<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0016-7169</journal-id>
<journal-title><![CDATA[Geofísica internacional]]></journal-title>
<abbrev-journal-title><![CDATA[Geofís. Intl]]></abbrev-journal-title>
<issn>0016-7169</issn>
<publisher>
<publisher-name><![CDATA[Universidad Nacional Autónoma de México, Instituto de Geofísica]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0016-71692020000300194</article-id>
<article-id pub-id-type="doi">10.22201/igeof.00167169p.2020.59.3.2094</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[&#8216;Preferred Trajectories&#8217; defined by mass and potential vorticity conservation]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Ochoa]]></surname>
<given-names><![CDATA[José]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Badan]]></surname>
<given-names><![CDATA[Antonio]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Sheinbaum]]></surname>
<given-names><![CDATA[Julio]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Castro]]></surname>
<given-names><![CDATA[Jorge]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,CICESE Departamento de Oceanografía Física ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad del Mar  ]]></institution>
<addr-line><![CDATA[Puerto Angel Oaxaca]]></addr-line>
<country>Mexico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>09</month>
<year>2020</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>09</month>
<year>2020</year>
</pub-date>
<volume>59</volume>
<numero>3</numero>
<fpage>194</fpage>
<lpage>207</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S0016-71692020000300194&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S0016-71692020000300194&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S0016-71692020000300194&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract Most schemes to estimate &#8216;absolute&#8217; geostrophic velocities, in the absence of actual velocity measurements, use directional constraints of the flow at different vertical levels. These constraints allow the determination, often as a least square problem, of the integration constants in the thermal-wind equation. Examples of such directions are those defined by the intersection of constant potential temperature and isohaline surfaces, which under appropriate approximation are material surfaces. Here we show that under adiabatic, non-diffusive, geostrophic, hydrostatic motions, but allowing for compressibility, hence the focus being on the large-scale circulation, a pair of orthogonality constraints, much closely related with dynamical balances than the conservation of potential temperature and salinity, yield a flow direction. These constraints are the conservation of &#8216;local&#8217; potential density and potential vorticity, in their reduction consistent with such approximations. &#8216;Neutral&#8217;, &#8216;Orthobaric&#8217;, and &#8216;Topobaric&#8217; surfaces are approximately material surfaces defined as a result of the conservation of &#8216;local&#8217; potential density, but in order to build such global surfaces additional assumptions are required. The conservation constraint is an inexact differential equation that cannot define, uniquely, a global surface. Here we explicitly show that to define the flow direction, there is no need to build global surfaces out of inexact differentials, as would also be the case with the iso-potential vorticity surfaces, thus avoiding additional assumptions. The &#8216;Preferred Trajectories&#8217; are then well-defined paths as integrals along this flow direction without being the intersection of global surfaces. Some examples are included for illustrative purposes. Further analysis including error propagation are beyond the scope of this work and left for future studies.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen La mayoría de los métodos para estimar velocidades geostróficas "absolutas", en ausencia de mediciones directas de velocidad, utilizan restricciones que definen la dirección del flujo a diferentes niveles verticales. Estas restricciones permiten determinar, a menudo mediante la solución de problemas de cuadrados mínimos, las constantes de integración de la ecuación de viento térmico. Ejemplos de tales direcciones son las definidas por la intersección de superficies de temperatura potencial constante y de superficies isohalinas, que, bajo aproximaciones adecuadas, son superficies materiales. En este trabajo nos enfocamos en la circulación oceánica de gran escala que puede considerarse como un flujo adiabático, no difusivo, en balance hidrostático y geostrófico, pero que puede ser compresible. Bajo estas suposiciones definimos dos restricciones ortogonales mas estrechamente relacionadas con la dinámica que las de conservación de temperatura potencial y salinidad para determinar la dirección del flujo. Dichas restricciones son la conservación de densidad potencial "local" y la de vorticidad potencial en su reducción consistente con las características del flujo antes mencionadas. En la literatura se han definido superficies denominadas "Neutrales", "Ortobáricas" y "Topobáricas" las cuales son aproximadamente superficies materiales que resultan de la conservación de densidad potencial "local", pero su construcción como superficies globales requiere de suposiciones adicionales. Esto se debe a que la restricción de conservación de densidad potencial &#8220;local&#8221; es una ecuación diferencial inexacta que no permite definir, unívocamente, dichas superficies. En este trabajo mostramos explícitamente que para definir la dirección del flujo no hay necesidad de construir superficies globales partir de diferenciales inexactos y hacer suposiciones adicionales, como sería el caso si buscáramos superficies de vorticidad potencial constante. En su lugar, utilizamos "Trayectorias preferenciales" que son trayectorias bien definidas que se obtienen al integrar a lo largo de la dirección del flujo sin necesidad de ser la intersección de superficies globales. Se incluyen ejemplos con fines ilustrativos. Análisis adicionales incluyendo el de propagación de errores está más allá del alcance de este trabajo y se deja para futuros estudios]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[circulación geostrófica de gran escala]]></kwd>
<kwd lng="es"><![CDATA[compresibilidad]]></kwd>
<kwd lng="es"><![CDATA[restricciones de dirección]]></kwd>
<kwd lng="es"><![CDATA[superficies neutrales]]></kwd>
<kwd lng="en"><![CDATA[large-scale geostrophic]]></kwd>
<kwd lng="en"><![CDATA[compressibility]]></kwd>
<kwd lng="en"><![CDATA[direction constraints]]></kwd>
<kwd lng="en"><![CDATA[neutral surfaces]]></kwd>
</kwd-group>
</article-meta>
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