.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle R}" loading="lazy"></span> der <a href="Radius" title="Radius">Radius</a> der Kreisbahn</dd>
<dd><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p}">
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<annotation encoding="application/x-tex">{\displaystyle p}</annotation>
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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/81eac1e205430d1f40810df36a0edffdc367af36.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.259ex; height:2.009ex;" alt="{\displaystyle p}" loading="lazy"></span> der <a href="Druck_(Physik)" title="Druck (Physik)">Druck</a></dd>
<dd><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho }">
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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/1f7d439671d1289b6a816e6af7a304be40608d64.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.202ex; height:2.176ex;" alt="{\displaystyle \rho }" loading="lazy"></span> die <a href="Luftdichte" title="Luftdichte">Luftdichte</a></dd>
<dd><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f_{\mathrm {c} }}">
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<mi mathvariant="normal">c</mi>
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</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle f_{\mathrm {c} }}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/654588e10fc524524c7ab9f979a0ece43bb96def.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.101ex; height:2.509ex;" alt="{\displaystyle f_{\mathrm {c} }}" loading="lazy"></span> der <a href="Corioliskraft#Bewegung_auf_der_Erdoberfläche_und_Coriolisparameter" title="Corioliskraft">Coriolisparameter</a></dd></dl>
<p>Weil die Corioliskraft hier zusammen mit der Zentrifugalkraft die Druckgradientkraft ausgleicht, ist der zyklonale Gradientwind langsamer als der <a href="Geostrophischer_Wind" title="Geostrophischer Wind">geostrophische Wind</a> (subgeostrophisch).
</p>
<div class="mw-heading mw-heading3"><h3 id="Antizyklonal">Antizyklonal</h3></div>
<p>Bei einer <a href="Antizyklonale_Rotation" title="Antizyklonale Rotation">antizyklonalen</a> Bewegung dreht sich die Luft um ein <a href="Hochdruckgebiet" title="Hochdruckgebiet">Hochdruckgebiet</a>. Die Druckgradientkraft <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{\mathrm {D} }}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>F</mi>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">D</mi>
</mrow>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle F_{\mathrm {D} }}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/332a0a0c700414dc34bab466aa7585a254c9c017.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.982ex; height:2.509ex;" alt="{\displaystyle F_{\mathrm {D} }}" loading="lazy"></span> zeigt dabei zusammen mit der Zentrifugalkraft <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{\mathrm {Z} }}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>F</mi>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">Z</mi>
</mrow>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle F_{\mathrm {Z} }}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/ae017f90c59400bb1dfaa9eb40139d0078e0b62b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.731ex; height:2.509ex;" alt="{\displaystyle F_{\mathrm {Z} }}" loading="lazy"></span> weg vom Zentrum, die Corioliskraft <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{\mathrm {C} }}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>F</mi>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">C</mi>
</mrow>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle F_{\mathrm {C} }}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/c099296fe1e34c029270715fd5fc2ebf2b996baf.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.913ex; height:2.509ex;" alt="{\displaystyle F_{\mathrm {C} }}" loading="lazy"></span> zeigt zum Zentrum. Es gilt folglich
</p><dl><dd><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{\mathrm {C} }-F_{\mathrm {Z} }=F_{\mathrm {D} }\quad \Leftrightarrow \quad f_{\mathrm {c} }v-{\frac {v^{2}}{R}}=-{\frac {1}{\rho }}{\frac {\partial p}{\partial n}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>F</mi>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">C</mi>
</mrow>
</mrow>
</msub>
<mo>−<!-- − --></mo>
<msub>
<mi>F</mi>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">Z</mi>
</mrow>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mi>F</mi>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">D</mi>
</mrow>
</mrow>
</msub>
<mspace width="1em"></mspace>
<mo stretchy="false">⇔<!-- ⇔ --></mo>
<mspace width="1em"></mspace>
<msub>
<mi>f</mi>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">c</mi>
</mrow>
</mrow>
</msub>
<mi>v</mi>
<mo>−<!-- − --></mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<msup>
<mi>v</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
<mi>R</mi>
</mfrac>
</mrow>
<mo>=</mo>
<mo>−<!-- − --></mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mn>1</mn>
<mi>ρ<!-- ρ --></mi>
</mfrac>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mi mathvariant="normal">∂<!-- ∂ --></mi>
<mi>p</mi>
</mrow>
<mrow>
<mi mathvariant="normal">∂<!-- ∂ --></mi>
<mi>n</mi>
</mrow>
</mfrac>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle F_{\mathrm {C} }-F_{\mathrm {Z} }=F_{\mathrm {D} }\quad \Leftrightarrow \quad f_{\mathrm {c} }v-{\frac {v^{2}}{R}}=-{\frac {1}{\rho }}{\frac {\partial p}{\partial n}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/82e31462f353a6053fe9f541a8a086414b01f24b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:42.406ex; height:6.176ex;" alt="{\displaystyle F_{\mathrm {C} }-F_{\mathrm {Z} }=F_{\mathrm {D} }\quad \Leftrightarrow \quad f_{\mathrm {c} }v-{\frac {v^{2}}{R}}=-{\frac {1}{\rho }}{\frac {\partial p}{\partial n}}}" loading="lazy"></span></dd></dl>
<p>Nach Auflösen nach der Geschwindigkeit <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>v</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle v}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/e07b00e7fc0847fbd16391c778d65bc25c452597.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.128ex; height:1.676ex;" alt="{\displaystyle v}" loading="lazy"></span> ergibt sich als Lösung
</p>
<dl><dd><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v={\frac {Rf_{\mathrm {c} }}{2}}-{\sqrt {\left({\frac {Rf_{\mathrm {c} }}{2}}\right)^{2}+{\frac {R}{\rho }}{\frac {\partial p}{\partial n}}}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>v</mi>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mi>R</mi>
<msub>
<mi>f</mi>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">c</mi>
</mrow>
</mrow>
</msub>
</mrow>
<mn>2</mn>
</mfrac>
</mrow>
<mo>−<!-- − --></mo>
<mrow class="MJX-TeXAtom-ORD">
<msqrt>
<msup>
<mrow>
<mo>(</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mi>R</mi>
<msub>
<mi>f</mi>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">c</mi>
</mrow>
</mrow>
</msub>
</mrow>
<mn>2</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
<mo>+</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mi>R</mi>
<mi>ρ<!-- ρ --></mi>
</mfrac>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mi mathvariant="normal">∂<!-- ∂ --></mi>
<mi>p</mi>
</mrow>
<mrow>
<mi mathvariant="normal">∂<!-- ∂ --></mi>
<mi>n</mi>
</mrow>
</mfrac>
</mrow>
</msqrt>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle v={\frac {Rf_{\mathrm {c} }}{2}}-{\sqrt {\left({\frac {Rf_{\mathrm {c} }}{2}}\right)^{2}+{\frac {R}{\rho }}{\frac {\partial p}{\partial n}}}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/882f86c7fc08b413435c19a865f5ee3840039a67.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:32.258ex; height:7.676ex;" alt="{\displaystyle v={\frac {Rf_{\mathrm {c} }}{2}}-{\sqrt {\left({\frac {Rf_{\mathrm {c} }}{2}}\right)^{2}+{\frac {R}{\rho }}{\frac {\partial p}{\partial n}}}}}" loading="lazy"></span></dd></dl>
<p>Hier gibt es wieder zwei theoretisch mögliche Lösungen, die Negative erfordert aber die geringere Geschwindigkeit und stellt sich deshalb in der Realität ein.
</p><p>Weil die Corioliskraft hier die Druckgradientkraft und die Zentrifugalkraft ausgleichen muss, ist der antizyklonale Gradientwind schneller als der geostrophische Wind (supergeostrophisch). Bei gleichem Druckgradienten weht der Wind folglich um ein Hochdruckgebiet stärker als um ein Tiefdruckgebiet.<sup id="cite_ref-:0_1-1" class="reference"><a href="#cite_note-:0-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading2"><h2 id="Kritische_Krümmung"><span id="Kritische_Kr.C3.BCmmung"></span>Kritische Krümmung</h2></div>
<p>Bei besonders kleinen Hochdruckgebieten mit starkem Druckgradienten führt die hohe Zentrifugalkraft dazu, dass der Gradientwind ein Gleichgewicht zwischen Corioliskraft und der Summe von Zentrifugal- und Druckgradientkraft <i>nicht</i> erreichen kann. Hochdruckgebiete werden deshalb unterhalb eines bestimmten minimalen Radius <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R_{\text{krit}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>R</mi>
<mrow class="MJX-TeXAtom-ORD">
<mtext>krit</mtext>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle R_{\text{krit}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/68f7bd02e7ce59db4d678a1d9717e5a08b10d67b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.606ex; height:2.509ex;" alt="{\displaystyle R_{\text{krit}}}" loading="lazy"></span>, gleichbedeutend mit einer großen <a href="Kr%C3%BCmmung" title="Krümmung">Krümmung</a>, instabil. Die Luft kann nicht mehr auf einer festen Kreisbahn strömen, sondern fließt nach außen vom Hochdruckgebiet weg. Dabei löst sich das Hochdruckgebiet teilweise auf, bis der <a href="Druckgradient" class="mw-redirect" title="Druckgradient">Druckgradient</a> so schwach ist, dass wieder eine stabile Bahn erreicht werden kann. Die kritische Krümmung <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \kappa _{\text{krit}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>κ<!-- κ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mtext>krit</mtext>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \kappa _{\text{krit}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7909510010a040b2f8a3a034e8b925b06bd3632c.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.181ex; height:2.009ex;" alt="{\displaystyle \kappa _{\text{krit}}}" loading="lazy"></span> folgt aus der quadratischen Gleichung zur Lösung des <a href="Kr%C3%A4ftegleichgewicht" class="mw-redirect" title="Kräftegleichgewicht">Kräftegleichgewichts</a> des antizyklonalen Gradientwindes.
</p><p>Für die Geschwindigkeit gibt es nur dann eine <a href="Reelle_Zahl" title="Reelle Zahl">reelle</a> Lösung, solange der Wert unter der Wurzel nicht negativ wird. Für den antizyklonalen Gradientwind steht dort
</p>
<dl><dd><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sqrt {\left({\frac {Rf_{\mathrm {c} }}{2}}\right)^{2}+{\frac {R}{\rho }}{\frac {\partial p}{\partial n}}}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mrow class="MJX-TeXAtom-ORD">
<msqrt>
<msup>
<mrow>
<mo>(</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mi>R</mi>
<msub>
<mi>f</mi>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">c</mi>
</mrow>
</mrow>
</msub>
</mrow>
<mn>2</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
<mo>+</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mi>R</mi>
<mi>ρ<!-- ρ --></mi>
</mfrac>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mi mathvariant="normal">∂<!-- ∂ --></mi>
<mi>p</mi>
</mrow>
<mrow>
<mi mathvariant="normal">∂<!-- ∂ --></mi>
<mi>n</mi>
</mrow>
</mfrac>
</mrow>
</msqrt>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle {\sqrt {\left({\frac {Rf_{\mathrm {c} }}{2}}\right)^{2}+{\frac {R}{\rho }}{\frac {\partial p}{\partial n}}}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/0e526646281e8f3b53ba9cda9684bdf53ccf744b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:20.49ex; height:7.676ex;" alt="{\displaystyle {\sqrt {\left({\frac {Rf_{\mathrm {c} }}{2}}\right)^{2}+{\frac {R}{\rho }}{\frac {\partial p}{\partial n}}}}}" loading="lazy"></span></dd></dl>
<p>Weil der <a href="Druckgradient" class="mw-redirect" title="Druckgradient">Druckgradient</a> <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \textstyle {\frac {\partial p}{\partial n}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mstyle displaystyle="false" scriptlevel="0">
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mi mathvariant="normal">∂<!-- ∂ --></mi>
<mi>p</mi>
</mrow>
<mrow>
<mi mathvariant="normal">∂<!-- ∂ --></mi>
<mi>n</mi>
</mrow>
</mfrac>
</mrow>
</mstyle>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \textstyle {\frac {\partial p}{\partial n}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/5f4b7c1f14ad608d5d01c1e2919621026d644ac5.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:2.754ex; height:4.176ex;" alt="{\displaystyle \textstyle {\frac {\partial p}{\partial n}}}" loading="lazy"></span> immer negativ ist, können negative Werte unter der Wurzel auftreten. Der minimale Radius <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R_{\text{krit}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>R</mi>
<mrow class="MJX-TeXAtom-ORD">
<mtext>krit</mtext>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle R_{\text{krit}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/68f7bd02e7ce59db4d678a1d9717e5a08b10d67b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.606ex; height:2.509ex;" alt="{\displaystyle R_{\text{krit}}}" loading="lazy"></span>, bei dem der Term unter der Wurzel gerade noch nicht negativ ist, wird erreicht, wenn gilt
</p>
<dl><dd><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {R_{\text{krit}}f_{\mathrm {c} }}{2}}\right)^{2}+{\frac {R_{\text{krit}}}{\rho }}{\frac {\partial p}{\partial n}}=0}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msup>
<mrow>
<mo>(</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<msub>
<mi>R</mi>
<mrow class="MJX-TeXAtom-ORD">
<mtext>krit</mtext>
</mrow>
</msub>
<msub>
<mi>f</mi>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">c</mi>
</mrow>
</mrow>
</msub>
</mrow>
<mn>2</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
<mo>+</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<msub>
<mi>R</mi>
<mrow class="MJX-TeXAtom-ORD">
<mtext>krit</mtext>
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</msub>
<mi>ρ<!-- ρ --></mi>
</mfrac>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mi mathvariant="normal">∂<!-- ∂ --></mi>
<mi>p</mi>
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<mrow>
<mi mathvariant="normal">∂<!-- ∂ --></mi>
<mi>n</mi>
</mrow>
</mfrac>
</mrow>
<mo>=</mo>
<mn>0</mn>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \left({\frac {R_{\text{krit}}f_{\mathrm {c} }}{2}}\right)^{2}+{\frac {R_{\text{krit}}}{\rho }}{\frac {\partial p}{\partial n}}=0}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/df77de1ee9db83368d190732d0357c9185d6a486.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:28.111ex; height:6.509ex;" alt="{\displaystyle \left({\frac {R_{\text{krit}}f_{\mathrm {c} }}{2}}\right)^{2}+{\frac {R_{\text{krit}}}{\rho }}{\frac {\partial p}{\partial n}}=0}" loading="lazy"></span></dd></dl>
<p>Nach dem Auflösen nach <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R_{\text{krit}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>R</mi>
<mrow class="MJX-TeXAtom-ORD">
<mtext>krit</mtext>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle R_{\text{krit}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/68f7bd02e7ce59db4d678a1d9717e5a08b10d67b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.606ex; height:2.509ex;" alt="{\displaystyle R_{\text{krit}}}" loading="lazy"></span> erhält man
</p>
<dl><dd><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R_{\text{krit}}={\frac {4}{f_{\mathrm {c} }^{2}\rho }}\left|{\frac {\partial p}{\partial n}}\right|={\frac {4}{f_{\mathrm {c} }v_{\mathrm {g} }}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>R</mi>
<mrow class="MJX-TeXAtom-ORD">
<mtext>krit</mtext>
</mrow>
</msub>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mn>4</mn>
<mrow>
<msubsup>
<mi>f</mi>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">c</mi>
</mrow>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msubsup>
<mi>ρ<!-- ρ --></mi>
</mrow>
</mfrac>
</mrow>
<mrow>
<mo>|</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mi mathvariant="normal">∂<!-- ∂ --></mi>
<mi>p</mi>
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<mrow>
<mi mathvariant="normal">∂<!-- ∂ --></mi>
<mi>n</mi>
</mrow>
</mfrac>
</mrow>
<mo>|</mo>
</mrow>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mn>4</mn>
<mrow>
<msub>
<mi>f</mi>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">c</mi>
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</msub>
<msub>
<mi>v</mi>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">g</mi>
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</mrow>
<annotation encoding="application/x-tex">{\displaystyle R_{\text{krit}}={\frac {4}{f_{\mathrm {c} }^{2}\rho }}\left|{\frac {\partial p}{\partial n}}\right|={\frac {4}{f_{\mathrm {c} }v_{\mathrm {g} }}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/47648b809b312621240a902ef3e45b94782b7fc6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:25.565ex; height:6.176ex;" alt="{\displaystyle R_{\text{krit}}={\frac {4}{f_{\mathrm {c} }^{2}\rho }}\left|{\frac {\partial p}{\partial n}}\right|={\frac {4}{f_{\mathrm {c} }v_{\mathrm {g} }}}}" loading="lazy"></span></dd></dl>
<p>Für die kritische Krümmung <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \kappa _{\text{krit}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>κ<!-- κ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mtext>krit</mtext>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \kappa _{\text{krit}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7909510010a040b2f8a3a034e8b925b06bd3632c.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.181ex; height:2.009ex;" alt="{\displaystyle \kappa _{\text{krit}}}" loading="lazy"></span> ergibt sich damit
</p>
<dl><dd><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \kappa _{\text{krit}}={\frac {1}{R_{\text{krit}}}}={\frac {f_{\mathrm {c} }v_{\mathrm {g} }}{4}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>κ<!-- κ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mtext>krit</mtext>
</mrow>
</msub>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mn>1</mn>
<msub>
<mi>R</mi>
<mrow class="MJX-TeXAtom-ORD">
<mtext>krit</mtext>
</mrow>
</msub>
</mfrac>
</mrow>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<msub>
<mi>f</mi>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">c</mi>
</mrow>
</mrow>
</msub>
<msub>
<mi>v</mi>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">g</mi>
</mrow>
</mrow>
</msub>
</mrow>
<mn>4</mn>
</mfrac>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \kappa _{\text{krit}}={\frac {1}{R_{\text{krit}}}}={\frac {f_{\mathrm {c} }v_{\mathrm {g} }}{4}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7cb4978d1b7b713c808aa3847e177c8c08dda154.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:20.939ex; height:6.176ex;" alt="{\displaystyle \kappa _{\text{krit}}={\frac {1}{R_{\text{krit}}}}={\frac {f_{\mathrm {c} }v_{\mathrm {g} }}{4}}}" loading="lazy"></span></dd></dl>
<p>Dabei ist
</p>
<ul><li><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{\mathrm {g} }}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>v</mi>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">g</mi>
</mrow>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle v_{\mathrm {g} }}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/8ce62c651cbce3fe714ab102bbca3adaac6453a6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.182ex; height:2.343ex;" alt="{\displaystyle v_{\mathrm {g} }}" loading="lazy"></span> die Geschwindigkeit des <a href="Geostrophischer_Wind" title="Geostrophischer Wind">geostrophischen Windes</a></li>
<li><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f_{\mathrm {c} }=2\,\Omega \,\sin \varphi }">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>f</mi>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">c</mi>
</mrow>
</mrow>
</msub>
<mo>=</mo>
<mn>2</mn>
<mspace width="thinmathspace"></mspace>
<mi mathvariant="normal">Ω<!-- Ω --></mi>
<mspace width="thinmathspace"></mspace>
<mi>sin</mi>
<mo>⁡<!-- ⁡ --></mo>
<mi>φ<!-- φ --></mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle f_{\mathrm {c} }=2\,\Omega \,\sin \varphi }</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/1e1895b18460d224b036eebd366ea473f8c95107.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.965ex; height:2.676ex;" alt="{\displaystyle f_{\mathrm {c} }=2\,\Omega \,\sin \varphi }" loading="lazy"></span> der <a href="Corioliskraft#Bewegung_auf_der_Erdoberfläche_und_Coriolisparameter" title="Corioliskraft">Coriolisparameter</a> mit
<ul><li>der <a href="Erdrotation" title="Erdrotation">Winkelgeschwindigkeit der Erde</a> <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Omega ={\frac {2\pi }{86164\;\mathrm {s} }}\approx {\frac {2\pi }{24\;\mathrm {h} }}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi mathvariant="normal">Ω<!-- Ω --></mi>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mn>2</mn>
<mi>π<!-- π --></mi>
</mrow>
<mrow>
<mn>86164</mn>
<mspace width="thickmathspace"></mspace>
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">s</mi>
</mrow>
</mrow>
</mfrac>
</mrow>
<mo>≈<!-- ≈ --></mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mn>2</mn>
<mi>π<!-- π --></mi>
</mrow>
<mrow>
<mn>24</mn>
<mspace width="thickmathspace"></mspace>
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">h</mi>
</mrow>
</mrow>
</mfrac>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \Omega ={\frac {2\pi }{86164\;\mathrm {s} }}\approx {\frac {2\pi }{24\;\mathrm {h} }}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7ca6286f29e459a7311f27299ca416f5be30020c.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:21.184ex; height:5.343ex;" alt="{\displaystyle \Omega ={\frac {2\pi }{86164\;\mathrm {s} }}\approx {\frac {2\pi }{24\;\mathrm {h} }}}" loading="lazy"></span></li>
<li>der <a href="Geographische_Breite" title="Geographische Breite">geographischen Breite</a> <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varphi }">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>φ<!-- φ --></mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \varphi }</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/33ee699558d09cf9d653f6351f9fda0b2f4aaa3e.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.52ex; height:2.176ex;" alt="{\displaystyle \varphi }" loading="lazy"></span>.</li></ul></li></ul>
<p>Weil der Coriolisparameter mit zunehmender geographischer Breite zunimmt, sind zu den <a href="Pol_(Geographie)" title="Pol (Geographie)">Polen</a> hin immer größere Krümmungen und damit immer kleinere Hochs möglich.
</p><p>Die Windgeschwindigkeiten um ein Hochdruckgebiet können durch diese Begrenzung der Druckgradientkraft nicht beliebig groß werden. Sehr starke Winde können deshalb nur um Tiefdruckgebiete auftreten.
</p>
<div class="mw-heading mw-heading2"><h2 id="Literatur">Literatur</h2></div>
<ul><li>Andreas Bott: <cite style="font-style:italic">Synoptische Meteorologie: Methoden der Wetteranalyse und -prognose</cite>. Springer, Berlin, Heidelberg 2012.<span class="Z3988" title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&amp;rfr_id=info:sid/de.wikipedia.org:Gradientwind&amp;rft.au=Andreas+Bott&amp;rft.btitle=Synoptische+Meteorologie%3A+Methoden+der+Wetteranalyse+und+-prognose&amp;rft.date=2012&amp;rft.genre=book&amp;rft.place=Berlin%2C+Heidelberg&amp;rft.pub=Springer" style="display:none">&nbsp;</span></li></ul>
<div class="mw-heading mw-heading2"><h2 id="Weblinks">Weblinks</h2></div>
<ul><li><a rel="nofollow" class="external text" href="http://www.diplomet.info/Gradientwind.html">Gradientwind - diplomet.info</a></li></ul>
<div class="mw-heading mw-heading2"><h2 id="Einzelnachweise">Einzelnachweise</h2></div>
<ol class="references">
<li id="cite_note-:0-1"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-:0_1-0">a</a></sup> <sup><a href="#cite_ref-:0_1-1">b</a></sup></span> <span class="reference-text">Brigitte Klose, Klose, Heinz,: <cite style="font-style:italic">Meteorologie&nbsp;: Eine interdisziplinäre Einführung in die Physik der Atmosphäre</cite>. 3. Auflage. Springer Spektrum, Berlin 2016, ISBN 978-3-662-43622-6, <span style="white-space:nowrap">S.<span style="display:inline-block;width:.2em">&nbsp;</span>295&nbsp;-&nbsp;297</span>.<span class="Z3988" title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&amp;rfr_id=info:sid/de.wikipedia.org:Gradientwind&amp;rft.au=Brigitte+Klose%2C+Klose%2C+Heinz%2C+...&amp;rft.btitle=Meteorologie+%3A+Eine+interdisziplin%C3%A4re+Einf%C3%BChrung+in+die+Physik+der+Atmosph%C3%A4re&amp;rft.date=2016&amp;rft.edition=3.+Aufl&amp;rft.genre=book&amp;rft.isbn=9783662436226&amp;rft.pages=295+-+297&amp;rft.place=Berlin&amp;rft.pub=Springer+Spektrum" style="display:none">&nbsp;</span></span>
</li>
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