懸浮顆粒渦環中的加速絮凝及線性穩定性分析

Abstract

海洋中之雙擴散對流沉降為帶動懸浮物質垂直傳輸之重要機制，其所引起之指狀流將隨時間發展為懸浮顆粒球滴向下沉降，並形成渦環結構，此外，渦環發生瑞利‐泰勒不穩定性將分裂為數個小型環狀。本研究考慮自然界之細小黏附性顆粒，顆粒間可發生絮凝現象形成絮團結構，而絮團相較於單顆顆粒具有較大之沉降速度，因此絮凝現象亦為加速懸浮物質垂直傳輸之關鍵機制。本研究利用尤拉-拉格朗日數值模式模擬球滴沉降至渦環發展過程，且應用絮凝模型，分析在此流況影響下之絮凝時變過程，並討論顆粒慣性、顆粒間作用之凝聚力與顆粒大小所造成的影響，另外亦針對過去文獻中絮凝模型比較其中差異，並發現在高顆粒數密度之下可達到較佳的加速絮凝效果。另一方面，針對渦環發生之瑞利‐泰勒不穩定性，在環形坐標系之下進行線性穩定性分析，若在無黏性假設下，可推導出成長率與波數之色散關係，發現系統中短波長具有較快之成長率。而在本研究之理論推導過程中亦可得知，若在完善考量之下(如考慮渦環形狀與黏滯性)欲求解問題，未來尚有許多努力空間。

Double-diffusive sedimentation is an important mechanism that can enhance vertical transport of suspended materials in the ocean. The resulting sediment-laden finger in double diffusion forms the spherical drop, which then evolves into the vortex ring. Moreover, Rayleigh-Taylor instability can occur in particle-laden rings, generating smaller rings. This study considers fine cohesive particles in nature which can form flocs due to the flocculation process. Flocs are associated with greater settling velocities compared to individual particles. Therefore, flocculation process also plays a key role in vertical transport of suspended matters. In this study, we conduct numerical simulations for the evolution of particle-laden drops and their transition to rings using an Eulerian-Largrangian model. By adding flocculation models, analysis of time-dependent flocculation process under the resulting hydrodynamic influence is made. The effects of the particle inertia, cohesive force, and particle size are discussed. Moreover, differences of flocculation models in the past literature are compared. We found that greater flocculation enhancement can be resulting from higher particle number density. In addition to the numerical study, the Rayleigh-Taylor instability of particle-laden rings is derived through the linear analysis on the toroidal coordinate system. Based on the inviscid assumption, the dispersion relation can be found, showing that short waves has a larger growth rate. Our derivation also shows that the solution with full consideration of the system (e.g., torus shape and viscosity) requires more effort in the future.