MPM BL - Revision history

Robertson at 12:02, 18 May 2016

2016-05-18T12:02:39Z

← Older revision		Revision as of 12:02, 18 May 2016
Line 1:		Line 1:
	<div class="title">Meyer-Peter Müeller Bedload Formulation</div>		<div class="title">Meyer-Peter Müeller Bedload Formulation</div>
	~~<wikitex>~~
	The [[Bibliography#Meyer-PeterE_1948a \| Meyer-Peter Müeller (1948)]] formulation is		The [[Bibliography#Meyer-PeterE_1948a \| Meyer-Peter Müeller (1948)]] formulation is
	$$
	~~\Phi = \max \left[ {8\left( {\theta _{sf} - \theta _c } \right)^{1.5} ,\quad 0} \right]~~
	$$
	~~where $\Phi$ is the magnitude of the non-dimensional transport rate for each sediment class,$\theta _{sf}$ is the non-dimensional Shields parameter for skin stress~~
	$$
	~~\theta _{sf} = \frac{{\tau _{sf} }}{{\left( {s - 1} \right)gD_{50} }}~~
	$$

	$\theta _c = 0.047$ is the critical Shields parameter, and $\tau _{sf}$ is the magnitude of total skin-friction component of bottom stress computed from		<math display="block">\Phi = \max \left[ {8\left( {\theta _{sf} - \theta _c } \right)^{1.5} ,\quad 0} \right]</math>
	$$
	\tau _{sf} = \left( {\tau _{bx}^2 + \tau _{by}^2 } \right)^{0.5}		where <math>\Phi</math> is the magnitude of the non-dimensional transport rate for each sediment class, <math>\theta _{sf}</math> is the non-dimensional Shields parameter for skin stress
	$$
	where ${\tau _{bx}}^2$ and ${\tau _{bx}}^2$ are the skin-friction components of bed stress, from currents alone or the maximum wave-current combined stress, in the $x$ and $y$ directions. These are computed at cell faces ($u$ and $v$ locations) and then interpolated to cell centers ($\rho$ points). The bedload transport vectors are partitioned into $x$ and $y$ components based on the magnitude of the bed shear stress as		<math display="block">\theta _{sf} = \frac{{\tau _{sf} }}{{\left( {s - 1} \right)gD_{50} }}</math>
	$$
	q_{blx} = q_{bl} \frac{{\tau _{bx} }}		<math>\theta _c = 0.047</math> is the critical Shields parameter, and <math>\tau _{sf}</math> is the magnitude of total skin-friction component of bottom stress computed from

			<math display="block">\tau _{sf} = \left( {\tau _{bx}^2 + \tau _{by}^2 } \right)^{0.5}</math>

			where <math>{\tau _{bx}}^2</math> and <math>{\tau _{bx}}^2</math> are the skin-friction components of bed stress, from currents alone or the maximum wave-current combined stress, in the <math>x</math> and <math>y</math> directions. These are computed at cell faces (<math>u</math> and <math>v</math> locations) and then interpolated to cell centers (<math>\rho</math> points). The bedload transport vectors are partitioned into <math>x</math> and <math>y</math> components based on the magnitude of the bed shear stress as

			<math display="block">q_{blx} = q_{bl} \frac{{\tau _{bx} }}
	{{\tau _{sf} }};\quad \quad q_{bly} = q_{bl} \frac{{\tau _{by} }}		{{\tau _{sf} }};\quad \quad q_{bly} = q_{bl} \frac{{\tau _{by} }}
	{{\tau _{sf} }}		{{\tau _{sf} }}</math>
	$$
	</~~wikitex~~>

Csherwood at 17:03, 3 November 2008

2008-11-03T17:03:41Z

← Older revision		Revision as of 17:03, 3 November 2008
Line 1:		Line 1:
	<div class="title">Meyer-Peter Müeller Bedload Formulation</div>		<div class="title">Meyer-Peter Müeller Bedload Formulation</div>
	<wikitex>		<wikitex>
	The Meyer-Peter Müeller (1948) formulation is		The [[Bibliography#Meyer-PeterE_1948a \| Meyer-Peter Müeller (1948)]] formulation is
	$$		$$
	\Phi = \max \left[ {8\left( {\theta _{sf} - \theta _c } \right)^{1.5} ,\quad 0} \right]		\Phi = \max \left[ {8\left( {\theta _{sf} - \theta _c } \right)^{1.5} ,\quad 0} \right]

Csherwood: New page:
Meyer-Peter Müeller Bedload Formulation
The Meyer-Peter Müeller (1948) formulation is $$ \Phi = \max \left[ {8\left( {\theta _{sf} - \theta _c } \rig...

2008-11-03T15:40:01Z

New page: <div class="title">Meyer-Peter Müeller Bedload Formulation</div> <wikitex> The Meyer-Peter Müeller (1948) formulation is $$ \Phi = \max \left[ {8\left( {\theta _{sf} - \theta _c } \rig...

New page

<div class="title">Meyer-Peter Müeller Bedload Formulation</div>
<wikitex>
The Meyer-Peter Müeller (1948) formulation is
$$
\Phi = \max \left[ {8\left( {\theta _{sf} - \theta _c } \right)^{1.5} ,\quad 0} \right]
$$
where $\Phi$ is the magnitude of the non-dimensional transport rate for each sediment class,$\theta _{sf}$ is the non-dimensional Shields parameter for skin stress
$$
\theta _{sf} = \frac{{\tau _{sf} }}{{\left( {s - 1} \right)gD_{50} }}
$$

$\theta _c = 0.047$ is the critical Shields parameter, and $\tau _{sf}$ is the magnitude of total skin-friction component of bottom stress computed from
$$
\tau _{sf} = \left( {\tau _{bx}^2 + \tau _{by}^2 } \right)^{0.5}
$$
where ${\tau _{bx}}^2$ and ${\tau _{bx}}^2$ are the skin-friction components of bed stress, from currents alone or the maximum wave-current combined stress, in the $x$ and $y$ directions. These are computed at cell faces ($u$ and $v$ locations) and then interpolated to cell centers ($\rho$ points). The bedload transport vectors are partitioned into $x$ and $y$ components based on the magnitude of the bed shear stress as
$$
q_{blx} = q_{bl} \frac{{\tau _{bx} }}
{{\tau _{sf} }};\quad \quad q_{bly} = q_{bl} \frac{{\tau _{by} }}
{{\tau _{sf} }}
$$
</wikitex>

MPM BL - Revision history

Robertson at 12:02, 18 May 2016

Csherwood at 17:03, 3 November 2008

Csherwood: New page: Meyer-Peter Müeller Bedload Formulation The Meyer-Peter Müeller (1948) formulation is $$ \Phi = \max \left[ {8\left( {\theta _{sf} - \theta _c } \rig...

Csherwood: New page:
Meyer-Peter Müeller Bedload Formulation
The Meyer-Peter Müeller (1948) formulation is $$ \Phi = \max \left[ {8\left( {\theta _{sf} - \theta _c } \rig...