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The Evolution of Internal Undular Bores over a Slope in the Presence of Rotation

机译：在旋转存在下斜坡上内部向外孔的演变

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Abstract >The large‐amplitude internal waves commonly observed in the coastal ocean often take the form of unsteady undular bores. Hence, here, we examine the long‐time combined effect of variable topography and background rotation on the propagation of internal undular bores, using the framework of a variable‐coefficient Ostrovsky equation. Because the leading waves in an internal undular bore are close to solitary waves, we first examine the evolution of a single solitary wave. Then, we consider an internal undular bore, for which two methods of generation are used. One method is the matured undular bore developed from an initial shock box in the Korteweg–de Vries equation, that is the Ostrovsky equation with the rotational term omitted, and the other method is a modulated cnoidal wave solution of the same Korteweg–de Vries equation. It transpires that in the long‐time model simulations, the rotational effect disintegrates the nonlinear waves into inertia‐gravity waves, and then there emerge complicated interactions between these inertia‐gravity waves and the modulated periodic waves of the undular bore, especially at the rear part of the undular bore. However, near the front of the undular bore, nonlinear effects further modulate these waves, with the eventual emergence of nonlinear envelope wave packets. </abstract> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> <div class="translation abstracttxt"> <span class="zhankaihshouqi fivelineshidden" id="abstract"> <span>机译：</span><abstract xmlns=”http://www.wiley.com/namespaces/wiley“type=“main”xml:lang=“en”><title type=“main”“>摘要>在沿海海洋中常见的大振幅内波通常以不稳定波状孔的形式出现。因此，在这里，我们使用变系数奥斯特罗夫斯基方程的框架来研究可变地形和背景旋转对内波状孔传播的长时间综合影响。因为当内部波状孔接近孤立波时，我们首先研究单个孤立波的演化。然后，我们考虑一个内部波状孔，其中使用两种生成方法。一种方法是从Korteweg–de Vries方程中的初始激波盒（即省略旋转项的Ostrovsky方程）发展而来的成熟波状孔，另一种方法是相同Korteweg–de Vries方程的调制椭圆余弦波解。结果表明，在长时间模型模拟中，旋转效应将非线性波分解为惯性重力波，然后这些惯性重力波与波状孔的调制周期波之间出现复杂的相互作用，尤其是在波状孔的后部。然而，在波状孔的前部附近，非线性效应进一步调制这些波，最终出现非线性包络波包 </abstract> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> </div> <div class="record"> <h2 class="all_title" id="enpatent33" >著录项</h2> <ul> <li> <span class="lefttit">来源</span> <div style="width: 86%;vertical-align: text-top;display: inline-block;"> <a href='/journal-foreign-29329/'>《Studies in Applied Mathematics》</a> <b style="margin: 0 2px;">|</b><span>2018年第4期</span><b style="margin: 0 2px;">|</b><span>共18页</span> </div> </li> <li> <div class="author"> <span class="lefttit">作者</span> <p id="fAuthorthree" class="threelineshidden zhankaihshouqi"> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Yuan Chunxin&option=202" target="_blank" rel="nofollow">Yuan Chunxin;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Grimshaw Roger&option=202" target="_blank" rel="nofollow">Grimshaw Roger;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Johnson Edward&option=202" target="_blank" rel="nofollow">Johnson Edward;</a> </p> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zkzz" style="display: none;">展开▼</span> </div> </li> <li> <div style="display: flex;"> <span class="lefttit">作者单位</span> <div style="position: relative;margin-left: 3px;max-width: 639px;"> <div class="threelineshidden zhankaihshouqi" id="fOrgthree"> <p>University College London;</p> <p>University College London;</p> <p>University College London;</p> </div> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zhdw" style="display: none;">展开▼</span> </div> </div> </li> <li > <span class="lefttit">收录信息</span> <span style="width: 86%;vertical-align: text-top;display: inline-block;"></span> </li> <li> <span class="lefttit">原文格式</span> <span>PDF</span> </li> <li> <span class="lefttit">正文语种</span> <span>eng</span> </li> <li> <span class="lefttit">中图分类</span> <span><a href="https://www.zhangqiaokeyan.com/clc/1147.html" title="应用数学">应用数学;</a></span> </li> <li class="antistop"> <span class="lefttit">关键词</span> <p style="width: 86%;vertical-align: text-top;"> </p> </li> </ul> </div> </div> <div class="literature cardcommon"> <div class="similarity "> <h3 class="all_title" 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Atif Nazir</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Sajjad Hussain&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">,Sajjad Hussain</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Mohammad Shafique&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">,Mohammad Shafique</a> <span> <a href="/journal-cn-56455/" target="_blank" rel="nofollow" class="tuijian_authcolor"> . 应用数学（英文） </a> </span> <span> . 2015</span><span>,第2期</span> </span> </div> </li> </ul> <ul style="display: none;"> <li> <div> <b>1. </b><a class="enjiyixqcontent" href="/patent-detail/06130436659738.html">Crankshaft angel position determining method for internal combustion engine, involves pulling falling and rising signal slopes of electrical signals for determining direction of rotation and increment of angle of rotation of crankshaft</a> <b>[P]</b> . <span> 外国专利：  DE102004043100A1 </span> <span> . 2006-03-09</span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：用于内燃机的曲轴天使位置确定方法，涉及拉动电信号的下降和上升信号斜率，以确定曲轴的旋转方向和旋转角度的增加 </span> </p> </li> <li> <div> <b>2. </b><a class="enjiyixqcontent" href="/patent-detail/06130495714355.html">Pump or motor with parallel piston in the circles in the bores of a rotation drum by means of a slope eccentric disk can be moved back and forth</a> <b>[P]</b> . <span> 外国专利：  DE529589C </span> <span> . 1931-07-15</span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：带有倾斜的偏心盘的旋转滚筒孔中带有圆形平行活塞的泵或电动机可以前后移动 </span> </p> </li> <li> <div> <b>3. </b><a class="enjiyixqcontent" href="/patent-detail/06130429266226.html">Screwed connection especially for hub with crankshaft of internal combustion engine has screw which screws into threaded bore in shaft, wherein screw and threaded bore are arranged eccentrically to rotational axis</a> <b>[P]</b> . <span> 外国专利：  DE102007054195A1 </span> <span> . 2009-05-20</span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：特别是用于内燃机曲轴的轮毂的螺纹连接具有螺钉，该螺钉拧入轴的螺纹孔中，其中，螺钉和螺纹孔相对于旋转轴线偏心地布置 </span> </p> </li> </ul> </div> </div> </div> <div class="theme cardcommon" style="overflow: auto;display:none"> <h3 class="all_title" id="enpatent55">相关主题</h3> <ul id="subject"> </ul> </div> </div> </div> </div> <div class="right rightcon"> <div class="details_img cardcommon clearfix" style="margin-bottom: 10px;display:none;" > </div> </div> </div> <div id="thesis_get_original1" class="downloadBth" style="bottom: 19px;z-index: 999;" onclick="ywcd('0704029019077','4',7,2,1,'',this,24)" class="delivery" prompt="010401" title="通过人工服务将文献原文发送至邮箱" >获取原文</div> <div class="journalsub-pop-up" 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