Transport phenomena, such as fluid flows, solute dispersion, and migration of aquatic species, are ubiquitous in surface water bodies. These transport phenomena are inherently nonlinear and stochastic, and analyzing their dynamics requires using mathematically and physically sophisticated knowledge. Numerical analysis assisted by firm mathematics can serve as an effective tool for comprehending the transport phenomena; however, there exist only a limited number of such kinds of approaches in regional environment science and related research areas. This paper provides a brief summary of our previous researches on mathematical and numerical modelling of the transport phenomena for promoting the use of the modelling techniques. Their applicability to the problems specific to the Hii River system, Japan, is also discussed in this paper.

地表水体では，流体の流動，溶質の分散，水棲生物の移動などの輸送現象が生じる．こうした輸送現象は非線型的かつ確率論的であり，その予測や評価には数物的知見の活用が効果的である．とりわけ，数学的に裏付けられた数理モデルと数値計算手法の適用が威力を発揮する．しかしながら，地域環境科学や関連研究分野におけるそのような手法の普及率は著しく低い．本報は，著者や共同研究者らによる輸送現象に対する数理・数値的な接近手法を紹介する．また，それらの斐伊川水系における実問題への適用性を論じる．