川のながれRiver Flows

1. Classification of river flows (free surface flows in open channels) Sub-critical vs Super-critical, Stable or Unstable流れの分類（常流・射流， 安定・不安定）

2. Enjoy watching vortices !! Kelvin Helmholtz type instability渦を楽しむ（ケルビン・ヘルムホルツの不安定）

3. Spiral motion induced stream line curvature 湾曲の２次流

Outline

River Eng. By Hosoda, T.

年に数回しか流れない川もある（Wadi Channel in Oman）Water flows a few times a year in arid areas, bur sever floods occur in the downstream area.

ミシシッピー川の閘門Lock & Dam in the Upper Mississippi

（輸送の道としての川）

川の流れは分類できるー速い流れ（射流）と普通の流れ（常流）ー

Super-critical or Sub-critical

普通の流れ

速い流れ

普通の流れ

跳水

斜め衝撃波

流れの遷移

Sub-critical flow

Flow transition

Super-critical flow

Hydraulic jump

Oblique shock waveSub-critical flow

速い流れから普通の流れへの遷移

常流：下流の影響を受ける．

射流：上流の影響のみ受ける．

跳水

定義速い流れ：フルード数が１を超える流れ普通の流れ：１以下の流れ

Transition from super-critical flow to sub-critical flow

Sub-critical flowSuper-critical flow

Hydraulic jump

波状跳水 Undular jump

動く跳水→段波 たとえばポロロッカ（アマゾン大逆流）

A hydraulic jump moving downstream or upstream is called bore.A bore moving upstream is generated near the river mouth of the Amazon due to the large tidal oscillation and the peculiar shape of the river mouth.

速い流れの特徴 Basic features of super-critical flows

流れは上流から下流に向かって順番に決まっていく．（下流の影響を受けない）Hydraulic variables such as depth and velocity can be calculated from the upstream region to the downstream region.

速い流れと普通の流れの説明Q: The flow shown in the lower photo is super-critical or sub-critical

when you observe the flow standing on a moving boat ?

時間をあけて水面を叩いてみたときの波紋の様子Two patterns can be observed when you beat the water surface standing on a moving boat.

速い流れ Super-critical flow 普通の流れ Sub-critical flow

波紋(water ring)の拡がる速さ(propagation speed) は√gh （津波の伝波速度）流れの速さV

速い流れV/ √gh >1普通の流れV/ √gh <1

V

速い流れの特徴 Typical features of super-critical flows

速い流れ Super-critical底が上に凸ならは水面も上に凸

普通の流れ Sub-critical

もっと速い流れの特徴もっと速い流れは不安定になる - 転波列（てんぱれつ）

Roll waves are generated when Froude number exceeds the critical value (1.5-2.0).

渦を楽しむEnjoy watching eddies !!

ケルビン・ヘルムホルツの不安定 Kelvin-Helmholtz type instability

by the courtesy of MLIT

The Super-Presentation(TED) by NHKCloudy with a chance of joy（曇時々 喜び）Mr. Gavin Pretor-Pinney, the Cloud Appreciation Society

The Kelvin-Helmholtz cloud.

This looks like a series of breaking waves, and it’s caused by shearing winds.

The wind above the cloud layer and below the cloud layer differ significantly, and in the middle, in between, you get this undulating of the air,

and if the difference in those speeds is just right, the tops of the undulations curl over in these beautiful breaking wave-like vortices.

by Lauraine Ayers-Brie, Maui, Hawaii, US

by Jason Cleverly, Bryher, Scilly Isles, UK

鳴門の渦潮も同じ現象Naruto Eddies are generated due to K-H instability

Simulation

橋脚周辺の3次元的流れ3-D flow structures around a bridge pier with vortex shedding

川の蛇行とらせん流Spiral flow(secondary currents) caused by stream line curvature

Stream-wise velocities

Transverse velocities

Plan view of depth averaged stream-wise velocities

湾曲流路の中の螺旋流発生のメカニズム（実用的に重要）Generation mechanism of spiral flow in a curved channel

A

BA

水圧 水圧遠心力

主流の流速分布（遠心力の元）

小 大

小 大

水圧と遠心力の差

せん断応力

横断方向の流速分布

Longitudinal velocity distribution

Transverse velocity distribution

Hydro-staticpressure

Centrifugal force

Imbalance between pressure and centrifugal force

Shear stresses

B

湾曲流路の外岸側で局所洗掘が発生The local scouring is caused due to secondary currents along the outer bank of a curved channel, resulting in the collapse of the river structure.

湾曲流路の内岸側で土砂堆積が発生Sediments deposit along the inner bank of a curved channel.