""" WAFO defintions and numenclature crossings : cycle_pairs : turning_points : wave_amplitudes : wave_periods : waves : Examples -------- In order to view the documentation do the following in an ipython window: >>> import wafo.definitions as wd >>> wd.crossings() or >>> wd.crossings? """ def wave_amplitudes(): r""" Wave amplitudes and heights definitions and nomenclature Definition of wave amplitudes and wave heights --------------------------------------------- <----- Direction of wave propagation |..............c_..........| | /| \ | Hd | _/ | \ | Hu M | / | \ | / \ | M / Ac | \_ | c_ F \ | / \m/ | \ | / \ ------d----|---u------------------d---|---u----d------ level v \ | /| \ | / \L \_ | / | At \_|_/ \|/..| t t Parameters ---------- Ac : crest amplitude At : trough amplitude Hd : wave height as defined for down crossing waves Hu : wave height as defined for up crossing waves See also -------- waves, crossings, turning_points """ print(wave_amplitudes.__doc__) def crossings(): r""" Level v crossing definitions and nomenclature Definition of level v crossings ------------------------------- M . . M M . . . . . . F d . . L -----------------------u-------d-------o----------------- level v . . . . u . m m Let the letters 'm', 'M', 'F', 'L','d' and 'u' in the figure above denote local minimum, maximum, first value, last value, down- and up-crossing, respectively. The remaining sampled values are indicated with a '.'. Values that are identical with v, but do not cross the level is indicated with the letter 'o'. We have a level up-crossing at index, k, if x(k) < v and v < x(k+1) or if x(k) == v and v < x(k+1) and x(r) < v for some di < r <= k-1 where di is the index to the previous downcrossing. Similarly there is a level down-crossing at index, k, if x(k) > v and v > x(k+1) or if x(k) == v and v > x(k+1) and x(r) > v for some ui < r <= k-1 where ui is the index to the previous upcrossing. The first (F) value is a up crossing if x(1) = v and x(2) > v. Similarly, it is a down crossing if x(1) = v and x(2) < v. See also -------- wave_periods, waves, turning_points, findcross, findtp """ print(crossings.__doc__) def cycle_pairs(): r""" Cycle pairs definitions and numenclature Definition of Max2min and min2Max cycle pair -------------------------------------------- A min2Max cycle pair (mM) is defined as the pair of a minimum and the following Maximum. Similarly a Max2min cycle pair (Mm) is defined as the pair of a Maximum and the following minimum. (all turning points possibly rainflowfiltered before pairing into cycles.) See also -------- turning_points """ print(cycle_pairs.__doc__) def wave_periods(): r""" Wave periods (lengths) definitions and nomenclature Definition of wave periods (lengths) ------------------------------------ <----- Direction of wave propagation <-------Tu---------> : : <---Tc-----> : : : : <------Tcc----> M : c : : : : / \ : M / \_ : : c_ c F \ :/ \m/ \: :/ \ / \ ------d--------u----------d-------u----d--------u---d-------- level v \ / \ / :\_ _/: :\_ L \_ / \_t_/ : \t_/ : : \m/ \t/ : : : : : : <---Tt---> : <--------Ttt-------> : : <-----Td-----> Tu = Up crossing period Td = Down crossing period Tc = Crest period, i.e., period between up crossing and the next down crossing Tt = Trough period, i.e., period between down crossing and the next up crossing Ttt = Trough2trough period Tcc = Crest2crest period <----- Direction of wave propagation <--Tcf-> Tuc : : <-Tcb-> <-> M : c : : : : / \ : M / \_ c_ : : c F \ :/ \m/ \ / \___: :/ \ ------d---------u----------d---------u-------d--------u---d------ level v :\_ / \ __/: \_ _/ \_ L : \_ / \_t_/ : \t_/ \m/ : \t/ : : : : : : <-Ttf-> <-Ttb-> Tcf = Crest front period, i.e., period between up crossing and crest Tcb = Crest back period, i.e., period between crest and down crossing Ttf = Trough front period, i.e., period between down crossing and trough Ttb = Trough back period, i.e., period between trough and up crossing Also note that Tcf and Ttf can also be abbreviated by their crossing marker, e.g. Tuc (u2c) and Tdt (d2t), respectively. Similar applies to all the other wave periods and wave lengths. (The nomenclature for wave length is similar, just substitute T and period with L and length, respectively) <----- Direction of wave propagation <--TMm--> <-TmM-> : : M : : M : / \ : M /:\_ : M_ M F \ : / \m/ : \ : /: \ / \ \ : / : \ : / : \ / \ \ : / : \ : / : \_ _/ \_ L \_ : / : \_m_/ : \m_/ \m/ \m/ : : : : <-----TMM-----> <----Tmm-----> TmM = Period between minimum and the following Maximum TMm = Period between Maximum and the following minimum TMM = Period between Maximum and the following Maximum Tmm = Period between minimum and the following minimum See also -------- waves, wave_amplitudes, crossings, turning_points """ print(wave_periods.__doc__) def turning_points(): r""" Turning points definitions and numenclature Definition of turningpoints --------------------------- <----- Direction of wave propagation M M / \ .... M /:\_ M_ M F \ | / \m/ : \ /: \ / \ \ h | / : \ / : \ / \ \ | / : \ / : \_ _/ \_ L \_ | / : \_m_/ : \m_/ \m/ \m/ : : : : <------Mw-----> <-----mw-----> Local minimum or maximum are indicated with the letters 'm' or 'M'. Turning points in this connection are all local max (M) and min (m) and the last (L) value and the first (F) value if the first local extremum is a max. (This choice is made in order to get the exact up-crossing intensity from rfc by mm2lc(tp2mm(rfc)) ) See also -------- waves, crossings, cycle_pairs findtp """ print(turning_points.__doc__) def waves(): r""" Wave definitions and nomenclature Definition of trough and crest ------------------------------ A trough (t) is defined as the global minimum between a level v down-crossing (d) and the next up-crossing (u) and a crest (c) is defined as the global maximum between a level v up-crossing and the following down-crossing. Definition of down- and up -crossing waves ------------------------------------------ A level v-down-crossing wave (dw) is a wave from a down-crossing to the following down-crossing. Similarly, a level v-up-crossing wave (uw) is a wave from an up-crossing to the next up-crossing. Definition of trough and crest waves ------------------------------------ A trough-to-trough wave (tw) is a wave from a trough (t) to the following trough. The crest-to-crest wave (cw) is defined similarly. Definition of min2min and Max2Max wave -------------------------------------- A min2min wave (mw) is defined starting from a minimum (m) and ending in the following minimum. Similarly a Max2Max wave (Mw) is thus a wave from a maximum (M) to the next maximum (all waves optionally rainflow filtered). <----- Direction of wave propagation <------Mw-----> <----mw----> M : : c : / \ M : / \_ : c_ c F \ / \m/ \ : /: \ /:\ ------d--------u----------d-------u----d--------u---d------ level v \ /: \ : /: : :\_ _/ : :\_ L \_ / : \_t_/ : : : \t_/ : : \m/ \t/ <-------uw---------> : <-----dw-----> : : : : <--------tw--------> <------cw-----> (F=first value and L=last value). See also -------- turning_points, crossings, wave_periods findtc, findcross """ print(waves.__doc__)