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Exact Solutions Modelling Nonlinear Atmospheric Gravity Waves 非线性大气重力波建模的精确解法
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2023-12-20 DOI: 10.1007/s00021-023-00842-3
David Henry
{"title":"Exact Solutions Modelling Nonlinear Atmospheric Gravity Waves","authors":"David Henry","doi":"10.1007/s00021-023-00842-3","DOIUrl":"10.1007/s00021-023-00842-3","url":null,"abstract":"<div><p>Exact solutions to the governing equations for atmospheric motion are derived which model nonlinear gravity wave propagation superimposed on atmospheric currents. Solutions are explicitly prescribed in terms of a Lagrangian formulation, which enables a detailed exposition of intricate flow characteristics. It is shown that our solutions are well-suited to modelling two distinct forms of mountain waves, namely: trapped lee waves in the Equatorial <i>f</i>-plane, and vertically propagating mountain waves at general latitudes.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"26 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-023-00842-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138820009","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Microscopic Expression of Anomalous Dissipation in Passive Scalar Transport 被动标量传输中反常耗散的微观表达
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2023-12-11 DOI: 10.1007/s00021-023-00834-3
Tomonori Tsuruhashi, Tsuyoshi Yoneda
{"title":"Microscopic Expression of Anomalous Dissipation in Passive Scalar Transport","authors":"Tomonori Tsuruhashi,&nbsp;Tsuyoshi Yoneda","doi":"10.1007/s00021-023-00834-3","DOIUrl":"10.1007/s00021-023-00834-3","url":null,"abstract":"<div><p>We study anomalous dissipation from a microscopic viewpoint. In the work by Drivas et al. (Arch Ration Mech Anal 243(3):1151–1180, 2022), the property of anomalous dissipation provides the existence of non-unique weak solutions for a transport equation with a singular velocity field. In this paper, we reconsider this solution in terms of kinetic theory and clarify its microscopic property. Consequently, energy loss can be expressed by non-vanishing microscopic obstruction.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"26 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138568320","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Well-Posedness of Solutions to Stochastic Fluid–Structure Interaction 随机流固耦合解的适定性
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2023-11-16 DOI: 10.1007/s00021-023-00839-y
Jeffrey Kuan, Sunčica Čanić
{"title":"Well-Posedness of Solutions to Stochastic Fluid–Structure Interaction","authors":"Jeffrey Kuan,&nbsp;Sunčica Čanić","doi":"10.1007/s00021-023-00839-y","DOIUrl":"10.1007/s00021-023-00839-y","url":null,"abstract":"<div><p>In this paper we introduce a constructive approach to study well-posedness of solutions to stochastic fluid–structure interaction with stochastic noise. We focus on a benchmark problem in stochastic fluid–structure interaction, and prove the existence of a unique weak solution in the probabilistically strong sense. The benchmark problem consists of the 2D time-dependent Stokes equations describing the flow of an incompressible, viscous fluid interacting with a linearly elastic membrane modeled by the 1D linear wave equation. The membrane is stochastically forced by the time-dependent white noise. The fluid and the structure are linearly coupled. The constructive existence proof is based on a time-discretization via an operator splitting approach. This introduces a sequence of approximate solutions, which are random variables. We show the existence of a subsequence of approximate solutions which converges, almost surely, to a weak solution in the probabilistically strong sense. The proof is based on uniform energy estimates in terms of the <i>expectation</i> of the energy norms, which are the backbone for a weak compactness argument giving rise to a weakly convergent subsequence of <i>probability measures</i> associated with the approximate solutions. Probabilistic techniques based on the Skorohod representation theorem and the Gyöngy–Krylov lemma are then employed to obtain almost sure convergence of a subsequence of the random approximate solutions to a weak solution in the probabilistically strong sense. The result shows that the deterministic benchmark FSI model is robust to stochastic noise, even in the presence of rough white noise in time. To the best of our knowledge, this is the first well-posedness result for stochastic fluid–structure interaction.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"26 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134796764","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Optimality of the Decay Estimate of Solutions to the Linearised Curl-Free Compressible Navier–Stokes Equations 线性化无旋流可压缩Navier-Stokes方程解衰减估计的最优性
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2023-11-14 DOI: 10.1007/s00021-023-00837-0
Tsukasa Iwabuchi, Dáithí Ó hAodha
{"title":"Optimality of the Decay Estimate of Solutions to the Linearised Curl-Free Compressible Navier–Stokes Equations","authors":"Tsukasa Iwabuchi,&nbsp;Dáithí Ó hAodha","doi":"10.1007/s00021-023-00837-0","DOIUrl":"10.1007/s00021-023-00837-0","url":null,"abstract":"<div><p>We discuss optimal estimates of solutions to the compressible Navier–Stokes equations in Besov norms. In particular, we consider the estimate of the curl-free part of the solution to the linearised equations, in the homogeneous case. We prove that our estimate is optimal in the <span>(L^infty )</span>-norm by showing that the norm is bounded from below by the same decay rate.\u0000</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"26 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-023-00837-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134878289","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
A Method for Finding Exact Solutions to the 2D and 3D Euler–Boussinesq Equations in Lagrangian Coordinates 拉格朗日坐标系下二维和三维Euler-Boussinesq方程精确解的一种方法
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2023-11-14 DOI: 10.1007/s00021-023-00835-2
Tomi Saleva, Jukka Tuomela
{"title":"A Method for Finding Exact Solutions to the 2D and 3D Euler–Boussinesq Equations in Lagrangian Coordinates","authors":"Tomi Saleva,&nbsp;Jukka Tuomela","doi":"10.1007/s00021-023-00835-2","DOIUrl":"10.1007/s00021-023-00835-2","url":null,"abstract":"<div><p>We study the Boussinesq approximation for the incompressible Euler equations using Lagrangian description. The conditions for the Lagrangian fluid map are derived in this setting, and a general method is presented to find exact fluid flows in both the two-dimensional and the three-dimensional case. There is a vast amount of solutions obtainable with this method and we can only showcase a handful of interesting examples here, including a Gerstner type solution to the two-dimensional Euler–Boussinesq equations. In two earlier papers we used the same method to find exact Lagrangian solutions to the homogeneous Euler equations, and this paper serves as an example of how these same ideas can be extended to provide solutions also to related, more involved models.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"26 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-023-00835-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134796342","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Nearly Toroidal, Periodic and Quasi-periodic Motions of Fluid Particles Driven by the Gavrilov Solutions of the Euler Equations Euler方程Gavrilov解驱动下流体粒子的近环面、周期和准周期运动
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2023-11-07 DOI: 10.1007/s00021-023-00836-1
Pietro Baldi
{"title":"Nearly Toroidal, Periodic and Quasi-periodic Motions of Fluid Particles Driven by the Gavrilov Solutions of the Euler Equations","authors":"Pietro Baldi","doi":"10.1007/s00021-023-00836-1","DOIUrl":"10.1007/s00021-023-00836-1","url":null,"abstract":"<div><p>We consider the smooth, compactly supported solutions of the steady 3D Euler equations of incompressible fluids constructed by Gavrilov (Geom Funct Anal (GAFA) 29(1):190–197, 2019), and we study the corresponding fluid particle dynamics. This is an <span>ode</span> analysis, which contributes to the description of Gavrilov’s vector field.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"26 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-023-00836-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71909781","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Asymptotic Stability of Rarefaction Waves for Hyperbolized Compressible Navier–Stokes Equations 双曲可压缩Navier-Stokes方程稀疏波的渐近稳定性
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2023-11-01 DOI: 10.1007/s00021-023-00833-4
Yuxi Hu, Xuefang Wang
{"title":"Asymptotic Stability of Rarefaction Waves for Hyperbolized Compressible Navier–Stokes Equations","authors":"Yuxi Hu,&nbsp;Xuefang Wang","doi":"10.1007/s00021-023-00833-4","DOIUrl":"10.1007/s00021-023-00833-4","url":null,"abstract":"<div><p>We consider a model of one dimensional isentropic compressible Navier–Stokes equations for which the classical Newtonian flow is replaced by a Maxwell flow. We establish the asymptotic stability of rarefaction waves for this model under some small conditions on initial perturbations and amplitude of the waves. The proof is based on <span>(L^2)</span> energy methods.\u0000</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"25 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134795389","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Allen–Cahn–Navier–Stokes–Voigt Systems with Moving Contact Lines 具有移动接触线的Allen-Cahn-Navier-Stokes-Voigt系统
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2023-10-31 DOI: 10.1007/s00021-023-00829-0
Ciprian G. Gal, Maurizio Grasselli, Andrea Poiatti
{"title":"Allen–Cahn–Navier–Stokes–Voigt Systems with Moving Contact Lines","authors":"Ciprian G. Gal,&nbsp;Maurizio Grasselli,&nbsp;Andrea Poiatti","doi":"10.1007/s00021-023-00829-0","DOIUrl":"10.1007/s00021-023-00829-0","url":null,"abstract":"<div><p>We consider a diffuse interface model for an incompressible binary fluid flow. The model consists of the Navier–Stokes–Voigt equations coupled with the mass-conserving Allen–Cahn equation with Flory–Huggins potential. The resulting system is subject to generalized Navier boundary conditions for the (volume averaged) fluid velocity <span>({{textbf {u}}})</span> and to a dynamic contact line boundary condition for the order parameter <span>(phi )</span>. These boundary conditions account for the moving contact line phenomenon. We establish the existence of a global weak solution which satisfies an energy inequality. A similar result is proven for the Allen–Cahn–Navier–Stokes system. In order to obtain some higher-order regularity (w.r.t. time) we propose the Voigt approximation: in this way we are able to prove the validity of the energy identity and of the strict separation property. Thanks to this property, we can show the uniqueness of quasi-strong solutions, even in dimension three. Regularization in finite time of weak solutions is also shown.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"25 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134797829","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
The Lagrangian Formulation for Wave Motion with a Shear Current and Surface Tension 具有剪切流和表面张力的波动的拉格朗日公式
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2023-10-17 DOI: 10.1007/s00021-023-00831-6
Conor Curtin, Rossen Ivanov
{"title":"The Lagrangian Formulation for Wave Motion with a Shear Current and Surface Tension","authors":"Conor Curtin,&nbsp;Rossen Ivanov","doi":"10.1007/s00021-023-00831-6","DOIUrl":"10.1007/s00021-023-00831-6","url":null,"abstract":"<div><p>The Lagrangian formulation for the irrotational wave motion is straightforward and follows from a Lagrangian functional which is the difference between the kinetic and the potential energy of the system. In the case of fluid with constant vorticity, which arises for example when a shear current is present, the separation of the energy into kinetic and potential is not at all obvious and neither is the Lagrangian formulation of the problem. Nevertheless, we use the known Hamiltonian formulation of the problem in this case to obtain the Lagrangian density function, and utilising the Euler–Lagrange equations we proceed to derive some model equations for different propagation regimes. While the long-wave regime reproduces the well known KdV equation, the short- and intermediate long wave regimes lead to highly nonlinear and nonlocal evolution equations.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"25 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134796671","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Regularity Criterion for the 2D Inviscid Boussinesq Equations 二维无粘Boussinesq方程的正则性判据
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2023-10-17 DOI: 10.1007/s00021-023-00832-5
Menghan Gong, Zhuan Ye
{"title":"Regularity Criterion for the 2D Inviscid Boussinesq Equations","authors":"Menghan Gong,&nbsp;Zhuan Ye","doi":"10.1007/s00021-023-00832-5","DOIUrl":"10.1007/s00021-023-00832-5","url":null,"abstract":"<div><p>The question of whether the two-dimensional inviscid Boussinesq equations can develop a finite-time singularity from general initial data is a challenging open problem. In this paper, we obtain two new regularity criteria for the local-in-time smooth solution to the two-dimensional inviscid Boussinesq equations. Similar result is also valid for the nonlocal perturbation of the two-dimensional incompressible Euler equations.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"25 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134796675","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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