<html><head><meta http-equiv="Content-Type" content="text/html; charset=us-ascii"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class="">Dear colleagues,<div class=""><br class=""></div><div class="">I am trying to calculate the circulation balance over a semi-enclosed area, by taking the vorticity balance and integrating over said area. One of the terms in the vorticity balance is div (fu, fv), which, when integrated over the area, should give the integral over the boundary of (fu,fv) \cdot n, where n is the normal to the boundary. Over the closed portion of the boundary, i.e. on the solid walls, (fu,fv) \cdot n should be zero. However, because the vorticity points are not on the velocity boundary faces, these terms do not vanish. The residual left from this contribution dominates the balance, so it is not a small error.</div><div class=""><br class=""></div><div class="">I have tried different versions of the vorticity definitions, i.e. the volume flux form as in (equation 13) of Adcroft et al <a href="https://journals.ametsoc.org/view/journals/mwre/132/12/mwr2823.1.xml" class="">https://journals.ametsoc.org/view/journals/mwre/132/12/mwr2823.1.xml</a>, or the simple derivatives and neither of them work. </div><div class=""><br class=""></div><div class="">Does anyone have any words of wisdom or references that could be helpful?</div><div class=""><br class=""></div><div class="">Many thanks,<br class=""><div class="">
<meta charset="UTF-8" class=""><div dir="auto" style="caret-color: rgb(0, 0, 0); color: rgb(0, 0, 0); letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div style="color: rgb(0, 0, 0); font-variant-caps: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px;"><span style="font-style: normal;" class="">Paola Cessi<br class=""></span><br class=""><span style="font-family: Helvetica; font-style: normal; font-weight: normal; font-size: 12px;" class="">--------------------------------------------------------------------------------------------<br class="">Paola Cessi </span><span style="font-family: Helvetica; font-style: normal; font-weight: normal; font-size: 12px;" class="">Tel: +1 858 534 0622 </span><span style="font-family: Helvetica; font-style: normal; font-weight: normal; font-size: 12px;" class=""><br class="">Scripps Institution of Oceanography </span><span style="font-family: Helvetica; font-style: normal; font-weight: normal; font-size: 12px;" class=""> Fax: +1 858 534 8045</span><span style="font-family: Helvetica; font-style: normal; font-weight: normal; font-size: 12px;" class=""><br class="">9500 Gilman Drive #0213 </span><span style="font-family: Helvetica; font-style: normal; font-weight: normal; font-size: 12px;" class=""><a href="mailto:pcessi@ucsd.edu" class="">e-mail: pcessi@ucsd.edu</a> </span><span style="font-family: Helvetica; font-style: normal; font-weight: normal; font-size: 12px;" class=""><br class="">La Jolla, CA 92093-0213 </span><span style="font-family: Helvetica; font-style: normal; font-weight: normal; font-size: 12px;" class="">Web: <a href="http://pordlabs.ucsd.edu/pcessi" class="">http://pordlabs.ucsd.edu/pcessi</a></span><span style="font-family: Helvetica; font-style: normal; font-weight: normal; font-size: 12px;" class=""><br class="">USA <br class=""><br class=""></span></div></div></div></div></div></body></html>