## Tidal Characteristic Numbers of Eff. Bed Shear Stress Action

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A graphic sketch for the definition of the various tidal characteristic numbers of effective bed shear stress is not available.

## Contents

- 1 Motivation
- 2 Definitions for the Tidal Characteristic Numbers of Effective Bed Shear Stress
- 2.1 Program NCANALYSE
- 2.1.1 Flood Current
- 2.1.2 Ebb Current
- 2.1.3 Tidal Cycle
- 2.1.3.1 Mean eff. Bed Shear Stress within a Tidal Cycle
- 2.1.3.2 Residual eff. Bed Shear Stress within a Tidal Cycle
- 2.1.3.3 Ratio of mean eff. Bed Shear Stress during Flood Current : mean eff. Bed Shear Stress during Ebb Current
- 2.1.3.4 Ratio of maximum eff. Bed Shear Stress during Flood Current : maximum eff. Bed Shear Stress during Ebb Current
- 2.1.3.5 Ratio of mean eff. Bed Shear Stress during Flood Current : mean eff. Bed Shear Stress during Tidal Cycle
- 2.1.3.6 Ratio of mean eff. Bed Shear Stress during Ebb Current : mean eff. Bed Shear Stress during Tidal Cycle
- 2.1.3.7 Ratio of maximum eff. Bed Shear Stress during Flood Current : mean eff. Bed Shear Stress during Tidal Cycle
- 2.1.3.8 Ratio of maximum eff. Bed Shear Stress during Ebb Current : mean eff. Bed Shear Stress during Tidal Cycle

- 2.2 Program TDKLF

- 2.1 Program NCANALYSE

## Motivation

The calculation as well as the graphic visualization of various tidal characteristic numbers of the effective bed shear stress contributes to an improved understanding of the impact of tidal flow on the bed as well as on bed load sediment transport for areas like coastal seas and estuaries as well.

- As the analysis is performed separately for the individual periods of ebb- and flood-current it can be demonstrated that the impact of the flow on the bed can differ significantly. This can be related to locally varying flood-ebb asymmetries for either ebb and flood current velocities or otherwise differences between flood and ebb current duration. Asymmetries may contribute significantly to residual ebb- or flood-oriented sediment transport.

An automatic analysis of all tidal characteristic numbers of effective bed shear stress is carried through by the computer programs TDKLF and NCANALYSE.

## Definitions for the Tidal Characteristic Numbers of Effective Bed Shear Stress

### Program NCANALYSE

#### Flood Current

##### Maximum eff. Bed Shear Stress due to Flood Current

Maximum value of effective bed shear stress during flood current. Vector quantity.

##### Mean eff. Bed Shear Stress due to Flood Current

Mean value (computed from magnitude) of effective bed shear stress during flood current. Vector quantity.
The magnitude corresponds to the mean value computed from the magnitude of all individual vectors (given for different dates).
Mean direction follows from vectorial addition of the individual vectors.

##### Residual eff. Bed Shear Stress due to Flood Current

Residual effective bed shear stress during flood current. Vector quantity.
Magnitude as well as (mean) direction follow from vectorial addition of the individual vectors (given for different dates).
In case all individual vectors point into the same direction mean and residual value are identical.
The residual can never be larger than the mean value.

#### Ebb Current

##### Maximum eff. Bed Shear Stress due to Ebb Current

Maximum value of effective bed shear stress during ebb current. Vector quantity.

##### Mean eff. Bed Shear Stress due to Ebb Current

Mean value (computed from magnitude) of effective bed shear stress during ebb current. Vector quantity.
The magnitude corresponds to the mean value computed from the magnitude of all individual vectors (given for different dates).
Mean direction follows from vectorial addition of the individual vectors.

##### Residual eff. Bed Shear Stress due to Ebb Current

Residual effective bed shear stress during ebb current. Vector quantity.
Magnitude as well as (mean) direction follow from vectorial addition of the individual vectors (given for different dates).
In case all individual vectors point into the same direction mean and residual value are identical.
The residual can never be larger than the mean value.

#### Tidal Cycle

##### Mean eff. Bed Shear Stress within a Tidal Cycle

Mean value (computed from magnitude) of effective bed shear stress during a tidal cycle (here this
corresponds to the period between two subsequent ebb slacks). Scalar quantity.
Magnitude corresponds to the mean value computed from the magnitude of all individual vectors (given for different dates).

##### Residual eff. Bed Shear Stress within a Tidal Cycle

Residual (computed from vectorial addition) of effective bed shear stress during a tidal cycle (here this
corresponds to the period between two subsequent ebb slacks). Vector quantity.
Magnitude and direction are computed from vectorial addition of the individual vectors (given for different dates).

##### Ratio of mean eff. Bed Shear Stress during Flood Current : mean eff. Bed Shear Stress during Ebb Current

Quotient computed from the magnitude of mean eff. bed shear stress during flood current and mean eff. bed shear stress during ebb current.

##### Ratio of maximum eff. Bed Shear Stress during Flood Current : maximum eff. Bed Shear Stress during Ebb Current

Quotient computed from the magnitude of maximum eff. bed shear stress during flood current and maximum eff. bed shear stress during ebb current.

##### Ratio of mean eff. Bed Shear Stress during Flood Current : mean eff. Bed Shear Stress during Tidal Cycle

Quotient computed from the magnitude of mean eff. bed shear stress during flood current and mean eff. bed shear stress during the tidal cycle.

##### Ratio of mean eff. Bed Shear Stress during Ebb Current : mean eff. Bed Shear Stress during Tidal Cycle

Quotient computed from the magnitude of mean eff. bed shear stress during ebb current and mean eff. bed shear stress during the tidal cycle.

##### Ratio of maximum eff. Bed Shear Stress during Flood Current : mean eff. Bed Shear Stress during Tidal Cycle

Quotient computed from the magnitude of maximum eff. bed shear stress during flood current and mean eff. bed shear stress during the tidal cycle.

##### Ratio of maximum eff. Bed Shear Stress during Ebb Current : mean eff. Bed Shear Stress during Tidal Cycle

Quotient computed from the magnitude of maximum eff. bed shear stress during ebb current and mean eff. bed shear stress during the tidal cycle.

### Program TDKLF

#### Flood Current

##### Action of Effective Bed Shear Stress due to Flood Current

Time integral of effective bed shear stress over flood current duration.

#### Ebb Current

#### Action of Effective Bed Shear Stress due to Ebb Current

Time integral of effective bed shear stress over ebb current duration.

#### Tidal Cycle

##### Residual Action of the Effective Bed Shear Stress

If the action of effective bed shear stress during flood current duration is equal but in opposite direction of the ebb current related action this will result in a zero residual action of the effective bed shear stress.

##### Ratio between Flood- and Ebb-Current induced Action of the Effective Bed Shear Stress

Flood to ebb ratio for the respective action of the effective bed shear stress.

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